/usr/include/libalglib/optimization.h is in libalglib-dev 3.10.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 2145 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 2162 2163 2164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 2177 2178 2179 2180 2181 2182 2183 2184 2185 2186 2187 2188 2189 2190 2191 2192 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202 2203 2204 2205 2206 2207 2208 2209 2210 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 2222 2223 2224 2225 2226 2227 2228 2229 2230 2231 2232 2233 2234 2235 2236 2237 2238 2239 2240 2241 2242 2243 2244 2245 2246 2247 2248 2249 2250 2251 2252 2253 2254 2255 2256 2257 2258 2259 2260 2261 2262 2263 2264 2265 2266 2267 2268 2269 2270 2271 2272 2273 2274 2275 2276 2277 2278 2279 2280 2281 2282 2283 2284 2285 2286 2287 2288 2289 2290 2291 2292 2293 2294 2295 2296 2297 2298 2299 2300 2301 2302 2303 2304 2305 2306 2307 2308 2309 2310 2311 2312 2313 2314 2315 2316 2317 2318 2319 2320 2321 2322 2323 2324 2325 2326 2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 2337 2338 2339 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 2350 2351 2352 2353 2354 2355 2356 2357 2358 2359 2360 2361 2362 2363 2364 2365 2366 2367 2368 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378 2379 2380 2381 2382 2383 2384 2385 2386 2387 2388 2389 2390 2391 2392 2393 2394 2395 2396 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406 2407 2408 2409 2410 2411 2412 2413 2414 2415 2416 2417 2418 2419 2420 2421 2422 2423 2424 2425 2426 2427 2428 2429 2430 2431 2432 2433 2434 2435 2436 2437 2438 2439 2440 2441 2442 2443 2444 2445 2446 2447 2448 2449 2450 2451 2452 2453 2454 2455 2456 2457 2458 2459 2460 2461 2462 2463 2464 2465 2466 2467 2468 2469 2470 2471 2472 2473 2474 2475 2476 2477 2478 2479 2480 2481 2482 2483 2484 2485 2486 2487 2488 2489 2490 2491 2492 2493 2494 2495 2496 2497 2498 2499 2500 2501 2502 2503 2504 2505 2506 2507 2508 2509 2510 2511 2512 2513 2514 2515 2516 2517 2518 2519 2520 2521 2522 2523 2524 2525 2526 2527 2528 2529 2530 2531 2532 2533 2534 2535 2536 2537 2538 2539 2540 2541 2542 2543 2544 2545 2546 2547 2548 2549 2550 2551 2552 2553 2554 2555 2556 2557 2558 2559 2560 2561 2562 2563 2564 2565 2566 2567 2568 2569 2570 2571 2572 2573 2574 2575 2576 2577 2578 2579 2580 2581 2582 2583 2584 2585 2586 2587 2588 2589 2590 2591 2592 2593 2594 2595 2596 2597 2598 2599 2600 2601 2602 2603 2604 2605 2606 2607 2608 2609 2610 2611 2612 2613 2614 2615 2616 2617 2618 2619 2620 2621 2622 2623 2624 2625 2626 2627 2628 2629 2630 2631 2632 2633 2634 2635 2636 2637 2638 2639 2640 2641 2642 2643 2644 2645 2646 2647 2648 2649 2650 2651 2652 2653 2654 2655 2656 2657 2658 2659 2660 2661 2662 2663 2664 2665 2666 2667 2668 2669 2670 2671 2672 2673 2674 2675 2676 2677 2678 2679 2680 2681 2682 2683 2684 2685 2686 2687 2688 2689 2690 2691 2692 2693 2694 2695 2696 2697 2698 2699 2700 2701 2702 2703 2704 2705 2706 2707 2708 2709 2710 2711 2712 2713 2714 2715 2716 2717 2718 2719 2720 2721 2722 2723 2724 2725 2726 2727 2728 2729 2730 2731 2732 2733 2734 2735 2736 2737 2738 2739 2740 2741 2742 2743 2744 2745 2746 2747 2748 2749 2750 2751 2752 2753 2754 2755 2756 2757 2758 2759 2760 2761 2762 2763 2764 2765 2766 2767 2768 2769 2770 2771 2772 2773 2774 2775 2776 2777 2778 2779 2780 2781 2782 2783 2784 2785 2786 2787 2788 2789 2790 2791 2792 2793 2794 2795 2796 2797 2798 2799 2800 2801 2802 2803 2804 2805 2806 2807 2808 2809 2810 2811 2812 2813 2814 2815 2816 2817 2818 2819 2820 2821 2822 2823 2824 2825 2826 2827 2828 2829 2830 2831 2832 2833 2834 2835 2836 2837 2838 2839 2840 2841 2842 2843 2844 2845 2846 2847 2848 2849 2850 2851 2852 2853 2854 2855 2856 2857 2858 2859 2860 2861 2862 2863 2864 2865 2866 2867 2868 2869 2870 2871 2872 2873 2874 2875 2876 2877 2878 2879 2880 2881 2882 2883 2884 2885 2886 2887 2888 2889 2890 2891 2892 2893 2894 2895 2896 2897 2898 2899 2900 2901 2902 2903 2904 2905 2906 2907 2908 2909 2910 2911 2912 2913 2914 2915 2916 2917 2918 2919 2920 2921 2922 2923 2924 2925 2926 2927 2928 2929 2930 2931 2932 2933 2934 2935 2936 2937 2938 2939 2940 2941 2942 2943 2944 2945 2946 2947 2948 2949 2950 2951 2952 2953 2954 2955 2956 2957 2958 2959 2960 2961 2962 2963 2964 2965 2966 2967 2968 2969 2970 2971 2972 2973 2974 2975 2976 2977 2978 2979 2980 2981 2982 2983 2984 2985 2986 2987 2988 2989 2990 2991 2992 2993 2994 2995 2996 2997 2998 2999 3000 3001 3002 3003 3004 3005 3006 3007 3008 3009 3010 3011 3012 3013 3014 3015 3016 3017 3018 3019 3020 3021 3022 3023 3024 3025 3026 3027 3028 3029 3030 3031 3032 3033 3034 3035 3036 3037 3038 3039 3040 3041 3042 3043 3044 3045 3046 3047 3048 3049 3050 3051 3052 3053 3054 3055 3056 3057 3058 3059 3060 3061 3062 3063 3064 3065 3066 3067 3068 3069 3070 3071 3072 3073 3074 3075 3076 3077 3078 3079 3080 3081 3082 3083 3084 3085 3086 3087 3088 3089 3090 3091 3092 3093 3094 3095 3096 3097 3098 3099 3100 3101 3102 3103 3104 3105 3106 3107 3108 3109 3110 3111 3112 3113 3114 3115 3116 3117 3118 3119 3120 3121 3122 3123 3124 3125 3126 3127 3128 3129 3130 3131 3132 3133 3134 3135 3136 3137 3138 3139 3140 3141 3142 3143 3144 3145 3146 3147 3148 3149 3150 3151 3152 3153 3154 3155 3156 3157 3158 3159 3160 3161 3162 3163 3164 3165 3166 3167 3168 3169 3170 3171 3172 3173 3174 3175 3176 3177 3178 3179 3180 3181 3182 3183 3184 3185 3186 3187 3188 3189 3190 3191 3192 3193 3194 3195 3196 3197 3198 3199 3200 3201 3202 3203 3204 3205 3206 3207 3208 3209 3210 3211 3212 3213 3214 3215 3216 3217 3218 3219 3220 3221 3222 3223 3224 3225 3226 3227 3228 3229 3230 3231 3232 3233 3234 3235 3236 3237 3238 3239 3240 3241 3242 3243 3244 3245 3246 3247 3248 3249 3250 3251 3252 3253 3254 3255 3256 3257 3258 3259 3260 3261 3262 3263 3264 3265 3266 3267 3268 3269 3270 3271 3272 3273 3274 3275 3276 3277 3278 3279 3280 3281 3282 3283 3284 3285 3286 3287 3288 3289 3290 3291 3292 3293 3294 3295 3296 3297 3298 3299 3300 3301 3302 3303 3304 3305 3306 3307 3308 3309 3310 3311 3312 3313 3314 3315 3316 3317 3318 3319 3320 3321 3322 3323 3324 3325 3326 3327 3328 3329 3330 3331 3332 3333 3334 3335 3336 3337 3338 3339 3340 3341 3342 3343 3344 3345 3346 3347 3348 3349 3350 3351 3352 3353 3354 3355 3356 3357 3358 3359 3360 3361 3362 3363 3364 3365 3366 3367 3368 3369 3370 3371 3372 3373 3374 3375 3376 3377 3378 3379 3380 3381 3382 3383 3384 3385 3386 3387 3388 3389 3390 3391 3392 3393 3394 3395 3396 3397 3398 3399 3400 3401 3402 3403 3404 3405 3406 3407 3408 3409 3410 3411 3412 3413 3414 3415 3416 3417 3418 3419 3420 3421 3422 3423 3424 3425 3426 3427 3428 3429 3430 3431 3432 3433 3434 3435 3436 3437 3438 3439 3440 3441 3442 3443 3444 3445 3446 3447 3448 3449 3450 3451 3452 3453 3454 3455 3456 3457 3458 3459 3460 3461 3462 3463 3464 3465 3466 3467 3468 3469 3470 3471 3472 3473 3474 3475 3476 3477 3478 3479 3480 3481 3482 3483 3484 3485 3486 3487 3488 3489 3490 3491 3492 3493 3494 3495 3496 3497 3498 3499 3500 3501 3502 3503 3504 3505 3506 3507 3508 3509 3510 3511 3512 3513 3514 3515 3516 3517 3518 3519 3520 3521 3522 3523 3524 3525 3526 3527 3528 3529 3530 3531 3532 3533 3534 3535 3536 3537 3538 3539 3540 3541 3542 3543 3544 3545 3546 3547 3548 3549 3550 3551 3552 3553 3554 3555 3556 3557 3558 3559 3560 3561 3562 3563 3564 3565 3566 3567 3568 3569 3570 3571 3572 3573 3574 3575 3576 3577 3578 3579 3580 3581 3582 3583 3584 3585 3586 3587 3588 3589 3590 3591 3592 3593 3594 3595 3596 3597 3598 3599 3600 3601 3602 3603 3604 3605 3606 3607 3608 3609 3610 3611 3612 3613 3614 3615 3616 3617 3618 3619 3620 3621 3622 3623 3624 3625 3626 3627 3628 3629 3630 3631 3632 3633 3634 3635 3636 3637 3638 3639 3640 3641 3642 3643 3644 3645 3646 3647 3648 3649 3650 3651 3652 3653 3654 3655 3656 3657 3658 3659 3660 3661 3662 3663 3664 3665 3666 3667 3668 3669 3670 3671 3672 3673 3674 3675 3676 3677 3678 3679 3680 3681 3682 3683 3684 3685 3686 3687 3688 3689 3690 3691 3692 3693 3694 3695 3696 3697 3698 3699 3700 3701 3702 3703 3704 3705 3706 3707 3708 3709 3710 3711 3712 3713 3714 3715 3716 3717 3718 3719 3720 3721 3722 3723 3724 3725 3726 3727 3728 3729 3730 3731 3732 3733 3734 3735 3736 3737 3738 3739 3740 3741 3742 3743 3744 3745 3746 3747 3748 3749 3750 3751 3752 3753 3754 3755 3756 3757 3758 3759 3760 3761 3762 3763 3764 3765 3766 3767 3768 3769 3770 3771 3772 3773 3774 3775 3776 3777 3778 3779 3780 3781 3782 3783 3784 3785 3786 3787 3788 3789 3790 3791 3792 3793 3794 3795 3796 3797 3798 3799 3800 3801 3802 3803 3804 3805 3806 3807 3808 3809 3810 3811 3812 3813 3814 3815 3816 3817 3818 3819 3820 3821 3822 3823 3824 3825 3826 3827 3828 3829 3830 3831 3832 3833 3834 3835 3836 3837 3838 3839 3840 3841 3842 3843 3844 3845 3846 3847 3848 3849 3850 3851 3852 3853 3854 3855 3856 3857 3858 3859 3860 3861 3862 3863 3864 3865 3866 3867 3868 3869 3870 3871 3872 3873 3874 3875 3876 3877 3878 3879 3880 3881 3882 3883 3884 3885 3886 3887 3888 3889 3890 3891 3892 3893 3894 3895 3896 3897 3898 3899 3900 3901 3902 3903 3904 3905 3906 3907 3908 3909 3910 3911 3912 3913 3914 3915 3916 3917 3918 3919 3920 3921 3922 3923 3924 3925 3926 3927 3928 3929 3930 3931 3932 3933 3934 3935 3936 3937 3938 3939 3940 3941 3942 3943 3944 3945 3946 3947 3948 3949 3950 3951 3952 3953 3954 3955 3956 3957 3958 3959 3960 3961 3962 3963 3964 3965 3966 3967 3968 3969 3970 3971 3972 3973 3974 3975 3976 3977 3978 3979 3980 3981 3982 3983 3984 3985 3986 3987 3988 3989 3990 3991 3992 3993 3994 3995 3996 3997 3998 3999 4000 4001 4002 4003 4004 4005 4006 4007 4008 4009 4010 4011 4012 4013 4014 4015 4016 4017 4018 4019 4020 4021 4022 4023 4024 4025 4026 4027 4028 4029 4030 4031 4032 4033 4034 4035 4036 4037 4038 4039 4040 4041 4042 4043 4044 4045 4046 4047 4048 4049 4050 4051 4052 4053 4054 4055 4056 4057 4058 4059 4060 4061 4062 4063 4064 4065 4066 4067 4068 4069 4070 4071 4072 4073 4074 4075 4076 4077 4078 4079 4080 4081 4082 4083 4084 4085 4086 4087 4088 4089 4090 4091 4092 4093 4094 4095 4096 4097 4098 4099 4100 4101 4102 4103 4104 4105 4106 4107 4108 4109 4110 4111 4112 4113 4114 4115 4116 4117 4118 4119 4120 4121 4122 4123 4124 4125 4126 4127 4128 4129 4130 4131 4132 4133 4134 4135 4136 4137 4138 4139 4140 4141 4142 4143 4144 4145 4146 4147 4148 4149 4150 4151 4152 4153 4154 4155 4156 4157 4158 4159 4160 4161 4162 4163 4164 4165 4166 4167 4168 4169 4170 4171 4172 4173 4174 4175 4176 4177 4178 4179 4180 4181 4182 4183 4184 4185 4186 4187 4188 4189 4190 4191 4192 4193 4194 4195 4196 4197 4198 4199 4200 4201 4202 4203 4204 4205 4206 4207 4208 4209 4210 4211 4212 4213 4214 4215 4216 4217 4218 4219 4220 4221 4222 4223 4224 4225 4226 4227 4228 4229 4230 4231 4232 4233 4234 4235 4236 4237 4238 4239 4240 4241 4242 4243 4244 4245 4246 4247 4248 4249 4250 4251 4252 4253 4254 4255 4256 4257 4258 4259 4260 4261 4262 4263 4264 4265 4266 4267 4268 4269 4270 4271 4272 4273 4274 4275 4276 4277 4278 4279 4280 4281 4282 4283 4284 4285 4286 4287 4288 4289 4290 4291 4292 4293 4294 4295 4296 4297 4298 4299 4300 4301 4302 4303 4304 4305 4306 4307 4308 4309 4310 4311 4312 4313 4314 4315 4316 4317 4318 4319 4320 4321 4322 4323 4324 4325 4326 4327 4328 4329 4330 4331 4332 4333 4334 4335 4336 4337 4338 4339 4340 4341 4342 4343 4344 4345 4346 4347 4348 4349 4350 4351 4352 4353 4354 4355 4356 4357 4358 4359 4360 4361 4362 4363 4364 4365 4366 4367 4368 4369 4370 4371 4372 4373 4374 4375 4376 4377 4378 4379 4380 4381 4382 4383 4384 4385 4386 4387 4388 4389 4390 4391 4392 4393 4394 4395 4396 4397 4398 4399 4400 4401 4402 4403 4404 4405 4406 4407 4408 4409 4410 4411 4412 4413 4414 4415 4416 4417 4418 4419 4420 4421 4422 4423 4424 4425 4426 4427 4428 4429 4430 4431 4432 4433 4434 4435 4436 4437 4438 4439 4440 4441 4442 4443 4444 4445 4446 4447 4448 4449 4450 4451 4452 4453 4454 4455 4456 4457 4458 4459 4460 4461 4462 4463 4464 4465 4466 4467 4468 4469 4470 4471 4472 4473 4474 4475 4476 4477 4478 4479 4480 4481 4482 4483 4484 4485 4486 4487 4488 4489 4490 4491 4492 4493 4494 4495 4496 4497 4498 4499 4500 4501 4502 4503 4504 4505 4506 4507 4508 4509 4510 4511 4512 4513 4514 4515 4516 4517 4518 4519 4520 4521 4522 4523 4524 4525 4526 4527 4528 4529 4530 4531 4532 4533 4534 4535 4536 4537 4538 4539 4540 4541 4542 4543 4544 4545 4546 4547 4548 4549 4550 4551 4552 4553 4554 4555 4556 4557 4558 4559 4560 4561 4562 4563 4564 4565 4566 4567 4568 4569 4570 4571 4572 4573 4574 4575 4576 4577 4578 4579 4580 4581 4582 4583 4584 4585 4586 4587 4588 4589 4590 4591 4592 4593 4594 4595 4596 4597 4598 4599 4600 4601 4602 4603 4604 4605 4606 4607 4608 4609 4610 4611 4612 4613 4614 4615 4616 4617 4618 4619 4620 4621 4622 4623 4624 4625 4626 4627 4628 4629 4630 4631 4632 4633 4634 4635 4636 4637 4638 4639 4640 4641 4642 4643 4644 4645 4646 4647 4648 4649 4650 4651 4652 4653 4654 4655 4656 4657 4658 4659 4660 4661 4662 4663 4664 4665 4666 4667 4668 4669 4670 4671 4672 4673 4674 4675 4676 4677 4678 4679 4680 4681 4682 4683 4684 4685 4686 4687 4688 4689 4690 4691 4692 4693 4694 4695 4696 4697 4698 4699 4700 4701 4702 4703 4704 4705 4706 4707 4708 4709 4710 4711 4712 4713 4714 4715 4716 4717 4718 4719 4720 4721 4722 4723 4724 4725 4726 4727 4728 4729 4730 4731 4732 4733 4734 4735 4736 4737 4738 4739 4740 4741 4742 4743 4744 4745 4746 4747 4748 4749 4750 4751 4752 4753 4754 4755 4756 4757 4758 4759 4760 4761 4762 4763 4764 4765 4766 4767 4768 4769 4770 4771 4772 4773 4774 4775 4776 4777 4778 4779 4780 4781 4782 4783 4784 4785 4786 4787 4788 4789 4790 4791 4792 4793 4794 4795 4796 4797 4798 4799 4800 4801 4802 4803 4804 4805 4806 4807 4808 4809 4810 4811 4812 4813 4814 4815 4816 4817 4818 4819 4820 4821 4822 4823 4824 4825 4826 4827 4828 4829 4830 4831 4832 4833 4834 4835 4836 4837 4838 4839 4840 4841 4842 4843 4844 4845 4846 4847 4848 4849 4850 4851 4852 4853 4854 4855 4856 4857 4858 4859 4860 4861 4862 4863 4864 4865 4866 4867 4868 4869 4870 4871 4872 4873 4874 4875 4876 4877 4878 4879 4880 4881 4882 4883 4884 4885 4886 4887 4888 4889 4890 4891 4892 4893 4894 4895 4896 4897 4898 4899 4900 4901 4902 4903 4904 4905 4906 4907 4908 4909 4910 4911 4912 4913 4914 4915 4916 4917 4918 4919 4920 4921 4922 4923 4924 4925 4926 4927 4928 4929 4930 4931 4932 4933 4934 4935 4936 4937 4938 4939 4940 4941 4942 4943 4944 4945 4946 4947 4948 4949 4950 4951 4952 4953 4954 4955 4956 4957 4958 4959 4960 4961 4962 4963 4964 4965 4966 4967 4968 4969 4970 4971 4972 4973 4974 4975 4976 4977 4978 4979 4980 4981 4982 4983 4984 4985 4986 4987 4988 4989 4990 4991 4992 4993 4994 4995 4996 4997 4998 4999 5000 5001 5002 5003 5004 5005 5006 5007 5008 5009 5010 5011 5012 5013 5014 5015 5016 5017 5018 5019 5020 5021 5022 5023 5024 5025 5026 5027 5028 5029 5030 5031 5032 5033 5034 5035 5036 5037 5038 5039 5040 5041 5042 5043 5044 5045 5046 5047 5048 5049 5050 5051 5052 5053 5054 5055 5056 5057 5058 5059 5060 5061 5062 5063 5064 5065 5066 5067 5068 5069 5070 5071 5072 5073 5074 5075 5076 5077 5078 5079 5080 5081 5082 5083 5084 5085 5086 5087 5088 5089 5090 5091 5092 5093 5094 5095 5096 5097 5098 5099 5100 5101 5102 5103 5104 5105 5106 5107 5108 5109 5110 5111 5112 5113 5114 5115 5116 5117 5118 5119 5120 5121 5122 5123 5124 5125 5126 5127 5128 5129 5130 5131 5132 5133 5134 5135 5136 5137 5138 5139 5140 5141 5142 5143 5144 5145 5146 5147 5148 5149 5150 5151 5152 5153 5154 5155 5156 5157 5158 5159 5160 5161 5162 5163 5164 5165 5166 5167 5168 5169 5170 5171 5172 5173 5174 5175 5176 5177 5178 5179 5180 5181 5182 5183 5184 5185 5186 5187 5188 5189 5190 5191 5192 5193 5194 5195 5196 5197 5198 5199 5200 5201 5202 5203 5204 5205 5206 5207 5208 5209 5210 5211 5212 5213 5214 5215 5216 5217 5218 5219 5220 5221 5222 5223 5224 5225 5226 5227 5228 5229 5230 5231 5232 5233 5234 5235 5236 5237 5238 5239 5240 5241 5242 5243 5244 5245 5246 5247 5248 5249 5250 5251 5252 5253 5254 5255 5256 5257 5258 5259 5260 5261 5262 5263 5264 5265 5266 5267 5268 5269 5270 5271 5272 5273 5274 5275 5276 5277 5278 5279 5280 5281 5282 5283 5284 5285 5286 5287 5288 5289 5290 5291 5292 5293 5294 5295 5296 5297 5298 5299 5300 5301 5302 5303 5304 5305 5306 5307 5308 5309 5310 5311 5312 5313 5314 5315 5316 5317 5318 5319 5320 5321 5322 5323 5324 5325 5326 5327 5328 5329 5330 5331 5332 5333 5334 5335 5336 5337 5338 5339 5340 5341 5342 5343 5344 5345 5346 5347 5348 5349 5350 5351 5352 5353 5354 5355 5356 5357 5358 5359 5360 5361 5362 5363 5364 5365 5366 5367 5368 5369 5370 5371 5372 5373 5374 5375 5376 5377 5378 5379 5380 5381 5382 5383 5384 5385 5386 5387 5388 5389 5390 5391 5392 5393 5394 5395 5396 5397 5398 5399 5400 5401 5402 5403 5404 5405 5406 5407 5408 5409 5410 5411 5412 5413 5414 5415 5416 5417 5418 5419 5420 5421 5422 5423 5424 5425 5426 5427 5428 5429 5430 5431 5432 5433 5434 5435 5436 5437 5438 5439 5440 5441 5442 5443 5444 5445 5446 5447 5448 5449 5450 5451 5452 5453 5454 5455 5456 5457 5458 5459 5460 5461 5462 5463 5464 5465 5466 5467 5468 5469 5470 5471 5472 5473 5474 5475 5476 5477 5478 5479 5480 5481 5482 5483 5484 5485 5486 5487 5488 5489 5490 5491 5492 5493 5494 5495 5496 5497 5498 5499 5500 5501 5502 5503 5504 5505 5506 5507 5508 5509 5510 5511 5512 5513 5514 5515 5516 5517 5518 5519 5520 5521 5522 5523 5524 5525 5526 5527 5528 5529 5530 5531 5532 5533 5534 5535 5536 5537 5538 5539 5540 5541 5542 5543 5544 5545 5546 5547 5548 5549 5550 5551 5552 5553 5554 5555 5556 5557 5558 5559 5560 5561 5562 5563 5564 5565 5566 5567 5568 5569 5570 5571 5572 5573 5574 5575 5576 5577 5578 5579 5580 5581 5582 5583 5584 5585 5586 5587 5588 5589 5590 5591 5592 5593 5594 5595 5596 5597 5598 5599 5600 5601 5602 5603 5604 5605 5606 5607 5608 5609 5610 5611 5612 5613 5614 5615 5616 5617 5618 5619 5620 5621 5622 5623 5624 5625 5626 5627 5628 5629 5630 5631 5632 5633 5634 5635 5636 5637 5638 5639 5640 5641 5642 5643 5644 5645 5646 5647 5648 5649 5650 5651 5652 5653 5654 5655 5656 5657 5658 5659 5660 5661 5662 5663 5664 5665 5666 5667 5668 5669 5670 5671 5672 5673 5674 5675 5676 5677 5678 5679 5680 5681 5682 5683 5684 5685 5686 5687 5688 5689 5690 5691 5692 5693 5694 5695 5696 5697 5698 5699 5700 5701 5702 5703 5704 5705 5706 5707 5708 5709 5710 5711 5712 5713 5714 5715 5716 5717 5718 5719 5720 5721 5722 5723 5724 5725 5726 5727 5728 5729 5730 5731 5732 5733 5734 5735 5736 5737 5738 5739 5740 5741 5742 5743 5744 5745 5746 5747 5748 5749 5750 5751 5752 5753 5754 5755 5756 5757 5758 5759 5760 5761 5762 5763 5764 5765 5766 5767 5768 5769 5770 5771 5772 5773 5774 5775 5776 5777 5778 5779 5780 5781 5782 5783 5784 5785 5786 5787 5788 5789 5790 5791 5792 5793 5794 5795 5796 5797 5798 5799 5800 5801 5802 5803 5804 5805 5806 5807 5808 5809 5810 5811 5812 5813 5814 5815 5816 5817 5818 5819 5820 5821 5822 5823 5824 5825 5826 5827 5828 5829 5830 5831 5832 5833 5834 5835 5836 5837 5838 5839 5840 5841 5842 5843 5844 5845 5846 5847 5848 5849 5850 5851 5852 5853 5854 5855 5856 5857 5858 5859 5860 5861 5862 5863 5864 5865 5866 5867 5868 5869 5870 5871 5872 5873 5874 5875 5876 5877 5878 5879 5880 5881 5882 5883 5884 5885 5886 5887 5888 5889 5890 5891 5892 5893 5894 5895 5896 5897 5898 5899 5900 5901 5902 5903 5904 5905 5906 5907 5908 5909 5910 5911 5912 5913 5914 5915 5916 5917 5918 5919 5920 5921 5922 5923 5924 5925 5926 5927 5928 5929 5930 5931 5932 5933 5934 5935 5936 5937 5938 5939 5940 5941 5942 5943 5944 5945 5946 5947 5948 5949 5950 5951 5952 5953 5954 5955 5956 5957 5958 5959 5960 5961 5962 5963 5964 5965 5966 5967 5968 5969 5970 5971 5972 5973 5974 5975 5976 5977 5978 5979 5980 5981 5982 5983 5984 5985 5986 5987 5988 5989 5990 5991 5992 5993 5994 5995 5996 5997 5998 5999 6000 6001 6002 6003 6004 6005 6006 6007 6008 6009 6010 6011 6012 6013 6014 6015 6016 6017 6018 6019 6020 6021 6022 6023 6024 6025 6026 6027 6028 6029 6030 6031 6032 6033 6034 6035 6036 6037 6038 6039 6040 6041 6042 6043 6044 6045 6046 6047 6048 6049 6050 6051 6052 6053 6054 6055 6056 6057 6058 6059 6060 6061 6062 6063 6064 6065 6066 6067 6068 6069 6070 6071 6072 6073 6074 6075 6076 6077 6078 6079 6080 6081 6082 6083 6084 6085 6086 6087 6088 6089 6090 6091 6092 6093 6094 6095 6096 6097 6098 6099 6100 6101 6102 6103 6104 6105 6106 6107 6108 6109 6110 6111 6112 6113 6114 6115 6116 6117 6118 6119 6120 6121 6122 6123 6124 6125 6126 6127 6128 6129 6130 6131 6132 6133 6134 6135 6136 6137 6138 6139 6140 6141 6142 6143 6144 6145 6146 6147 6148 6149 6150 6151 6152 6153 6154 6155 6156 6157 6158 6159 6160 6161 6162 6163 6164 6165 6166 6167 6168 6169 6170 6171 6172 6173 6174 6175 6176 6177 6178 6179 6180 6181 6182 6183 6184 6185 6186 6187 6188 6189 6190 6191 6192 6193 6194 6195 6196 6197 6198 6199 6200 6201 6202 6203 6204 6205 6206 6207 6208 6209 6210 6211 6212 6213 6214 6215 6216 6217 6218 6219 6220 6221 6222 6223 6224 6225 6226 6227 6228 6229 6230 6231 6232 6233 6234 6235 6236 6237 6238 6239 6240 6241 6242 6243 6244 6245 6246 6247 6248 6249 6250 6251 6252 6253 6254 6255 6256 6257 6258 6259 6260 6261 6262 6263 6264 6265 6266 6267 6268 6269 6270 6271 6272 6273 6274 6275 6276 6277 6278 6279 6280 6281 6282 6283 6284 6285 6286 6287 6288 6289 6290 6291 6292 6293 6294 6295 6296 6297 6298 6299 6300 6301 6302 6303 6304 6305 6306 6307 6308 6309 6310 6311 6312 6313 6314 6315 6316 6317 6318 6319 6320 6321 6322 6323 6324 6325 6326 6327 6328 6329 6330 6331 6332 6333 6334 6335 6336 6337 6338 6339 6340 6341 6342 6343 6344 6345 6346 6347 6348 6349 6350 6351 6352 6353 6354 6355 6356 6357 6358 6359 6360 6361 6362 6363 6364 6365 6366 6367 6368 6369 6370 6371 6372 6373 6374 6375 6376 6377 6378 6379 6380 6381 6382 6383 6384 6385 6386 6387 6388 6389 6390 6391 6392 6393 6394 6395 6396 6397 6398 6399 6400 6401 6402 6403 6404 6405 6406 6407 6408 6409 6410 6411 6412 6413 6414 6415 6416 6417 6418 6419 6420 6421 6422 6423 6424 6425 6426 6427 6428 6429 6430 6431 6432 6433 6434 6435 6436 6437 6438 6439 6440 6441 6442 6443 6444 6445 6446 6447 6448 6449 6450 6451 6452 6453 6454 6455 6456 6457 6458 6459 6460 6461 6462 6463 6464 6465 6466 6467 6468 6469 6470 6471 6472 6473 6474 6475 6476 6477 6478 6479 6480 6481 6482 6483 6484 6485 6486 6487 6488 6489 6490 6491 6492 6493 6494 6495 6496 6497 6498 6499 6500 6501 6502 6503 6504 6505 6506 6507 6508 6509 6510 6511 6512 6513 6514 6515 6516 6517 6518 6519 6520 6521 6522 6523 6524 6525 6526 6527 6528 6529 6530 6531 6532 6533 6534 6535 6536 6537 6538 6539 6540 6541 6542 6543 6544 6545 6546 6547 6548 6549 6550 6551 6552 6553 6554 6555 6556 6557 6558 6559 6560 6561 6562 6563 6564 6565 6566 6567 6568 6569 6570 6571 6572 6573 6574 6575 6576 6577 6578 6579 6580 6581 6582 6583 6584 6585 6586 6587 6588 6589 6590 6591 6592 6593 6594 6595 6596 6597 6598 6599 6600 6601 6602 6603 6604 6605 6606 6607 6608 6609 6610 6611 6612 6613 6614 6615 6616 6617 6618 6619 6620 6621 6622 6623 6624 6625 6626 6627 6628 6629 6630 6631 6632 6633 6634 6635 6636 6637 6638 6639 6640 6641 6642 6643 6644 6645 6646 6647 6648 6649 6650 6651 6652 6653 6654 6655 6656 6657 6658 6659 6660 6661 6662 6663 6664 6665 6666 6667 6668 6669 6670 6671 6672 6673 6674 6675 6676 6677 6678 6679 6680 6681 6682 6683 6684 6685 6686 6687 6688 6689 6690 6691 6692 6693 6694 6695 6696 6697 6698 6699 6700 6701 6702 6703 6704 6705 6706 6707 6708 6709 6710 6711 6712 6713 6714 6715 6716 6717 6718 6719 6720 6721 6722 6723 6724 6725 6726 6727 6728 6729 6730 6731 6732 6733 6734 6735 6736 6737 6738 6739 6740 6741 6742 6743 6744 6745 6746 6747 6748 6749 6750 6751 6752 6753 6754 6755 6756 6757 6758 6759 6760 6761 6762 6763 6764 6765 6766 6767 6768 6769 6770 6771 6772 6773 6774 6775 6776 6777 6778 6779 6780 6781 6782 6783 6784 6785 6786 6787 6788 6789 6790 6791 6792 6793 6794 6795 6796 6797 6798 6799 6800 6801 6802 6803 6804 6805 6806 6807 6808 6809 6810 6811 6812 6813 6814 6815 6816 6817 6818 6819 6820 6821 6822 6823 6824 6825 6826 6827 6828 6829 6830 6831 6832 6833 6834 6835 6836 6837 6838 6839 6840 6841 6842 6843 6844 6845 6846 6847 6848 6849 6850 6851 6852 6853 6854 6855 6856 6857 6858 6859 6860 6861 6862 6863 6864 6865 6866 6867 6868 6869 6870 6871 6872 6873 6874 6875 6876 6877 6878 6879 | /*************************************************************************
ALGLIB 3.10.0 (source code generated 2015-08-19)
Copyright (c) Sergey Bochkanov (ALGLIB project).
>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#ifndef _optimization_pkg_h
#define _optimization_pkg_h
#include "ap.h"
#include "alglibinternal.h"
#include "alglibmisc.h"
#include "linalg.h"
#include "solvers.h"
/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS COMPUTATIONAL CORE DECLARATIONS (DATATYPES)
//
/////////////////////////////////////////////////////////////////////////
namespace alglib_impl
{
typedef struct
{
ae_vector norms;
ae_vector alpha;
ae_vector rho;
ae_matrix yk;
ae_vector idx;
ae_vector bufa;
ae_vector bufb;
} precbuflbfgs;
typedef struct
{
ae_int_t n;
ae_int_t k;
ae_vector d;
ae_matrix v;
ae_vector bufc;
ae_matrix bufz;
ae_matrix bufw;
ae_vector tmp;
} precbuflowrank;
typedef struct
{
ae_int_t n;
ae_int_t k;
double alpha;
double tau;
double theta;
ae_matrix a;
ae_matrix q;
ae_vector b;
ae_vector r;
ae_vector xc;
ae_vector d;
ae_vector activeset;
ae_matrix tq2dense;
ae_matrix tk2;
ae_vector tq2diag;
ae_vector tq1;
ae_vector tk1;
double tq0;
double tk0;
ae_vector txc;
ae_vector tb;
ae_int_t nfree;
ae_int_t ecakind;
ae_matrix ecadense;
ae_matrix eq;
ae_matrix eccm;
ae_vector ecadiag;
ae_vector eb;
double ec;
ae_vector tmp0;
ae_vector tmp1;
ae_vector tmpg;
ae_matrix tmp2;
ae_bool ismaintermchanged;
ae_bool issecondarytermchanged;
ae_bool islineartermchanged;
ae_bool isactivesetchanged;
} convexquadraticmodel;
typedef struct
{
ae_int_t ns;
ae_int_t nd;
ae_int_t nr;
ae_matrix densea;
ae_vector b;
ae_vector nnc;
double debugflops;
ae_int_t debugmaxinnerits;
ae_vector xn;
ae_vector xp;
ae_matrix tmpz;
ae_matrix tmpca;
ae_matrix tmplq;
ae_matrix trda;
ae_vector trdd;
ae_vector crb;
ae_vector g;
ae_vector d;
ae_vector dx;
ae_vector diagaa;
ae_vector cb;
ae_vector cx;
ae_vector cborg;
ae_vector tmpcholesky;
ae_vector r;
ae_vector regdiag;
ae_vector tmp0;
ae_vector tmp1;
ae_vector tmp2;
ae_vector rdtmprowmap;
} snnlssolver;
typedef struct
{
ae_int_t n;
ae_int_t algostate;
ae_vector xc;
ae_bool hasxc;
ae_vector s;
ae_vector h;
ae_vector activeset;
ae_bool basisisready;
ae_matrix sbasis;
ae_matrix pbasis;
ae_matrix ibasis;
ae_int_t basissize;
ae_bool constraintschanged;
ae_vector hasbndl;
ae_vector hasbndu;
ae_vector bndl;
ae_vector bndu;
ae_matrix cleic;
ae_int_t nec;
ae_int_t nic;
ae_vector mtx;
ae_vector mtas;
ae_vector cdtmp;
ae_vector corrtmp;
ae_vector unitdiagonal;
snnlssolver solver;
ae_vector scntmp;
ae_vector tmp0;
ae_vector tmpfeas;
ae_matrix tmpm0;
ae_vector rctmps;
ae_vector rctmpg;
ae_vector rctmprightpart;
ae_matrix rctmpdense0;
ae_matrix rctmpdense1;
ae_vector rctmpisequality;
ae_vector rctmpconstraintidx;
ae_vector rctmplambdas;
ae_matrix tmpbasis;
} sactiveset;
typedef struct
{
ae_int_t n;
double epsg;
double epsf;
double epsx;
ae_int_t maxits;
double stpmax;
double suggestedstep;
ae_bool xrep;
ae_bool drep;
ae_int_t cgtype;
ae_int_t prectype;
ae_vector diagh;
ae_vector diaghl2;
ae_matrix vcorr;
ae_int_t vcnt;
ae_vector s;
double diffstep;
ae_int_t nfev;
ae_int_t mcstage;
ae_int_t k;
ae_vector xk;
ae_vector dk;
ae_vector xn;
ae_vector dn;
ae_vector d;
double fold;
double stp;
double curstpmax;
ae_vector yk;
double lastgoodstep;
double lastscaledstep;
ae_int_t mcinfo;
ae_bool innerresetneeded;
ae_bool terminationneeded;
double trimthreshold;
ae_int_t rstimer;
ae_vector x;
double f;
ae_vector g;
ae_bool needf;
ae_bool needfg;
ae_bool xupdated;
ae_bool algpowerup;
ae_bool lsstart;
ae_bool lsend;
ae_bool userterminationneeded;
double teststep;
rcommstate rstate;
ae_int_t repiterationscount;
ae_int_t repnfev;
ae_int_t repvaridx;
ae_int_t repterminationtype;
ae_int_t debugrestartscount;
linminstate lstate;
double fbase;
double fm2;
double fm1;
double fp1;
double fp2;
double betahs;
double betady;
ae_vector work0;
ae_vector work1;
} mincgstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
ae_int_t varidx;
ae_int_t terminationtype;
} mincgreport;
typedef struct
{
ae_int_t nmain;
ae_int_t nslack;
double epsg;
double epsf;
double epsx;
ae_int_t maxits;
ae_bool xrep;
ae_bool drep;
double stpmax;
double diffstep;
sactiveset sas;
ae_vector s;
ae_int_t prectype;
ae_vector diagh;
ae_vector x;
double f;
ae_vector g;
ae_bool needf;
ae_bool needfg;
ae_bool xupdated;
ae_bool lsstart;
ae_bool steepestdescentstep;
ae_bool boundedstep;
ae_bool userterminationneeded;
double teststep;
rcommstate rstate;
ae_vector ugc;
ae_vector cgc;
ae_vector xn;
ae_vector ugn;
ae_vector cgn;
ae_vector xp;
double fc;
double fn;
double fp;
ae_vector d;
ae_matrix cleic;
ae_int_t nec;
ae_int_t nic;
double lastgoodstep;
double lastscaledgoodstep;
double maxscaledgrad;
ae_vector hasbndl;
ae_vector hasbndu;
ae_vector bndl;
ae_vector bndu;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
ae_int_t repnfev;
ae_int_t repvaridx;
ae_int_t repterminationtype;
double repdebugeqerr;
double repdebugfs;
double repdebugff;
double repdebugdx;
ae_int_t repdebugfeasqpits;
ae_int_t repdebugfeasgpaits;
ae_vector xstart;
snnlssolver solver;
double fbase;
double fm2;
double fm1;
double fp1;
double fp2;
double xm1;
double xp1;
double gm1;
double gp1;
ae_int_t cidx;
double cval;
ae_vector tmpprec;
ae_vector tmp0;
ae_int_t nfev;
ae_int_t mcstage;
double stp;
double curstpmax;
double activationstep;
ae_vector work;
linminstate lstate;
double trimthreshold;
ae_int_t nonmonotoniccnt;
ae_matrix bufyk;
ae_matrix bufsk;
ae_vector bufrho;
ae_vector buftheta;
ae_int_t bufsize;
} minbleicstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
ae_int_t varidx;
ae_int_t terminationtype;
double debugeqerr;
double debugfs;
double debugff;
double debugdx;
ae_int_t debugfeasqpits;
ae_int_t debugfeasgpaits;
ae_int_t inneriterationscount;
ae_int_t outeriterationscount;
} minbleicreport;
typedef struct
{
ae_int_t n;
ae_int_t m;
double epsg;
double epsf;
double epsx;
ae_int_t maxits;
ae_bool xrep;
double stpmax;
ae_vector s;
double diffstep;
ae_int_t nfev;
ae_int_t mcstage;
ae_int_t k;
ae_int_t q;
ae_int_t p;
ae_vector rho;
ae_matrix yk;
ae_matrix sk;
ae_vector xp;
ae_vector theta;
ae_vector d;
double stp;
ae_vector work;
double fold;
double trimthreshold;
ae_int_t prectype;
double gammak;
ae_matrix denseh;
ae_vector diagh;
ae_vector precc;
ae_vector precd;
ae_matrix precw;
ae_int_t preck;
precbuflbfgs precbuf;
precbuflowrank lowrankbuf;
double fbase;
double fm2;
double fm1;
double fp1;
double fp2;
ae_vector autobuf;
ae_vector x;
double f;
ae_vector g;
ae_bool needf;
ae_bool needfg;
ae_bool xupdated;
ae_bool userterminationneeded;
double teststep;
rcommstate rstate;
ae_int_t repiterationscount;
ae_int_t repnfev;
ae_int_t repvaridx;
ae_int_t repterminationtype;
linminstate lstate;
} minlbfgsstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
ae_int_t varidx;
ae_int_t terminationtype;
} minlbfgsreport;
typedef struct
{
double epsg;
double epsf;
double epsx;
ae_int_t maxouterits;
ae_bool cgphase;
ae_bool cnphase;
ae_int_t cgminits;
ae_int_t cgmaxits;
ae_int_t cnmaxupdates;
ae_int_t sparsesolver;
} qqpsettings;
typedef struct
{
ae_int_t n;
ae_int_t nmain;
ae_int_t nslack;
ae_int_t nec;
ae_int_t nic;
ae_int_t akind;
ae_matrix densea;
sparsematrix sparsea;
ae_bool sparseupper;
double absamax;
double absasum;
double absasum2;
ae_vector b;
ae_vector bndl;
ae_vector bndu;
ae_vector havebndl;
ae_vector havebndu;
ae_matrix cleic;
ae_vector xs;
ae_vector gc;
ae_vector xp;
ae_vector dc;
ae_vector dp;
ae_vector cgc;
ae_vector cgp;
sactiveset sas;
ae_vector activated;
ae_int_t nfree;
ae_int_t cnmodelage;
ae_matrix densez;
sparsematrix sparsecca;
ae_vector yidx;
ae_vector regdiag;
ae_vector regx0;
ae_vector tmpcn;
ae_vector tmpcni;
ae_vector tmpcnb;
ae_vector tmp0;
ae_vector stpbuf;
sparsebuffers sbuf;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
ae_int_t repncholesky;
ae_int_t repncupdates;
} qqpbuffers;
typedef struct
{
double epsg;
double epsf;
double epsx;
ae_int_t maxits;
} qpbleicsettings;
typedef struct
{
minbleicstate solver;
minbleicreport solverrep;
ae_vector tmp0;
ae_vector tmp1;
ae_vector tmpi;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
} qpbleicbuffers;
typedef struct
{
double epsg;
double epsf;
double epsx;
ae_int_t maxits;
} qpcholeskysettings;
typedef struct
{
sactiveset sas;
ae_vector pg;
ae_vector gc;
ae_vector xs;
ae_vector xn;
ae_vector workbndl;
ae_vector workbndu;
ae_vector havebndl;
ae_vector havebndu;
ae_matrix workcleic;
ae_vector rctmpg;
ae_vector tmp0;
ae_vector tmp1;
ae_vector tmpb;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
ae_int_t repncholesky;
} qpcholeskybuffers;
typedef struct
{
ae_int_t n;
qqpsettings qqpsettingsuser;
qqpsettings qqpsettingscurrent;
qpbleicsettings qpbleicsettingsuser;
qpbleicsettings qpbleicsettingscurrent;
ae_int_t algokind;
ae_int_t akind;
convexquadraticmodel a;
sparsematrix sparsea;
ae_bool sparseaupper;
double absamax;
double absasum;
double absasum2;
ae_vector b;
ae_vector bndl;
ae_vector bndu;
ae_vector s;
ae_vector havebndl;
ae_vector havebndu;
ae_vector xorigin;
ae_vector startx;
ae_bool havex;
ae_matrix cleic;
ae_int_t nec;
ae_int_t nic;
ae_vector xs;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
ae_int_t repncholesky;
ae_int_t repnmv;
ae_int_t repterminationtype;
ae_vector tmp0;
ae_bool qpbleicfirstcall;
qpbleicbuffers qpbleicbuf;
qqpbuffers qqpbuf;
qpcholeskybuffers qpcholeskybuf;
normestimatorstate estimator;
} minqpstate;
typedef struct
{
ae_int_t inneriterationscount;
ae_int_t outeriterationscount;
ae_int_t nmv;
ae_int_t ncholesky;
ae_int_t terminationtype;
} minqpreport;
typedef struct
{
ae_int_t n;
ae_int_t m;
double diffstep;
double epsg;
double epsf;
double epsx;
ae_int_t maxits;
ae_bool xrep;
double stpmax;
ae_int_t maxmodelage;
ae_bool makeadditers;
ae_vector x;
double f;
ae_vector fi;
ae_matrix j;
ae_matrix h;
ae_vector g;
ae_bool needf;
ae_bool needfg;
ae_bool needfgh;
ae_bool needfij;
ae_bool needfi;
ae_bool xupdated;
ae_bool userterminationneeded;
ae_int_t algomode;
ae_bool hasf;
ae_bool hasfi;
ae_bool hasg;
ae_vector xbase;
double fbase;
ae_vector fibase;
ae_vector gbase;
ae_matrix quadraticmodel;
ae_vector bndl;
ae_vector bndu;
ae_vector havebndl;
ae_vector havebndu;
ae_vector s;
double lambdav;
double nu;
ae_int_t modelage;
ae_vector xdir;
ae_vector deltax;
ae_vector deltaf;
ae_bool deltaxready;
ae_bool deltafready;
double teststep;
ae_int_t repiterationscount;
ae_int_t repterminationtype;
ae_int_t repfuncidx;
ae_int_t repvaridx;
ae_int_t repnfunc;
ae_int_t repnjac;
ae_int_t repngrad;
ae_int_t repnhess;
ae_int_t repncholesky;
rcommstate rstate;
ae_vector choleskybuf;
ae_vector tmp0;
double actualdecrease;
double predicteddecrease;
double xm1;
double xp1;
ae_vector fm1;
ae_vector fp1;
ae_vector fc1;
ae_vector gm1;
ae_vector gp1;
ae_vector gc1;
minlbfgsstate internalstate;
minlbfgsreport internalrep;
minqpstate qpstate;
minqpreport qprep;
} minlmstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t terminationtype;
ae_int_t funcidx;
ae_int_t varidx;
ae_int_t nfunc;
ae_int_t njac;
ae_int_t ngrad;
ae_int_t nhess;
ae_int_t ncholesky;
} minlmreport;
typedef struct
{
ae_int_t n;
double epsg;
double epsf;
double epsx;
ae_int_t maxits;
ae_bool xrep;
double stpmax;
ae_int_t cgtype;
ae_int_t k;
ae_int_t nfev;
ae_int_t mcstage;
ae_vector bndl;
ae_vector bndu;
ae_int_t curalgo;
ae_int_t acount;
double mu;
double finit;
double dginit;
ae_vector ak;
ae_vector xk;
ae_vector dk;
ae_vector an;
ae_vector xn;
ae_vector dn;
ae_vector d;
double fold;
double stp;
ae_vector work;
ae_vector yk;
ae_vector gc;
double laststep;
ae_vector x;
double f;
ae_vector g;
ae_bool needfg;
ae_bool xupdated;
rcommstate rstate;
ae_int_t repiterationscount;
ae_int_t repnfev;
ae_int_t repterminationtype;
ae_int_t debugrestartscount;
linminstate lstate;
double betahs;
double betady;
} minasastate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
ae_int_t terminationtype;
ae_int_t activeconstraints;
} minasareport;
typedef struct
{
double stabilizingpoint;
double initialinequalitymultiplier;
ae_int_t solvertype;
ae_int_t prectype;
ae_int_t updatefreq;
double rho;
ae_int_t n;
double epsg;
double epsf;
double epsx;
ae_int_t maxits;
ae_int_t aulitscnt;
ae_bool xrep;
double diffstep;
double teststep;
ae_vector s;
ae_vector bndl;
ae_vector bndu;
ae_vector hasbndl;
ae_vector hasbndu;
ae_int_t nec;
ae_int_t nic;
ae_matrix cleic;
ae_int_t ng;
ae_int_t nh;
ae_vector x;
double f;
ae_vector fi;
ae_matrix j;
ae_bool needfij;
ae_bool needfi;
ae_bool xupdated;
rcommstate rstate;
rcommstate rstateaul;
ae_vector scaledbndl;
ae_vector scaledbndu;
ae_matrix scaledcleic;
ae_vector xc;
ae_vector xstart;
ae_vector xbase;
ae_vector fbase;
ae_vector dfbase;
ae_vector fm2;
ae_vector fm1;
ae_vector fp1;
ae_vector fp2;
ae_vector dfm1;
ae_vector dfp1;
ae_vector bufd;
ae_vector bufc;
ae_matrix bufw;
ae_vector xk;
ae_vector xk1;
ae_vector gk;
ae_vector gk1;
double gammak;
ae_bool xkpresent;
minlbfgsstate auloptimizer;
minlbfgsreport aulreport;
ae_vector nubc;
ae_vector nulc;
ae_vector nunlc;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
ae_int_t repnfev;
ae_int_t repvaridx;
ae_int_t repfuncidx;
ae_int_t repterminationtype;
ae_int_t repdbgphase0its;
} minnlcstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
ae_int_t varidx;
ae_int_t funcidx;
ae_int_t terminationtype;
ae_int_t dbgphase0its;
} minnlcreport;
typedef struct
{
double fc;
double fn;
ae_vector xc;
ae_vector xn;
ae_vector x0;
ae_vector gc;
ae_vector d;
ae_matrix uh;
ae_matrix ch;
ae_matrix rk;
ae_vector invutc;
ae_vector tmp0;
ae_vector tmpidx;
ae_vector tmpd;
ae_vector tmpc;
ae_vector tmplambdas;
ae_matrix tmpc2;
ae_vector tmpb;
snnlssolver nnls;
} minnsqp;
typedef struct
{
ae_int_t solvertype;
ae_int_t n;
double epsx;
ae_int_t maxits;
ae_bool xrep;
double diffstep;
ae_vector s;
ae_vector bndl;
ae_vector bndu;
ae_vector hasbndl;
ae_vector hasbndu;
ae_int_t nec;
ae_int_t nic;
ae_matrix cleic;
ae_int_t ng;
ae_int_t nh;
ae_vector x;
double f;
ae_vector fi;
ae_matrix j;
ae_bool needfij;
ae_bool needfi;
ae_bool xupdated;
rcommstate rstate;
rcommstate rstateags;
hqrndstate agsrs;
double agsradius;
ae_int_t agssamplesize;
double agsraddecay;
double agsalphadecay;
double agsdecrease;
double agsinitstp;
double agsstattold;
double agsshortstpabs;
double agsshortstprel;
double agsshortf;
ae_int_t agsshortlimit;
double agsrhononlinear;
ae_int_t agsminupdate;
ae_int_t agsmaxraddecays;
ae_int_t agsmaxbacktrack;
ae_int_t agsmaxbacktracknonfull;
double agspenaltylevel;
double agspenaltyincrease;
ae_vector xstart;
ae_vector xc;
ae_vector xn;
ae_vector grs;
ae_vector d;
ae_vector colmax;
ae_vector diagh;
ae_vector signmin;
ae_vector signmax;
ae_bool userterminationneeded;
ae_vector scaledbndl;
ae_vector scaledbndu;
ae_matrix scaledcleic;
ae_vector rholinear;
ae_matrix samplex;
ae_matrix samplegm;
ae_matrix samplegmbc;
ae_vector samplef;
ae_vector samplef0;
minnsqp nsqp;
ae_vector tmp0;
ae_vector tmp1;
ae_matrix tmp2;
ae_vector tmp3;
ae_vector xbase;
ae_vector fp;
ae_vector fm;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
ae_int_t repnfev;
ae_int_t repvaridx;
ae_int_t repfuncidx;
ae_int_t repterminationtype;
double replcerr;
double repnlcerr;
ae_int_t dbgncholesky;
} minnsstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
double cerr;
double lcerr;
double nlcerr;
ae_int_t terminationtype;
ae_int_t varidx;
ae_int_t funcidx;
} minnsreport;
}
/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS C++ INTERFACE
//
/////////////////////////////////////////////////////////////////////////
namespace alglib
{
/*************************************************************************
This object stores state of the nonlinear CG optimizer.
You should use ALGLIB functions to work with this object.
*************************************************************************/
class _mincgstate_owner
{
public:
_mincgstate_owner();
_mincgstate_owner(const _mincgstate_owner &rhs);
_mincgstate_owner& operator=(const _mincgstate_owner &rhs);
virtual ~_mincgstate_owner();
alglib_impl::mincgstate* c_ptr();
alglib_impl::mincgstate* c_ptr() const;
protected:
alglib_impl::mincgstate *p_struct;
};
class mincgstate : public _mincgstate_owner
{
public:
mincgstate();
mincgstate(const mincgstate &rhs);
mincgstate& operator=(const mincgstate &rhs);
virtual ~mincgstate();
ae_bool &needf;
ae_bool &needfg;
ae_bool &xupdated;
double &f;
real_1d_array g;
real_1d_array x;
};
/*************************************************************************
This structure stores optimization report:
* IterationsCount total number of inner iterations
* NFEV number of gradient evaluations
* TerminationType termination type (see below)
TERMINATION CODES
TerminationType field contains completion code, which can be:
-8 internal integrity control detected infinite or NAN values in
function/gradient. Abnormal termination signalled.
-7 gradient verification failed.
See MinCGSetGradientCheck() for more information.
1 relative function improvement is no more than EpsF.
2 relative step is no more than EpsX.
4 gradient norm is no more than EpsG
5 MaxIts steps was taken
7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
8 terminated by user who called mincgrequesttermination(). X contains
point which was "current accepted" when termination request was
submitted.
Other fields of this structure are not documented and should not be used!
*************************************************************************/
class _mincgreport_owner
{
public:
_mincgreport_owner();
_mincgreport_owner(const _mincgreport_owner &rhs);
_mincgreport_owner& operator=(const _mincgreport_owner &rhs);
virtual ~_mincgreport_owner();
alglib_impl::mincgreport* c_ptr();
alglib_impl::mincgreport* c_ptr() const;
protected:
alglib_impl::mincgreport *p_struct;
};
class mincgreport : public _mincgreport_owner
{
public:
mincgreport();
mincgreport(const mincgreport &rhs);
mincgreport& operator=(const mincgreport &rhs);
virtual ~mincgreport();
ae_int_t &iterationscount;
ae_int_t &nfev;
ae_int_t &varidx;
ae_int_t &terminationtype;
};
/*************************************************************************
This object stores nonlinear optimizer state.
You should use functions provided by MinBLEIC subpackage to work with this
object
*************************************************************************/
class _minbleicstate_owner
{
public:
_minbleicstate_owner();
_minbleicstate_owner(const _minbleicstate_owner &rhs);
_minbleicstate_owner& operator=(const _minbleicstate_owner &rhs);
virtual ~_minbleicstate_owner();
alglib_impl::minbleicstate* c_ptr();
alglib_impl::minbleicstate* c_ptr() const;
protected:
alglib_impl::minbleicstate *p_struct;
};
class minbleicstate : public _minbleicstate_owner
{
public:
minbleicstate();
minbleicstate(const minbleicstate &rhs);
minbleicstate& operator=(const minbleicstate &rhs);
virtual ~minbleicstate();
ae_bool &needf;
ae_bool &needfg;
ae_bool &xupdated;
double &f;
real_1d_array g;
real_1d_array x;
};
/*************************************************************************
This structure stores optimization report:
* IterationsCount number of iterations
* NFEV number of gradient evaluations
* TerminationType termination type (see below)
TERMINATION CODES
TerminationType field contains completion code, which can be:
-8 internal integrity control detected infinite or NAN values in
function/gradient. Abnormal termination signalled.
-7 gradient verification failed.
See MinBLEICSetGradientCheck() for more information.
-3 inconsistent constraints. Feasible point is
either nonexistent or too hard to find. Try to
restart optimizer with better initial approximation
1 relative function improvement is no more than EpsF.
2 relative step is no more than EpsX.
4 gradient norm is no more than EpsG
5 MaxIts steps was taken
7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
8 terminated by user who called minbleicrequesttermination(). X contains
point which was "current accepted" when termination request was
submitted.
ADDITIONAL FIELDS
There are additional fields which can be used for debugging:
* DebugEqErr error in the equality constraints (2-norm)
* DebugFS f, calculated at projection of initial point
to the feasible set
* DebugFF f, calculated at the final point
* DebugDX |X_start-X_final|
*************************************************************************/
class _minbleicreport_owner
{
public:
_minbleicreport_owner();
_minbleicreport_owner(const _minbleicreport_owner &rhs);
_minbleicreport_owner& operator=(const _minbleicreport_owner &rhs);
virtual ~_minbleicreport_owner();
alglib_impl::minbleicreport* c_ptr();
alglib_impl::minbleicreport* c_ptr() const;
protected:
alglib_impl::minbleicreport *p_struct;
};
class minbleicreport : public _minbleicreport_owner
{
public:
minbleicreport();
minbleicreport(const minbleicreport &rhs);
minbleicreport& operator=(const minbleicreport &rhs);
virtual ~minbleicreport();
ae_int_t &iterationscount;
ae_int_t &nfev;
ae_int_t &varidx;
ae_int_t &terminationtype;
double &debugeqerr;
double &debugfs;
double &debugff;
double &debugdx;
ae_int_t &debugfeasqpits;
ae_int_t &debugfeasgpaits;
ae_int_t &inneriterationscount;
ae_int_t &outeriterationscount;
};
/*************************************************************************
*************************************************************************/
class _minlbfgsstate_owner
{
public:
_minlbfgsstate_owner();
_minlbfgsstate_owner(const _minlbfgsstate_owner &rhs);
_minlbfgsstate_owner& operator=(const _minlbfgsstate_owner &rhs);
virtual ~_minlbfgsstate_owner();
alglib_impl::minlbfgsstate* c_ptr();
alglib_impl::minlbfgsstate* c_ptr() const;
protected:
alglib_impl::minlbfgsstate *p_struct;
};
class minlbfgsstate : public _minlbfgsstate_owner
{
public:
minlbfgsstate();
minlbfgsstate(const minlbfgsstate &rhs);
minlbfgsstate& operator=(const minlbfgsstate &rhs);
virtual ~minlbfgsstate();
ae_bool &needf;
ae_bool &needfg;
ae_bool &xupdated;
double &f;
real_1d_array g;
real_1d_array x;
};
/*************************************************************************
This structure stores optimization report:
* IterationsCount total number of inner iterations
* NFEV number of gradient evaluations
* TerminationType termination type (see below)
TERMINATION CODES
TerminationType field contains completion code, which can be:
-8 internal integrity control detected infinite or NAN values in
function/gradient. Abnormal termination signalled.
-7 gradient verification failed.
See MinLBFGSSetGradientCheck() for more information.
1 relative function improvement is no more than EpsF.
2 relative step is no more than EpsX.
4 gradient norm is no more than EpsG
5 MaxIts steps was taken
7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
8 terminated by user who called minlbfgsrequesttermination().
X contains point which was "current accepted" when termination
request was submitted.
Other fields of this structure are not documented and should not be used!
*************************************************************************/
class _minlbfgsreport_owner
{
public:
_minlbfgsreport_owner();
_minlbfgsreport_owner(const _minlbfgsreport_owner &rhs);
_minlbfgsreport_owner& operator=(const _minlbfgsreport_owner &rhs);
virtual ~_minlbfgsreport_owner();
alglib_impl::minlbfgsreport* c_ptr();
alglib_impl::minlbfgsreport* c_ptr() const;
protected:
alglib_impl::minlbfgsreport *p_struct;
};
class minlbfgsreport : public _minlbfgsreport_owner
{
public:
minlbfgsreport();
minlbfgsreport(const minlbfgsreport &rhs);
minlbfgsreport& operator=(const minlbfgsreport &rhs);
virtual ~minlbfgsreport();
ae_int_t &iterationscount;
ae_int_t &nfev;
ae_int_t &varidx;
ae_int_t &terminationtype;
};
/*************************************************************************
This object stores nonlinear optimizer state.
You should use functions provided by MinQP subpackage to work with this
object
*************************************************************************/
class _minqpstate_owner
{
public:
_minqpstate_owner();
_minqpstate_owner(const _minqpstate_owner &rhs);
_minqpstate_owner& operator=(const _minqpstate_owner &rhs);
virtual ~_minqpstate_owner();
alglib_impl::minqpstate* c_ptr();
alglib_impl::minqpstate* c_ptr() const;
protected:
alglib_impl::minqpstate *p_struct;
};
class minqpstate : public _minqpstate_owner
{
public:
minqpstate();
minqpstate(const minqpstate &rhs);
minqpstate& operator=(const minqpstate &rhs);
virtual ~minqpstate();
};
/*************************************************************************
This structure stores optimization report:
* InnerIterationsCount number of inner iterations
* OuterIterationsCount number of outer iterations
* NCholesky number of Cholesky decomposition
* NMV number of matrix-vector products
(only products calculated as part of iterative
process are counted)
* TerminationType completion code (see below)
Completion codes:
* -5 inappropriate solver was used:
* QuickQP solver for problem with general linear constraints
* Cholesky solver for semidefinite or indefinite problems
* Cholesky solver for problems with non-boundary constraints
* -4 BLEIC-QP or QuickQP solver found unconstrained direction
of negative curvature (function is unbounded from
below even under constraints), no meaningful
minimum can be found.
* -3 inconsistent constraints (or, maybe, feasible point is
too hard to find). If you are sure that constraints are feasible,
try to restart optimizer with better initial approximation.
* -1 solver error
* 1..4 successful completion
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
*************************************************************************/
class _minqpreport_owner
{
public:
_minqpreport_owner();
_minqpreport_owner(const _minqpreport_owner &rhs);
_minqpreport_owner& operator=(const _minqpreport_owner &rhs);
virtual ~_minqpreport_owner();
alglib_impl::minqpreport* c_ptr();
alglib_impl::minqpreport* c_ptr() const;
protected:
alglib_impl::minqpreport *p_struct;
};
class minqpreport : public _minqpreport_owner
{
public:
minqpreport();
minqpreport(const minqpreport &rhs);
minqpreport& operator=(const minqpreport &rhs);
virtual ~minqpreport();
ae_int_t &inneriterationscount;
ae_int_t &outeriterationscount;
ae_int_t &nmv;
ae_int_t &ncholesky;
ae_int_t &terminationtype;
};
/*************************************************************************
Levenberg-Marquardt optimizer.
This structure should be created using one of the MinLMCreate???()
functions. You should not access its fields directly; use ALGLIB functions
to work with it.
*************************************************************************/
class _minlmstate_owner
{
public:
_minlmstate_owner();
_minlmstate_owner(const _minlmstate_owner &rhs);
_minlmstate_owner& operator=(const _minlmstate_owner &rhs);
virtual ~_minlmstate_owner();
alglib_impl::minlmstate* c_ptr();
alglib_impl::minlmstate* c_ptr() const;
protected:
alglib_impl::minlmstate *p_struct;
};
class minlmstate : public _minlmstate_owner
{
public:
minlmstate();
minlmstate(const minlmstate &rhs);
minlmstate& operator=(const minlmstate &rhs);
virtual ~minlmstate();
ae_bool &needf;
ae_bool &needfg;
ae_bool &needfgh;
ae_bool &needfi;
ae_bool &needfij;
ae_bool &xupdated;
double &f;
real_1d_array fi;
real_1d_array g;
real_2d_array h;
real_2d_array j;
real_1d_array x;
};
/*************************************************************************
Optimization report, filled by MinLMResults() function
FIELDS:
* TerminationType, completetion code:
* -7 derivative correctness check failed;
see rep.funcidx, rep.varidx for
more information.
* -3 constraints are inconsistent
* 1 relative function improvement is no more than
EpsF.
* 2 relative step is no more than EpsX.
* 4 gradient is no more than EpsG.
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible
* 8 terminated by user who called MinLMRequestTermination().
X contains point which was "current accepted" when termination
request was submitted.
* IterationsCount, contains iterations count
* NFunc, number of function calculations
* NJac, number of Jacobi matrix calculations
* NGrad, number of gradient calculations
* NHess, number of Hessian calculations
* NCholesky, number of Cholesky decomposition calculations
*************************************************************************/
class _minlmreport_owner
{
public:
_minlmreport_owner();
_minlmreport_owner(const _minlmreport_owner &rhs);
_minlmreport_owner& operator=(const _minlmreport_owner &rhs);
virtual ~_minlmreport_owner();
alglib_impl::minlmreport* c_ptr();
alglib_impl::minlmreport* c_ptr() const;
protected:
alglib_impl::minlmreport *p_struct;
};
class minlmreport : public _minlmreport_owner
{
public:
minlmreport();
minlmreport(const minlmreport &rhs);
minlmreport& operator=(const minlmreport &rhs);
virtual ~minlmreport();
ae_int_t &iterationscount;
ae_int_t &terminationtype;
ae_int_t &funcidx;
ae_int_t &varidx;
ae_int_t &nfunc;
ae_int_t &njac;
ae_int_t &ngrad;
ae_int_t &nhess;
ae_int_t &ncholesky;
};
/*************************************************************************
*************************************************************************/
class _minasastate_owner
{
public:
_minasastate_owner();
_minasastate_owner(const _minasastate_owner &rhs);
_minasastate_owner& operator=(const _minasastate_owner &rhs);
virtual ~_minasastate_owner();
alglib_impl::minasastate* c_ptr();
alglib_impl::minasastate* c_ptr() const;
protected:
alglib_impl::minasastate *p_struct;
};
class minasastate : public _minasastate_owner
{
public:
minasastate();
minasastate(const minasastate &rhs);
minasastate& operator=(const minasastate &rhs);
virtual ~minasastate();
ae_bool &needfg;
ae_bool &xupdated;
double &f;
real_1d_array g;
real_1d_array x;
};
/*************************************************************************
*************************************************************************/
class _minasareport_owner
{
public:
_minasareport_owner();
_minasareport_owner(const _minasareport_owner &rhs);
_minasareport_owner& operator=(const _minasareport_owner &rhs);
virtual ~_minasareport_owner();
alglib_impl::minasareport* c_ptr();
alglib_impl::minasareport* c_ptr() const;
protected:
alglib_impl::minasareport *p_struct;
};
class minasareport : public _minasareport_owner
{
public:
minasareport();
minasareport(const minasareport &rhs);
minasareport& operator=(const minasareport &rhs);
virtual ~minasareport();
ae_int_t &iterationscount;
ae_int_t &nfev;
ae_int_t &terminationtype;
ae_int_t &activeconstraints;
};
/*************************************************************************
This object stores nonlinear optimizer state.
You should use functions provided by MinNLC subpackage to work with this
object
*************************************************************************/
class _minnlcstate_owner
{
public:
_minnlcstate_owner();
_minnlcstate_owner(const _minnlcstate_owner &rhs);
_minnlcstate_owner& operator=(const _minnlcstate_owner &rhs);
virtual ~_minnlcstate_owner();
alglib_impl::minnlcstate* c_ptr();
alglib_impl::minnlcstate* c_ptr() const;
protected:
alglib_impl::minnlcstate *p_struct;
};
class minnlcstate : public _minnlcstate_owner
{
public:
minnlcstate();
minnlcstate(const minnlcstate &rhs);
minnlcstate& operator=(const minnlcstate &rhs);
virtual ~minnlcstate();
ae_bool &needfi;
ae_bool &needfij;
ae_bool &xupdated;
double &f;
real_1d_array fi;
real_2d_array j;
real_1d_array x;
};
/*************************************************************************
This structure stores optimization report:
* IterationsCount total number of inner iterations
* NFEV number of gradient evaluations
* TerminationType termination type (see below)
TERMINATION CODES
TerminationType field contains completion code, which can be:
-8 internal integrity control detected infinite or NAN values in
function/gradient. Abnormal termination signalled.
-7 gradient verification failed.
See MinNLCSetGradientCheck() for more information.
1 relative function improvement is no more than EpsF.
2 relative step is no more than EpsX.
4 gradient norm is no more than EpsG
5 MaxIts steps was taken
7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
Other fields of this structure are not documented and should not be used!
*************************************************************************/
class _minnlcreport_owner
{
public:
_minnlcreport_owner();
_minnlcreport_owner(const _minnlcreport_owner &rhs);
_minnlcreport_owner& operator=(const _minnlcreport_owner &rhs);
virtual ~_minnlcreport_owner();
alglib_impl::minnlcreport* c_ptr();
alglib_impl::minnlcreport* c_ptr() const;
protected:
alglib_impl::minnlcreport *p_struct;
};
class minnlcreport : public _minnlcreport_owner
{
public:
minnlcreport();
minnlcreport(const minnlcreport &rhs);
minnlcreport& operator=(const minnlcreport &rhs);
virtual ~minnlcreport();
ae_int_t &iterationscount;
ae_int_t &nfev;
ae_int_t &varidx;
ae_int_t &funcidx;
ae_int_t &terminationtype;
ae_int_t &dbgphase0its;
};
/*************************************************************************
This object stores nonlinear optimizer state.
You should use functions provided by MinNS subpackage to work with this
object
*************************************************************************/
class _minnsstate_owner
{
public:
_minnsstate_owner();
_minnsstate_owner(const _minnsstate_owner &rhs);
_minnsstate_owner& operator=(const _minnsstate_owner &rhs);
virtual ~_minnsstate_owner();
alglib_impl::minnsstate* c_ptr();
alglib_impl::minnsstate* c_ptr() const;
protected:
alglib_impl::minnsstate *p_struct;
};
class minnsstate : public _minnsstate_owner
{
public:
minnsstate();
minnsstate(const minnsstate &rhs);
minnsstate& operator=(const minnsstate &rhs);
virtual ~minnsstate();
ae_bool &needfi;
ae_bool &needfij;
ae_bool &xupdated;
double &f;
real_1d_array fi;
real_2d_array j;
real_1d_array x;
};
/*************************************************************************
This structure stores optimization report:
* IterationsCount total number of inner iterations
* NFEV number of gradient evaluations
* TerminationType termination type (see below)
* CErr maximum violation of all types of constraints
* LCErr maximum violation of linear constraints
* NLCErr maximum violation of nonlinear constraints
TERMINATION CODES
TerminationType field contains completion code, which can be:
-8 internal integrity control detected infinite or NAN values in
function/gradient. Abnormal termination signalled.
-3 box constraints are inconsistent
-1 inconsistent parameters were passed:
* penalty parameter for minnssetalgoags() is zero,
but we have nonlinear constraints set by minnssetnlc()
2 sampling radius decreased below epsx
5 MaxIts steps was taken
7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
8 User requested termination via MinNSRequestTermination()
Other fields of this structure are not documented and should not be used!
*************************************************************************/
class _minnsreport_owner
{
public:
_minnsreport_owner();
_minnsreport_owner(const _minnsreport_owner &rhs);
_minnsreport_owner& operator=(const _minnsreport_owner &rhs);
virtual ~_minnsreport_owner();
alglib_impl::minnsreport* c_ptr();
alglib_impl::minnsreport* c_ptr() const;
protected:
alglib_impl::minnsreport *p_struct;
};
class minnsreport : public _minnsreport_owner
{
public:
minnsreport();
minnsreport(const minnsreport &rhs);
minnsreport& operator=(const minnsreport &rhs);
virtual ~minnsreport();
ae_int_t &iterationscount;
ae_int_t &nfev;
double &cerr;
double &lcerr;
double &nlcerr;
ae_int_t &terminationtype;
ae_int_t &varidx;
ae_int_t &funcidx;
};
/*************************************************************************
NONLINEAR CONJUGATE GRADIENT METHOD
DESCRIPTION:
The subroutine minimizes function F(x) of N arguments by using one of the
nonlinear conjugate gradient methods.
These CG methods are globally convergent (even on non-convex functions) as
long as grad(f) is Lipschitz continuous in a some neighborhood of the
L = { x : f(x)<=f(x0) }.
REQUIREMENTS:
Algorithm will request following information during its operation:
* function value F and its gradient G (simultaneously) at given point X
USAGE:
1. User initializes algorithm state with MinCGCreate() call
2. User tunes solver parameters with MinCGSetCond(), MinCGSetStpMax() and
other functions
3. User calls MinCGOptimize() function which takes algorithm state and
pointer (delegate, etc.) to callback function which calculates F/G.
4. User calls MinCGResults() to get solution
5. Optionally, user may call MinCGRestartFrom() to solve another problem
with same N but another starting point and/or another function.
MinCGRestartFrom() allows to reuse already initialized structure.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
X - starting point, array[0..N-1].
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 25.03.2010 by Bochkanov Sergey
*************************************************************************/
void mincgcreate(const ae_int_t n, const real_1d_array &x, mincgstate &state);
void mincgcreate(const real_1d_array &x, mincgstate &state);
/*************************************************************************
The subroutine is finite difference variant of MinCGCreate(). It uses
finite differences in order to differentiate target function.
Description below contains information which is specific to this function
only. We recommend to read comments on MinCGCreate() in order to get more
information about creation of CG optimizer.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
X - starting point, array[0..N-1].
DiffStep- differentiation step, >0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
1. algorithm uses 4-point central formula for differentiation.
2. differentiation step along I-th axis is equal to DiffStep*S[I] where
S[] is scaling vector which can be set by MinCGSetScale() call.
3. we recommend you to use moderate values of differentiation step. Too
large step will result in too large truncation errors, while too small
step will result in too large numerical errors. 1.0E-6 can be good
value to start with.
4. Numerical differentiation is very inefficient - one gradient
calculation needs 4*N function evaluations. This function will work for
any N - either small (1...10), moderate (10...100) or large (100...).
However, performance penalty will be too severe for any N's except for
small ones.
We should also say that code which relies on numerical differentiation
is less robust and precise. L-BFGS needs exact gradient values.
Imprecise gradient may slow down convergence, especially on highly
nonlinear problems.
Thus we recommend to use this function for fast prototyping on small-
dimensional problems only, and to implement analytical gradient as soon
as possible.
-- ALGLIB --
Copyright 16.05.2011 by Bochkanov Sergey
*************************************************************************/
void mincgcreatef(const ae_int_t n, const real_1d_array &x, const double diffstep, mincgstate &state);
void mincgcreatef(const real_1d_array &x, const double diffstep, mincgstate &state);
/*************************************************************************
This function sets stopping conditions for CG optimization algorithm.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsG - >=0
The subroutine finishes its work if the condition
|v|<EpsG is satisfied, where:
* |.| means Euclidian norm
* v - scaled gradient vector, v[i]=g[i]*s[i]
* g - gradient
* s - scaling coefficients set by MinCGSetScale()
EpsF - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |F(k+1)-F(k)|<=EpsF*max{|F(k)|,|F(k+1)|,1}
is satisfied.
EpsX - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |v|<=EpsX is fulfilled, where:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - ste pvector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinCGSetScale()
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited.
Passing EpsG=0, EpsF=0, EpsX=0 and MaxIts=0 (simultaneously) will lead to
automatic stopping criterion selection (small EpsX).
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsetcond(const mincgstate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxits);
/*************************************************************************
This function sets scaling coefficients for CG optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Scaling is also used by finite difference variant of CG optimizer - step
along I-th axis is equal to DiffStep*S[I].
In most optimizers (and in the CG too) scaling is NOT a form of
preconditioning. It just affects stopping conditions. You should set
preconditioner by separate call to one of the MinCGSetPrec...() functions.
There is special preconditioning mode, however, which uses scaling
coefficients to form diagonal preconditioning matrix. You can turn this
mode on, if you want. But you should understand that scaling is not the
same thing as preconditioning - these are two different, although related
forms of tuning solver.
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void mincgsetscale(const mincgstate &state, const real_1d_array &s);
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
If NeedXRep is True, algorithm will call rep() callback function if it is
provided to MinCGOptimize().
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsetxrep(const mincgstate &state, const bool needxrep);
/*************************************************************************
This function sets CG algorithm.
INPUT PARAMETERS:
State - structure which stores algorithm state
CGType - algorithm type:
* -1 automatic selection of the best algorithm
* 0 DY (Dai and Yuan) algorithm
* 1 Hybrid DY-HS algorithm
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsetcgtype(const mincgstate &state, const ae_int_t cgtype);
/*************************************************************************
This function sets maximum step length
INPUT PARAMETERS:
State - structure which stores algorithm state
StpMax - maximum step length, >=0. Set StpMax to 0.0, if you don't
want to limit step length.
Use this subroutine when you optimize target function which contains exp()
or other fast growing functions, and optimization algorithm makes too
large steps which leads to overflow. This function allows us to reject
steps that are too large (and therefore expose us to the possible
overflow) without actually calculating function value at the x+stp*d.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsetstpmax(const mincgstate &state, const double stpmax);
/*************************************************************************
This function allows to suggest initial step length to the CG algorithm.
Suggested step length is used as starting point for the line search. It
can be useful when you have badly scaled problem, i.e. when ||grad||
(which is used as initial estimate for the first step) is many orders of
magnitude different from the desired step.
Line search may fail on such problems without good estimate of initial
step length. Imagine, for example, problem with ||grad||=10^50 and desired
step equal to 0.1 Line search function will use 10^50 as initial step,
then it will decrease step length by 2 (up to 20 attempts) and will get
10^44, which is still too large.
This function allows us to tell than line search should be started from
some moderate step length, like 1.0, so algorithm will be able to detect
desired step length in a several searches.
Default behavior (when no step is suggested) is to use preconditioner, if
it is available, to generate initial estimate of step length.
This function influences only first iteration of algorithm. It should be
called between MinCGCreate/MinCGRestartFrom() call and MinCGOptimize call.
Suggested step is ignored if you have preconditioner.
INPUT PARAMETERS:
State - structure used to store algorithm state.
Stp - initial estimate of the step length.
Can be zero (no estimate).
-- ALGLIB --
Copyright 30.07.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsuggeststep(const mincgstate &state, const double stp);
/*************************************************************************
Modification of the preconditioner: preconditioning is turned off.
INPUT PARAMETERS:
State - structure which stores algorithm state
NOTE: you can change preconditioner "on the fly", during algorithm
iterations.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsetprecdefault(const mincgstate &state);
/*************************************************************************
Modification of the preconditioner: diagonal of approximate Hessian is
used.
INPUT PARAMETERS:
State - structure which stores algorithm state
D - diagonal of the approximate Hessian, array[0..N-1],
(if larger, only leading N elements are used).
NOTE: you can change preconditioner "on the fly", during algorithm
iterations.
NOTE 2: D[i] should be positive. Exception will be thrown otherwise.
NOTE 3: you should pass diagonal of approximate Hessian - NOT ITS INVERSE.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsetprecdiag(const mincgstate &state, const real_1d_array &d);
/*************************************************************************
Modification of the preconditioner: scale-based diagonal preconditioning.
This preconditioning mode can be useful when you don't have approximate
diagonal of Hessian, but you know that your variables are badly scaled
(for example, one variable is in [1,10], and another in [1000,100000]),
and most part of the ill-conditioning comes from different scales of vars.
In this case simple scale-based preconditioner, with H[i] = 1/(s[i]^2),
can greatly improve convergence.
IMPRTANT: you should set scale of your variables with MinCGSetScale() call
(before or after MinCGSetPrecScale() call). Without knowledge of the scale
of your variables scale-based preconditioner will be just unit matrix.
INPUT PARAMETERS:
State - structure which stores algorithm state
NOTE: you can change preconditioner "on the fly", during algorithm
iterations.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsetprecscale(const mincgstate &state);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool mincgiteration(const mincgstate &state);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
func - callback which calculates function (or merit function)
value func at given point x
grad - callback which calculates function (or merit function)
value func and gradient grad at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
NOTES:
1. This function has two different implementations: one which uses exact
(analytical) user-supplied gradient, and one which uses function value
only and numerically differentiates function in order to obtain
gradient.
Depending on the specific function used to create optimizer object
(either MinCGCreate() for analytical gradient or MinCGCreateF() for
numerical differentiation) you should choose appropriate variant of
MinCGOptimize() - one which accepts function AND gradient or one which
accepts function ONLY.
Be careful to choose variant of MinCGOptimize() which corresponds to
your optimization scheme! Table below lists different combinations of
callback (function/gradient) passed to MinCGOptimize() and specific
function used to create optimizer.
| USER PASSED TO MinCGOptimize()
CREATED WITH | function only | function and gradient
------------------------------------------------------------
MinCGCreateF() | work FAIL
MinCGCreate() | FAIL work
Here "FAIL" denotes inappropriate combinations of optimizer creation
function and MinCGOptimize() version. Attemps to use such combination
(for example, to create optimizer with MinCGCreateF() and to pass
gradient information to MinCGOptimize()) will lead to exception being
thrown. Either you did not pass gradient when it WAS needed or you
passed gradient when it was NOT needed.
-- ALGLIB --
Copyright 20.04.2009 by Bochkanov Sergey
*************************************************************************/
void mincgoptimize(mincgstate &state,
void (*func)(const real_1d_array &x, double &func, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
void mincgoptimize(mincgstate &state,
void (*grad)(const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
/*************************************************************************
Conjugate gradient results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report:
* Rep.TerminationType completetion code:
* -8 internal integrity control detected infinite
or NAN values in function/gradient. Abnormal
termination signalled.
* -7 gradient verification failed.
See MinCGSetGradientCheck() for more information.
* 1 relative function improvement is no more than
EpsF.
* 2 relative step is no more than EpsX.
* 4 gradient norm is no more than EpsG
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible,
we return best X found so far
* 8 terminated by user
* Rep.IterationsCount contains iterations count
* NFEV countains number of function calculations
-- ALGLIB --
Copyright 20.04.2009 by Bochkanov Sergey
*************************************************************************/
void mincgresults(const mincgstate &state, real_1d_array &x, mincgreport &rep);
/*************************************************************************
Conjugate gradient results
Buffered implementation of MinCGResults(), which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 20.04.2009 by Bochkanov Sergey
*************************************************************************/
void mincgresultsbuf(const mincgstate &state, real_1d_array &x, mincgreport &rep);
/*************************************************************************
This subroutine restarts CG algorithm from new point. All optimization
parameters are left unchanged.
This function allows to solve multiple optimization problems (which
must have same number of dimensions) without object reallocation penalty.
INPUT PARAMETERS:
State - structure used to store algorithm state.
X - new starting point.
-- ALGLIB --
Copyright 30.07.2010 by Bochkanov Sergey
*************************************************************************/
void mincgrestartfrom(const mincgstate &state, const real_1d_array &x);
/*************************************************************************
This subroutine submits request for termination of running optimizer. It
should be called from user-supplied callback when user decides that it is
time to "smoothly" terminate optimization process. As result, optimizer
stops at point which was "current accepted" when termination request was
submitted and returns error code 8 (successful termination).
INPUT PARAMETERS:
State - optimizer structure
NOTE: after request for termination optimizer may perform several
additional calls to user-supplied callbacks. It does NOT guarantee
to stop immediately - it just guarantees that these additional calls
will be discarded later.
NOTE: calling this function on optimizer which is NOT running will have no
effect.
NOTE: multiple calls to this function are possible. First call is counted,
subsequent calls are silently ignored.
-- ALGLIB --
Copyright 08.10.2014 by Bochkanov Sergey
*************************************************************************/
void mincgrequesttermination(const mincgstate &state);
/*************************************************************************
This subroutine turns on verification of the user-supplied analytic
gradient:
* user calls this subroutine before optimization begins
* MinCGOptimize() is called
* prior to actual optimization, for each component of parameters being
optimized X[i] algorithm performs following steps:
* two trial steps are made to X[i]-TestStep*S[i] and X[i]+TestStep*S[i],
where X[i] is i-th component of the initial point and S[i] is a scale
of i-th parameter
* F(X) is evaluated at these trial points
* we perform one more evaluation in the middle point of the interval
* we build cubic model using function values and derivatives at trial
points and we compare its prediction with actual value in the middle
point
* in case difference between prediction and actual value is higher than
some predetermined threshold, algorithm stops with completion code -7;
Rep.VarIdx is set to index of the parameter with incorrect derivative.
* after verification is over, algorithm proceeds to the actual optimization.
NOTE 1: verification needs N (parameters count) gradient evaluations. It
is very costly and you should use it only for low dimensional
problems, when you want to be sure that you've correctly
calculated analytic derivatives. You should not use it in the
production code (unless you want to check derivatives provided by
some third party).
NOTE 2: you should carefully choose TestStep. Value which is too large
(so large that function behaviour is significantly non-cubic) will
lead to false alarms. You may use different step for different
parameters by means of setting scale with MinCGSetScale().
NOTE 3: this function may lead to false positives. In case it reports that
I-th derivative was calculated incorrectly, you may decrease test
step and try one more time - maybe your function changes too
sharply and your step is too large for such rapidly chanding
function.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step:
* TestStep=0 turns verification off
* TestStep>0 activates verification
-- ALGLIB --
Copyright 31.05.2012 by Bochkanov Sergey
*************************************************************************/
void mincgsetgradientcheck(const mincgstate &state, const double teststep);
/*************************************************************************
BOUND CONSTRAINED OPTIMIZATION
WITH ADDITIONAL LINEAR EQUALITY AND INEQUALITY CONSTRAINTS
DESCRIPTION:
The subroutine minimizes function F(x) of N arguments subject to any
combination of:
* bound constraints
* linear inequality constraints
* linear equality constraints
REQUIREMENTS:
* user must provide function value and gradient
* starting point X0 must be feasible or
not too far away from the feasible set
* grad(f) must be Lipschitz continuous on a level set:
L = { x : f(x)<=f(x0) }
* function must be defined everywhere on the feasible set F
USAGE:
Constrained optimization if far more complex than the unconstrained one.
Here we give very brief outline of the BLEIC optimizer. We strongly recommend
you to read examples in the ALGLIB Reference Manual and to read ALGLIB User Guide
on optimization, which is available at http://www.alglib.net/optimization/
1. User initializes algorithm state with MinBLEICCreate() call
2. USer adds boundary and/or linear constraints by calling
MinBLEICSetBC() and MinBLEICSetLC() functions.
3. User sets stopping conditions with MinBLEICSetCond().
4. User calls MinBLEICOptimize() function which takes algorithm state and
pointer (delegate, etc.) to callback function which calculates F/G.
5. User calls MinBLEICResults() to get solution
6. Optionally user may call MinBLEICRestartFrom() to solve another problem
with same N but another starting point.
MinBLEICRestartFrom() allows to reuse already initialized structure.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size ofX
X - starting point, array[N]:
* it is better to set X to a feasible point
* but X can be infeasible, in which case algorithm will try
to find feasible point first, using X as initial
approximation.
OUTPUT PARAMETERS:
State - structure stores algorithm state
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleiccreate(const ae_int_t n, const real_1d_array &x, minbleicstate &state);
void minbleiccreate(const real_1d_array &x, minbleicstate &state);
/*************************************************************************
The subroutine is finite difference variant of MinBLEICCreate(). It uses
finite differences in order to differentiate target function.
Description below contains information which is specific to this function
only. We recommend to read comments on MinBLEICCreate() in order to get
more information about creation of BLEIC optimizer.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
X - starting point, array[0..N-1].
DiffStep- differentiation step, >0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
1. algorithm uses 4-point central formula for differentiation.
2. differentiation step along I-th axis is equal to DiffStep*S[I] where
S[] is scaling vector which can be set by MinBLEICSetScale() call.
3. we recommend you to use moderate values of differentiation step. Too
large step will result in too large truncation errors, while too small
step will result in too large numerical errors. 1.0E-6 can be good
value to start with.
4. Numerical differentiation is very inefficient - one gradient
calculation needs 4*N function evaluations. This function will work for
any N - either small (1...10), moderate (10...100) or large (100...).
However, performance penalty will be too severe for any N's except for
small ones.
We should also say that code which relies on numerical differentiation
is less robust and precise. CG needs exact gradient values. Imprecise
gradient may slow down convergence, especially on highly nonlinear
problems.
Thus we recommend to use this function for fast prototyping on small-
dimensional problems only, and to implement analytical gradient as soon
as possible.
-- ALGLIB --
Copyright 16.05.2011 by Bochkanov Sergey
*************************************************************************/
void minbleiccreatef(const ae_int_t n, const real_1d_array &x, const double diffstep, minbleicstate &state);
void minbleiccreatef(const real_1d_array &x, const double diffstep, minbleicstate &state);
/*************************************************************************
This function sets boundary constraints for BLEIC optimizer.
Boundary constraints are inactive by default (after initial creation).
They are preserved after algorithm restart with MinBLEICRestartFrom().
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bounds, array[N].
If some (all) variables are unbounded, you may specify
very small number or -INF.
BndU - upper bounds, array[N].
If some (all) variables are unbounded, you may specify
very large number or +INF.
NOTE 1: it is possible to specify BndL[i]=BndU[i]. In this case I-th
variable will be "frozen" at X[i]=BndL[i]=BndU[i].
NOTE 2: this solver has following useful properties:
* bound constraints are always satisfied exactly
* function is evaluated only INSIDE area specified by bound constraints,
even when numerical differentiation is used (algorithm adjusts nodes
according to boundary constraints)
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetbc(const minbleicstate &state, const real_1d_array &bndl, const real_1d_array &bndu);
/*************************************************************************
This function sets linear constraints for BLEIC optimizer.
Linear constraints are inactive by default (after initial creation).
They are preserved after algorithm restart with MinBLEICRestartFrom().
INPUT PARAMETERS:
State - structure previously allocated with MinBLEICCreate call.
C - linear constraints, array[K,N+1].
Each row of C represents one constraint, either equality
or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of C (including right part) must be finite.
CT - type of constraints, array[K]:
* if CT[i]>0, then I-th constraint is C[i,*]*x >= C[i,n+1]
* if CT[i]=0, then I-th constraint is C[i,*]*x = C[i,n+1]
* if CT[i]<0, then I-th constraint is C[i,*]*x <= C[i,n+1]
K - number of equality/inequality constraints, K>=0:
* if given, only leading K elements of C/CT are used
* if not given, automatically determined from sizes of C/CT
NOTE 1: linear (non-bound) constraints are satisfied only approximately:
* there always exists some minor violation (about Epsilon in magnitude)
due to rounding errors
* numerical differentiation, if used, may lead to function evaluations
outside of the feasible area, because algorithm does NOT change
numerical differentiation formula according to linear constraints.
If you want constraints to be satisfied exactly, try to reformulate your
problem in such manner that all constraints will become boundary ones
(this kind of constraints is always satisfied exactly, both in the final
solution and in all intermediate points).
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetlc(const minbleicstate &state, const real_2d_array &c, const integer_1d_array &ct, const ae_int_t k);
void minbleicsetlc(const minbleicstate &state, const real_2d_array &c, const integer_1d_array &ct);
/*************************************************************************
This function sets stopping conditions for the optimizer.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsG - >=0
The subroutine finishes its work if the condition
|v|<EpsG is satisfied, where:
* |.| means Euclidian norm
* v - scaled gradient vector, v[i]=g[i]*s[i]
* g - gradient
* s - scaling coefficients set by MinBLEICSetScale()
EpsF - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |F(k+1)-F(k)|<=EpsF*max{|F(k)|,|F(k+1)|,1}
is satisfied.
EpsX - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |v|<=EpsX is fulfilled, where:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - step vector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinBLEICSetScale()
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited.
Passing EpsG=0, EpsF=0 and EpsX=0 and MaxIts=0 (simultaneously) will lead
to automatic stopping criterion selection.
NOTE: when SetCond() called with non-zero MaxIts, BLEIC solver may perform
slightly more than MaxIts iterations. I.e., MaxIts sets non-strict
limit on iterations count.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetcond(const minbleicstate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxits);
/*************************************************************************
This function sets scaling coefficients for BLEIC optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Scaling is also used by finite difference variant of the optimizer - step
along I-th axis is equal to DiffStep*S[I].
In most optimizers (and in the BLEIC too) scaling is NOT a form of
preconditioning. It just affects stopping conditions. You should set
preconditioner by separate call to one of the MinBLEICSetPrec...()
functions.
There is a special preconditioning mode, however, which uses scaling
coefficients to form diagonal preconditioning matrix. You can turn this
mode on, if you want. But you should understand that scaling is not the
same thing as preconditioning - these are two different, although related
forms of tuning solver.
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void minbleicsetscale(const minbleicstate &state, const real_1d_array &s);
/*************************************************************************
Modification of the preconditioner: preconditioning is turned off.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetprecdefault(const minbleicstate &state);
/*************************************************************************
Modification of the preconditioner: diagonal of approximate Hessian is
used.
INPUT PARAMETERS:
State - structure which stores algorithm state
D - diagonal of the approximate Hessian, array[0..N-1],
(if larger, only leading N elements are used).
NOTE 1: D[i] should be positive. Exception will be thrown otherwise.
NOTE 2: you should pass diagonal of approximate Hessian - NOT ITS INVERSE.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetprecdiag(const minbleicstate &state, const real_1d_array &d);
/*************************************************************************
Modification of the preconditioner: scale-based diagonal preconditioning.
This preconditioning mode can be useful when you don't have approximate
diagonal of Hessian, but you know that your variables are badly scaled
(for example, one variable is in [1,10], and another in [1000,100000]),
and most part of the ill-conditioning comes from different scales of vars.
In this case simple scale-based preconditioner, with H[i] = 1/(s[i]^2),
can greatly improve convergence.
IMPRTANT: you should set scale of your variables with MinBLEICSetScale()
call (before or after MinBLEICSetPrecScale() call). Without knowledge of
the scale of your variables scale-based preconditioner will be just unit
matrix.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetprecscale(const minbleicstate &state);
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
If NeedXRep is True, algorithm will call rep() callback function if it is
provided to MinBLEICOptimize().
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetxrep(const minbleicstate &state, const bool needxrep);
/*************************************************************************
This function sets maximum step length
IMPORTANT: this feature is hard to combine with preconditioning. You can't
set upper limit on step length, when you solve optimization problem with
linear (non-boundary) constraints AND preconditioner turned on.
When non-boundary constraints are present, you have to either a) use
preconditioner, or b) use upper limit on step length. YOU CAN'T USE BOTH!
In this case algorithm will terminate with appropriate error code.
INPUT PARAMETERS:
State - structure which stores algorithm state
StpMax - maximum step length, >=0. Set StpMax to 0.0, if you don't
want to limit step length.
Use this subroutine when you optimize target function which contains exp()
or other fast growing functions, and optimization algorithm makes too
large steps which lead to overflow. This function allows us to reject
steps that are too large (and therefore expose us to the possible
overflow) without actually calculating function value at the x+stp*d.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetstpmax(const minbleicstate &state, const double stpmax);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool minbleiciteration(const minbleicstate &state);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
func - callback which calculates function (or merit function)
value func at given point x
grad - callback which calculates function (or merit function)
value func and gradient grad at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
NOTES:
1. This function has two different implementations: one which uses exact
(analytical) user-supplied gradient, and one which uses function value
only and numerically differentiates function in order to obtain
gradient.
Depending on the specific function used to create optimizer object
(either MinBLEICCreate() for analytical gradient or MinBLEICCreateF()
for numerical differentiation) you should choose appropriate variant of
MinBLEICOptimize() - one which accepts function AND gradient or one
which accepts function ONLY.
Be careful to choose variant of MinBLEICOptimize() which corresponds to
your optimization scheme! Table below lists different combinations of
callback (function/gradient) passed to MinBLEICOptimize() and specific
function used to create optimizer.
| USER PASSED TO MinBLEICOptimize()
CREATED WITH | function only | function and gradient
------------------------------------------------------------
MinBLEICCreateF() | work FAIL
MinBLEICCreate() | FAIL work
Here "FAIL" denotes inappropriate combinations of optimizer creation
function and MinBLEICOptimize() version. Attemps to use such
combination (for example, to create optimizer with MinBLEICCreateF()
and to pass gradient information to MinCGOptimize()) will lead to
exception being thrown. Either you did not pass gradient when it WAS
needed or you passed gradient when it was NOT needed.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicoptimize(minbleicstate &state,
void (*func)(const real_1d_array &x, double &func, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
void minbleicoptimize(minbleicstate &state,
void (*grad)(const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
/*************************************************************************
BLEIC results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report. You should check Rep.TerminationType
in order to distinguish successful termination from
unsuccessful one:
* -8 internal integrity control detected infinite or
NAN values in function/gradient. Abnormal
termination signalled.
* -7 gradient verification failed.
See MinBLEICSetGradientCheck() for more information.
* -3 inconsistent constraints. Feasible point is
either nonexistent or too hard to find. Try to
restart optimizer with better initial approximation
* 1 relative function improvement is no more than EpsF.
* 2 scaled step is no more than EpsX.
* 4 scaled gradient norm is no more than EpsG.
* 5 MaxIts steps was taken
* 8 terminated by user who called minbleicrequesttermination().
X contains point which was "current accepted" when
termination request was submitted.
More information about fields of this structure can be
found in the comments on MinBLEICReport datatype.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicresults(const minbleicstate &state, real_1d_array &x, minbleicreport &rep);
/*************************************************************************
BLEIC results
Buffered implementation of MinBLEICResults() which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicresultsbuf(const minbleicstate &state, real_1d_array &x, minbleicreport &rep);
/*************************************************************************
This subroutine restarts algorithm from new point.
All optimization parameters (including constraints) are left unchanged.
This function allows to solve multiple optimization problems (which
must have same number of dimensions) without object reallocation penalty.
INPUT PARAMETERS:
State - structure previously allocated with MinBLEICCreate call.
X - new starting point.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicrestartfrom(const minbleicstate &state, const real_1d_array &x);
/*************************************************************************
This subroutine submits request for termination of running optimizer. It
should be called from user-supplied callback when user decides that it is
time to "smoothly" terminate optimization process. As result, optimizer
stops at point which was "current accepted" when termination request was
submitted and returns error code 8 (successful termination).
INPUT PARAMETERS:
State - optimizer structure
NOTE: after request for termination optimizer may perform several
additional calls to user-supplied callbacks. It does NOT guarantee
to stop immediately - it just guarantees that these additional calls
will be discarded later.
NOTE: calling this function on optimizer which is NOT running will have no
effect.
NOTE: multiple calls to this function are possible. First call is counted,
subsequent calls are silently ignored.
-- ALGLIB --
Copyright 08.10.2014 by Bochkanov Sergey
*************************************************************************/
void minbleicrequesttermination(const minbleicstate &state);
/*************************************************************************
This subroutine turns on verification of the user-supplied analytic
gradient:
* user calls this subroutine before optimization begins
* MinBLEICOptimize() is called
* prior to actual optimization, for each component of parameters being
optimized X[i] algorithm performs following steps:
* two trial steps are made to X[i]-TestStep*S[i] and X[i]+TestStep*S[i],
where X[i] is i-th component of the initial point and S[i] is a scale
of i-th parameter
* if needed, steps are bounded with respect to constraints on X[]
* F(X) is evaluated at these trial points
* we perform one more evaluation in the middle point of the interval
* we build cubic model using function values and derivatives at trial
points and we compare its prediction with actual value in the middle
point
* in case difference between prediction and actual value is higher than
some predetermined threshold, algorithm stops with completion code -7;
Rep.VarIdx is set to index of the parameter with incorrect derivative.
* after verification is over, algorithm proceeds to the actual optimization.
NOTE 1: verification needs N (parameters count) gradient evaluations. It
is very costly and you should use it only for low dimensional
problems, when you want to be sure that you've correctly
calculated analytic derivatives. You should not use it in the
production code (unless you want to check derivatives provided by
some third party).
NOTE 2: you should carefully choose TestStep. Value which is too large
(so large that function behaviour is significantly non-cubic) will
lead to false alarms. You may use different step for different
parameters by means of setting scale with MinBLEICSetScale().
NOTE 3: this function may lead to false positives. In case it reports that
I-th derivative was calculated incorrectly, you may decrease test
step and try one more time - maybe your function changes too
sharply and your step is too large for such rapidly chanding
function.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step:
* TestStep=0 turns verification off
* TestStep>0 activates verification
-- ALGLIB --
Copyright 15.06.2012 by Bochkanov Sergey
*************************************************************************/
void minbleicsetgradientcheck(const minbleicstate &state, const double teststep);
/*************************************************************************
LIMITED MEMORY BFGS METHOD FOR LARGE SCALE OPTIMIZATION
DESCRIPTION:
The subroutine minimizes function F(x) of N arguments by using a quasi-
Newton method (LBFGS scheme) which is optimized to use a minimum amount
of memory.
The subroutine generates the approximation of an inverse Hessian matrix by
using information about the last M steps of the algorithm (instead of N).
It lessens a required amount of memory from a value of order N^2 to a
value of order 2*N*M.
REQUIREMENTS:
Algorithm will request following information during its operation:
* function value F and its gradient G (simultaneously) at given point X
USAGE:
1. User initializes algorithm state with MinLBFGSCreate() call
2. User tunes solver parameters with MinLBFGSSetCond() MinLBFGSSetStpMax()
and other functions
3. User calls MinLBFGSOptimize() function which takes algorithm state and
pointer (delegate, etc.) to callback function which calculates F/G.
4. User calls MinLBFGSResults() to get solution
5. Optionally user may call MinLBFGSRestartFrom() to solve another problem
with same N/M but another starting point and/or another function.
MinLBFGSRestartFrom() allows to reuse already initialized structure.
INPUT PARAMETERS:
N - problem dimension. N>0
M - number of corrections in the BFGS scheme of Hessian
approximation update. Recommended value: 3<=M<=7. The smaller
value causes worse convergence, the bigger will not cause a
considerably better convergence, but will cause a fall in the
performance. M<=N.
X - initial solution approximation, array[0..N-1].
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
1. you may tune stopping conditions with MinLBFGSSetCond() function
2. if target function contains exp() or other fast growing functions, and
optimization algorithm makes too large steps which leads to overflow,
use MinLBFGSSetStpMax() function to bound algorithm's steps. However,
L-BFGS rarely needs such a tuning.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgscreate(const ae_int_t n, const ae_int_t m, const real_1d_array &x, minlbfgsstate &state);
void minlbfgscreate(const ae_int_t m, const real_1d_array &x, minlbfgsstate &state);
/*************************************************************************
The subroutine is finite difference variant of MinLBFGSCreate(). It uses
finite differences in order to differentiate target function.
Description below contains information which is specific to this function
only. We recommend to read comments on MinLBFGSCreate() in order to get
more information about creation of LBFGS optimizer.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
M - number of corrections in the BFGS scheme of Hessian
approximation update. Recommended value: 3<=M<=7. The smaller
value causes worse convergence, the bigger will not cause a
considerably better convergence, but will cause a fall in the
performance. M<=N.
X - starting point, array[0..N-1].
DiffStep- differentiation step, >0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
1. algorithm uses 4-point central formula for differentiation.
2. differentiation step along I-th axis is equal to DiffStep*S[I] where
S[] is scaling vector which can be set by MinLBFGSSetScale() call.
3. we recommend you to use moderate values of differentiation step. Too
large step will result in too large truncation errors, while too small
step will result in too large numerical errors. 1.0E-6 can be good
value to start with.
4. Numerical differentiation is very inefficient - one gradient
calculation needs 4*N function evaluations. This function will work for
any N - either small (1...10), moderate (10...100) or large (100...).
However, performance penalty will be too severe for any N's except for
small ones.
We should also say that code which relies on numerical differentiation
is less robust and precise. LBFGS needs exact gradient values.
Imprecise gradient may slow down convergence, especially on highly
nonlinear problems.
Thus we recommend to use this function for fast prototyping on small-
dimensional problems only, and to implement analytical gradient as soon
as possible.
-- ALGLIB --
Copyright 16.05.2011 by Bochkanov Sergey
*************************************************************************/
void minlbfgscreatef(const ae_int_t n, const ae_int_t m, const real_1d_array &x, const double diffstep, minlbfgsstate &state);
void minlbfgscreatef(const ae_int_t m, const real_1d_array &x, const double diffstep, minlbfgsstate &state);
/*************************************************************************
This function sets stopping conditions for L-BFGS optimization algorithm.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsG - >=0
The subroutine finishes its work if the condition
|v|<EpsG is satisfied, where:
* |.| means Euclidian norm
* v - scaled gradient vector, v[i]=g[i]*s[i]
* g - gradient
* s - scaling coefficients set by MinLBFGSSetScale()
EpsF - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |F(k+1)-F(k)|<=EpsF*max{|F(k)|,|F(k+1)|,1}
is satisfied.
EpsX - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |v|<=EpsX is fulfilled, where:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - ste pvector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinLBFGSSetScale()
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited.
Passing EpsG=0, EpsF=0, EpsX=0 and MaxIts=0 (simultaneously) will lead to
automatic stopping criterion selection (small EpsX).
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetcond(const minlbfgsstate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxits);
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
If NeedXRep is True, algorithm will call rep() callback function if it is
provided to MinLBFGSOptimize().
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetxrep(const minlbfgsstate &state, const bool needxrep);
/*************************************************************************
This function sets maximum step length
INPUT PARAMETERS:
State - structure which stores algorithm state
StpMax - maximum step length, >=0. Set StpMax to 0.0 (default), if
you don't want to limit step length.
Use this subroutine when you optimize target function which contains exp()
or other fast growing functions, and optimization algorithm makes too
large steps which leads to overflow. This function allows us to reject
steps that are too large (and therefore expose us to the possible
overflow) without actually calculating function value at the x+stp*d.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetstpmax(const minlbfgsstate &state, const double stpmax);
/*************************************************************************
This function sets scaling coefficients for LBFGS optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Scaling is also used by finite difference variant of the optimizer - step
along I-th axis is equal to DiffStep*S[I].
In most optimizers (and in the LBFGS too) scaling is NOT a form of
preconditioning. It just affects stopping conditions. You should set
preconditioner by separate call to one of the MinLBFGSSetPrec...()
functions.
There is special preconditioning mode, however, which uses scaling
coefficients to form diagonal preconditioning matrix. You can turn this
mode on, if you want. But you should understand that scaling is not the
same thing as preconditioning - these are two different, although related
forms of tuning solver.
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetscale(const minlbfgsstate &state, const real_1d_array &s);
/*************************************************************************
Modification of the preconditioner: default preconditioner (simple
scaling, same for all elements of X) is used.
INPUT PARAMETERS:
State - structure which stores algorithm state
NOTE: you can change preconditioner "on the fly", during algorithm
iterations.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetprecdefault(const minlbfgsstate &state);
/*************************************************************************
Modification of the preconditioner: Cholesky factorization of approximate
Hessian is used.
INPUT PARAMETERS:
State - structure which stores algorithm state
P - triangular preconditioner, Cholesky factorization of
the approximate Hessian. array[0..N-1,0..N-1],
(if larger, only leading N elements are used).
IsUpper - whether upper or lower triangle of P is given
(other triangle is not referenced)
After call to this function preconditioner is changed to P (P is copied
into the internal buffer).
NOTE: you can change preconditioner "on the fly", during algorithm
iterations.
NOTE 2: P should be nonsingular. Exception will be thrown otherwise.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetpreccholesky(const minlbfgsstate &state, const real_2d_array &p, const bool isupper);
/*************************************************************************
Modification of the preconditioner: diagonal of approximate Hessian is
used.
INPUT PARAMETERS:
State - structure which stores algorithm state
D - diagonal of the approximate Hessian, array[0..N-1],
(if larger, only leading N elements are used).
NOTE: you can change preconditioner "on the fly", during algorithm
iterations.
NOTE 2: D[i] should be positive. Exception will be thrown otherwise.
NOTE 3: you should pass diagonal of approximate Hessian - NOT ITS INVERSE.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetprecdiag(const minlbfgsstate &state, const real_1d_array &d);
/*************************************************************************
Modification of the preconditioner: scale-based diagonal preconditioning.
This preconditioning mode can be useful when you don't have approximate
diagonal of Hessian, but you know that your variables are badly scaled
(for example, one variable is in [1,10], and another in [1000,100000]),
and most part of the ill-conditioning comes from different scales of vars.
In this case simple scale-based preconditioner, with H[i] = 1/(s[i]^2),
can greatly improve convergence.
IMPRTANT: you should set scale of your variables with MinLBFGSSetScale()
call (before or after MinLBFGSSetPrecScale() call). Without knowledge of
the scale of your variables scale-based preconditioner will be just unit
matrix.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetprecscale(const minlbfgsstate &state);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool minlbfgsiteration(const minlbfgsstate &state);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
func - callback which calculates function (or merit function)
value func at given point x
grad - callback which calculates function (or merit function)
value func and gradient grad at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
NOTES:
1. This function has two different implementations: one which uses exact
(analytical) user-supplied gradient, and one which uses function value
only and numerically differentiates function in order to obtain
gradient.
Depending on the specific function used to create optimizer object
(either MinLBFGSCreate() for analytical gradient or MinLBFGSCreateF()
for numerical differentiation) you should choose appropriate variant of
MinLBFGSOptimize() - one which accepts function AND gradient or one
which accepts function ONLY.
Be careful to choose variant of MinLBFGSOptimize() which corresponds to
your optimization scheme! Table below lists different combinations of
callback (function/gradient) passed to MinLBFGSOptimize() and specific
function used to create optimizer.
| USER PASSED TO MinLBFGSOptimize()
CREATED WITH | function only | function and gradient
------------------------------------------------------------
MinLBFGSCreateF() | work FAIL
MinLBFGSCreate() | FAIL work
Here "FAIL" denotes inappropriate combinations of optimizer creation
function and MinLBFGSOptimize() version. Attemps to use such
combination (for example, to create optimizer with MinLBFGSCreateF() and
to pass gradient information to MinCGOptimize()) will lead to exception
being thrown. Either you did not pass gradient when it WAS needed or
you passed gradient when it was NOT needed.
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlbfgsoptimize(minlbfgsstate &state,
void (*func)(const real_1d_array &x, double &func, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
void minlbfgsoptimize(minlbfgsstate &state,
void (*grad)(const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
/*************************************************************************
L-BFGS algorithm results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report:
* Rep.TerminationType completetion code:
* -8 internal integrity control detected infinite
or NAN values in function/gradient. Abnormal
termination signalled.
* -7 gradient verification failed.
See MinLBFGSSetGradientCheck() for more information.
* -2 rounding errors prevent further improvement.
X contains best point found.
* -1 incorrect parameters were specified
* 1 relative function improvement is no more than
EpsF.
* 2 relative step is no more than EpsX.
* 4 gradient norm is no more than EpsG
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible
* 8 terminated by user who called minlbfgsrequesttermination().
X contains point which was "current accepted" when
termination request was submitted.
* Rep.IterationsCount contains iterations count
* NFEV countains number of function calculations
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgsresults(const minlbfgsstate &state, real_1d_array &x, minlbfgsreport &rep);
/*************************************************************************
L-BFGS algorithm results
Buffered implementation of MinLBFGSResults which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 20.08.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgsresultsbuf(const minlbfgsstate &state, real_1d_array &x, minlbfgsreport &rep);
/*************************************************************************
This subroutine restarts LBFGS algorithm from new point. All optimization
parameters are left unchanged.
This function allows to solve multiple optimization problems (which
must have same number of dimensions) without object reallocation penalty.
INPUT PARAMETERS:
State - structure used to store algorithm state
X - new starting point.
-- ALGLIB --
Copyright 30.07.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgsrestartfrom(const minlbfgsstate &state, const real_1d_array &x);
/*************************************************************************
This subroutine submits request for termination of running optimizer. It
should be called from user-supplied callback when user decides that it is
time to "smoothly" terminate optimization process. As result, optimizer
stops at point which was "current accepted" when termination request was
submitted and returns error code 8 (successful termination).
INPUT PARAMETERS:
State - optimizer structure
NOTE: after request for termination optimizer may perform several
additional calls to user-supplied callbacks. It does NOT guarantee
to stop immediately - it just guarantees that these additional calls
will be discarded later.
NOTE: calling this function on optimizer which is NOT running will have no
effect.
NOTE: multiple calls to this function are possible. First call is counted,
subsequent calls are silently ignored.
-- ALGLIB --
Copyright 08.10.2014 by Bochkanov Sergey
*************************************************************************/
void minlbfgsrequesttermination(const minlbfgsstate &state);
/*************************************************************************
This subroutine turns on verification of the user-supplied analytic
gradient:
* user calls this subroutine before optimization begins
* MinLBFGSOptimize() is called
* prior to actual optimization, for each component of parameters being
optimized X[i] algorithm performs following steps:
* two trial steps are made to X[i]-TestStep*S[i] and X[i]+TestStep*S[i],
where X[i] is i-th component of the initial point and S[i] is a scale
of i-th parameter
* if needed, steps are bounded with respect to constraints on X[]
* F(X) is evaluated at these trial points
* we perform one more evaluation in the middle point of the interval
* we build cubic model using function values and derivatives at trial
points and we compare its prediction with actual value in the middle
point
* in case difference between prediction and actual value is higher than
some predetermined threshold, algorithm stops with completion code -7;
Rep.VarIdx is set to index of the parameter with incorrect derivative.
* after verification is over, algorithm proceeds to the actual optimization.
NOTE 1: verification needs N (parameters count) gradient evaluations. It
is very costly and you should use it only for low dimensional
problems, when you want to be sure that you've correctly
calculated analytic derivatives. You should not use it in the
production code (unless you want to check derivatives provided by
some third party).
NOTE 2: you should carefully choose TestStep. Value which is too large
(so large that function behaviour is significantly non-cubic) will
lead to false alarms. You may use different step for different
parameters by means of setting scale with MinLBFGSSetScale().
NOTE 3: this function may lead to false positives. In case it reports that
I-th derivative was calculated incorrectly, you may decrease test
step and try one more time - maybe your function changes too
sharply and your step is too large for such rapidly chanding
function.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step:
* TestStep=0 turns verification off
* TestStep>0 activates verification
-- ALGLIB --
Copyright 24.05.2012 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetgradientcheck(const minlbfgsstate &state, const double teststep);
/*************************************************************************
CONSTRAINED QUADRATIC PROGRAMMING
The subroutine creates QP optimizer. After initial creation, it contains
default optimization problem with zero quadratic and linear terms and no
constraints. You should set quadratic/linear terms with calls to functions
provided by MinQP subpackage.
You should also choose appropriate QP solver and set it and its stopping
criteria by means of MinQPSetAlgo??????() function. Then, you should start
solution process by means of MinQPOptimize() call. Solution itself can be
obtained with MinQPResults() function.
INPUT PARAMETERS:
N - problem size
OUTPUT PARAMETERS:
State - optimizer with zero quadratic/linear terms
and no constraints
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpcreate(const ae_int_t n, minqpstate &state);
/*************************************************************************
This function sets linear term for QP solver.
By default, linear term is zero.
INPUT PARAMETERS:
State - structure which stores algorithm state
B - linear term, array[N].
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetlinearterm(const minqpstate &state, const real_1d_array &b);
/*************************************************************************
This function sets dense quadratic term for QP solver. By default,
quadratic term is zero.
SUPPORT BY ALGLIB QP ALGORITHMS:
Dense quadratic term can be handled by any of the QP algorithms supported
by ALGLIB QP Solver.
IMPORTANT:
This solver minimizes following function:
f(x) = 0.5*x'*A*x + b'*x.
Note that quadratic term has 0.5 before it. So if you want to minimize
f(x) = x^2 + x
you should rewrite your problem as follows:
f(x) = 0.5*(2*x^2) + x
and your matrix A will be equal to [[2.0]], not to [[1.0]]
INPUT PARAMETERS:
State - structure which stores algorithm state
A - matrix, array[N,N]
IsUpper - (optional) storage type:
* if True, symmetric matrix A is given by its upper
triangle, and the lower triangle isn�t used
* if False, symmetric matrix A is given by its lower
triangle, and the upper triangle isn�t used
* if not given, both lower and upper triangles must be
filled.
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetquadraticterm(const minqpstate &state, const real_2d_array &a, const bool isupper);
void minqpsetquadraticterm(const minqpstate &state, const real_2d_array &a);
/*************************************************************************
This function sets sparse quadratic term for QP solver. By default,
quadratic term is zero.
IMPORTANT:
This solver minimizes following function:
f(x) = 0.5*x'*A*x + b'*x.
Note that quadratic term has 0.5 before it. So if you want to minimize
f(x) = x^2 + x
you should rewrite your problem as follows:
f(x) = 0.5*(2*x^2) + x
and your matrix A will be equal to [[2.0]], not to [[1.0]]
INPUT PARAMETERS:
State - structure which stores algorithm state
A - matrix, array[N,N]
IsUpper - (optional) storage type:
* if True, symmetric matrix A is given by its upper
triangle, and the lower triangle isn�t used
* if False, symmetric matrix A is given by its lower
triangle, and the upper triangle isn�t used
* if not given, both lower and upper triangles must be
filled.
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetquadratictermsparse(const minqpstate &state, const sparsematrix &a, const bool isupper);
/*************************************************************************
This function sets starting point for QP solver. It is useful to have
good initial approximation to the solution, because it will increase
speed of convergence and identification of active constraints.
INPUT PARAMETERS:
State - structure which stores algorithm state
X - starting point, array[N].
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetstartingpoint(const minqpstate &state, const real_1d_array &x);
/*************************************************************************
This function sets origin for QP solver. By default, following QP program
is solved:
min(0.5*x'*A*x+b'*x)
This function allows to solve different problem:
min(0.5*(x-x_origin)'*A*(x-x_origin)+b'*(x-x_origin))
INPUT PARAMETERS:
State - structure which stores algorithm state
XOrigin - origin, array[N].
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetorigin(const minqpstate &state, const real_1d_array &xorigin);
/*************************************************************************
This function sets scaling coefficients.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
BLEIC-based QP solver uses scale for two purposes:
* to evaluate stopping conditions
* for preconditioning of the underlying BLEIC solver
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetscale(const minqpstate &state, const real_1d_array &s);
/*************************************************************************
This function tells solver to use Cholesky-based algorithm. This algorithm
was deprecated in ALGLIB 3.9.0 because its performance is inferior to that
of BLEIC-QP or QuickQP on high-dimensional problems. Furthermore, it
supports only dense convex QP problems.
This solver is no longer active by default.
We recommend you to switch to BLEIC-QP or QuickQP solver.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetalgocholesky(const minqpstate &state);
/*************************************************************************
This function tells solver to use BLEIC-based algorithm and sets stopping
criteria for the algorithm.
ALGORITHM FEATURES:
* supports dense and sparse QP problems
* supports boundary and general linear equality/inequality constraints
* can solve all types of problems (convex, semidefinite, nonconvex) as
long as they are bounded from below under constraints.
Say, it is possible to solve "min{-x^2} subject to -1<=x<=+1".
Of course, global minimum is found only for positive definite and
semidefinite problems. As for indefinite ones - only local minimum is
found.
ALGORITHM OUTLINE:
* BLEIC-QP solver is just a driver function for MinBLEIC solver; it solves
quadratic programming problem as general linearly constrained
optimization problem, which is solved by means of BLEIC solver (part of
ALGLIB, active set method).
ALGORITHM LIMITATIONS:
* unlike QuickQP solver, this algorithm does not perform Newton steps and
does not use Level 3 BLAS. Being general-purpose active set method, it
can activate constraints only one-by-one. Thus, its performance is lower
than that of QuickQP.
* its precision is also a bit inferior to that of QuickQP. BLEIC-QP
performs only LBFGS steps (no Newton steps), which are good at detecting
neighborhood of the solution, buy need many iterations to find solution
with more than 6 digits of precision.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsG - >=0
The subroutine finishes its work if the condition
|v|<EpsG is satisfied, where:
* |.| means Euclidian norm
* v - scaled constrained gradient vector, v[i]=g[i]*s[i]
* g - gradient
* s - scaling coefficients set by MinQPSetScale()
EpsF - >=0
The subroutine finishes its work if exploratory steepest
descent step on k+1-th iteration satisfies following
condition: |F(k+1)-F(k)|<=EpsF*max{|F(k)|,|F(k+1)|,1}
EpsX - >=0
The subroutine finishes its work if exploratory steepest
descent step on k+1-th iteration satisfies following
condition:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - step vector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinQPSetScale()
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited. NOTE: this algorithm uses LBFGS
iterations, which are relatively cheap, but improve
function value only a bit. So you will need many iterations
to converge - from 0.1*N to 10*N, depending on problem's
condition number.
IT IS VERY IMPORTANT TO CALL MinQPSetScale() WHEN YOU USE THIS ALGORITHM
BECAUSE ITS STOPPING CRITERIA ARE SCALE-DEPENDENT!
Passing EpsG=0, EpsF=0 and EpsX=0 and MaxIts=0 (simultaneously) will lead
to automatic stopping criterion selection (presently it is small step
length, but it may change in the future versions of ALGLIB).
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetalgobleic(const minqpstate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxits);
/*************************************************************************
This function tells solver to use QuickQP algorithm: special extra-fast
algorithm for problems with boundary-only constrants. It may solve
non-convex problems as long as they are bounded from below under
constraints.
ALGORITHM FEATURES:
* many times (from 5x to 50x!) faster than BLEIC-based QP solver; utilizes
accelerated methods for activation of constraints.
* supports dense and sparse QP problems
* supports ONLY boundary constraints; general linear constraints are NOT
supported by this solver
* can solve all types of problems (convex, semidefinite, nonconvex) as
long as they are bounded from below under constraints.
Say, it is possible to solve "min{-x^2} subject to -1<=x<=+1".
In convex/semidefinite case global minimum is returned, in nonconvex
case - algorithm returns one of the local minimums.
ALGORITHM OUTLINE:
* algorithm performs two kinds of iterations: constrained CG iterations
and constrained Newton iterations
* initially it performs small number of constrained CG iterations, which
can efficiently activate/deactivate multiple constraints
* after CG phase algorithm tries to calculate Cholesky decomposition and
to perform several constrained Newton steps. If Cholesky decomposition
failed (matrix is indefinite even under constraints), we perform more
CG iterations until we converge to such set of constraints that system
matrix becomes positive definite. Constrained Newton steps greatly
increase convergence speed and precision.
* algorithm interleaves CG and Newton iterations which allows to handle
indefinite matrices (CG phase) and quickly converge after final set of
constraints is found (Newton phase). Combination of CG and Newton phases
is called "outer iteration".
* it is possible to turn off Newton phase (beneficial for semidefinite
problems - Cholesky decomposition will fail too often)
ALGORITHM LIMITATIONS:
* algorithm does not support general linear constraints; only boundary
ones are supported
* Cholesky decomposition for sparse problems is performed with Skyline
Cholesky solver, which is intended for low-profile matrices. No profile-
reducing reordering of variables is performed in this version of ALGLIB.
* problems with near-zero negative eigenvalues (or exacty zero ones) may
experience about 2-3x performance penalty. The reason is that Cholesky
decomposition can not be performed until we identify directions of zero
and negative curvature and activate corresponding boundary constraints -
but we need a lot of trial and errors because these directions are hard
to notice in the matrix spectrum.
In this case you may turn off Newton phase of algorithm.
Large negative eigenvalues are not an issue, so highly non-convex
problems can be solved very efficiently.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsG - >=0
The subroutine finishes its work if the condition
|v|<EpsG is satisfied, where:
* |.| means Euclidian norm
* v - scaled constrained gradient vector, v[i]=g[i]*s[i]
* g - gradient
* s - scaling coefficients set by MinQPSetScale()
EpsF - >=0
The subroutine finishes its work if exploratory steepest
descent step on k+1-th iteration satisfies following
condition: |F(k+1)-F(k)|<=EpsF*max{|F(k)|,|F(k+1)|,1}
EpsX - >=0
The subroutine finishes its work if exploratory steepest
descent step on k+1-th iteration satisfies following
condition:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - step vector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinQPSetScale()
MaxOuterIts-maximum number of OUTER iterations. One outer iteration
includes some amount of CG iterations (from 5 to ~N) and
one or several (usually small amount) Newton steps. Thus,
one outer iteration has high cost, but can greatly reduce
funcation value.
UseNewton- use Newton phase or not:
* Newton phase improves performance of positive definite
dense problems (about 2 times improvement can be observed)
* can result in some performance penalty on semidefinite
or slightly negative definite problems - each Newton
phase will bring no improvement (Cholesky failure), but
still will require computational time.
* if you doubt, you can turn off this phase - optimizer
will retain its most of its high speed.
IT IS VERY IMPORTANT TO CALL MinQPSetScale() WHEN YOU USE THIS ALGORITHM
BECAUSE ITS STOPPING CRITERIA ARE SCALE-DEPENDENT!
Passing EpsG=0, EpsF=0 and EpsX=0 and MaxIts=0 (simultaneously) will lead
to automatic stopping criterion selection (presently it is small step
length, but it may change in the future versions of ALGLIB).
-- ALGLIB --
Copyright 22.05.2014 by Bochkanov Sergey
*************************************************************************/
void minqpsetalgoquickqp(const minqpstate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxouterits, const bool usenewton);
/*************************************************************************
This function sets boundary constraints for QP solver
Boundary constraints are inactive by default (after initial creation).
After being set, they are preserved until explicitly turned off with
another SetBC() call.
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bounds, array[N].
If some (all) variables are unbounded, you may specify
very small number or -INF (latter is recommended because
it will allow solver to use better algorithm).
BndU - upper bounds, array[N].
If some (all) variables are unbounded, you may specify
very large number or +INF (latter is recommended because
it will allow solver to use better algorithm).
NOTE: it is possible to specify BndL[i]=BndU[i]. In this case I-th
variable will be "frozen" at X[i]=BndL[i]=BndU[i].
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetbc(const minqpstate &state, const real_1d_array &bndl, const real_1d_array &bndu);
/*************************************************************************
This function sets linear constraints for QP optimizer.
Linear constraints are inactive by default (after initial creation).
INPUT PARAMETERS:
State - structure previously allocated with MinQPCreate call.
C - linear constraints, array[K,N+1].
Each row of C represents one constraint, either equality
or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of C (including right part) must be finite.
CT - type of constraints, array[K]:
* if CT[i]>0, then I-th constraint is C[i,*]*x >= C[i,n+1]
* if CT[i]=0, then I-th constraint is C[i,*]*x = C[i,n+1]
* if CT[i]<0, then I-th constraint is C[i,*]*x <= C[i,n+1]
K - number of equality/inequality constraints, K>=0:
* if given, only leading K elements of C/CT are used
* if not given, automatically determined from sizes of C/CT
NOTE 1: linear (non-bound) constraints are satisfied only approximately -
there always exists some minor violation (about 10^-10...10^-13)
due to numerical errors.
-- ALGLIB --
Copyright 19.06.2012 by Bochkanov Sergey
*************************************************************************/
void minqpsetlc(const minqpstate &state, const real_2d_array &c, const integer_1d_array &ct, const ae_int_t k);
void minqpsetlc(const minqpstate &state, const real_2d_array &c, const integer_1d_array &ct);
/*************************************************************************
This function solves quadratic programming problem.
Prior to calling this function you should choose solver by means of one of
the following functions:
* MinQPSetAlgoQuickQP() - for QuickQP solver
* MinQPSetAlgoBLEIC() - for BLEIC-QP solver
These functions also allow you to control stopping criteria of the solver.
If you did not set solver, MinQP subpackage will automatically select
solver for your problem and will run it with default stopping criteria.
However, it is better to set explicitly solver and its stopping criteria.
INPUT PARAMETERS:
State - algorithm state
You should use MinQPResults() function to access results after calls
to this function.
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey.
Special thanks to Elvira Illarionova for important suggestions on
the linearly constrained QP algorithm.
*************************************************************************/
void minqpoptimize(const minqpstate &state);
/*************************************************************************
QP solver results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution.
This array is allocated and initialized only when
Rep.TerminationType parameter is positive (success).
Rep - optimization report. You should check Rep.TerminationType,
which contains completion code, and you may check another
fields which contain another information about algorithm
functioning.
Failure codes returned by algorithm are:
* -5 inappropriate solver was used:
* Cholesky solver for (semi)indefinite problems
* Cholesky solver for problems with sparse matrix
* QuickQP solver for problem with general linear
constraints
* -4 BLEIC-QP/QuickQP solver found unconstrained
direction of negative curvature (function is
unbounded from below even under constraints), no
meaningful minimum can be found.
* -3 inconsistent constraints (or maybe feasible point
is too hard to find). If you are sure that
constraints are feasible, try to restart optimizer
with better initial approximation.
Completion codes specific for Cholesky algorithm:
* 4 successful completion
Completion codes specific for BLEIC/QuickQP algorithms:
* 1 relative function improvement is no more than EpsF.
* 2 scaled step is no more than EpsX.
* 4 scaled gradient norm is no more than EpsG.
* 5 MaxIts steps was taken
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpresults(const minqpstate &state, real_1d_array &x, minqpreport &rep);
/*************************************************************************
QP results
Buffered implementation of MinQPResults() which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpresultsbuf(const minqpstate &state, real_1d_array &x, minqpreport &rep);
/*************************************************************************
IMPROVED LEVENBERG-MARQUARDT METHOD FOR
NON-LINEAR LEAST SQUARES OPTIMIZATION
DESCRIPTION:
This function is used to find minimum of function which is represented as
sum of squares:
F(x) = f[0]^2(x[0],...,x[n-1]) + ... + f[m-1]^2(x[0],...,x[n-1])
using value of function vector f[] and Jacobian of f[].
REQUIREMENTS:
This algorithm will request following information during its operation:
* function vector f[] at given point X
* function vector f[] and Jacobian of f[] (simultaneously) at given point
There are several overloaded versions of MinLMOptimize() function which
correspond to different LM-like optimization algorithms provided by this
unit. You should choose version which accepts fvec() and jac() callbacks.
First one is used to calculate f[] at given point, second one calculates
f[] and Jacobian df[i]/dx[j].
You can try to initialize MinLMState structure with VJ function and then
use incorrect version of MinLMOptimize() (for example, version which
works with general form function and does not provide Jacobian), but it
will lead to exception being thrown after first attempt to calculate
Jacobian.
USAGE:
1. User initializes algorithm state with MinLMCreateVJ() call
2. User tunes solver parameters with MinLMSetCond(), MinLMSetStpMax() and
other functions
3. User calls MinLMOptimize() function which takes algorithm state and
callback functions.
4. User calls MinLMResults() to get solution
5. Optionally, user may call MinLMRestartFrom() to solve another problem
with same N/M but another starting point and/or another function.
MinLMRestartFrom() allows to reuse already initialized structure.
INPUT PARAMETERS:
N - dimension, N>1
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
M - number of functions f[i]
X - initial solution, array[0..N-1]
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
1. you may tune stopping conditions with MinLMSetCond() function
2. if target function contains exp() or other fast growing functions, and
optimization algorithm makes too large steps which leads to overflow,
use MinLMSetStpMax() function to bound algorithm's steps.
-- ALGLIB --
Copyright 30.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmcreatevj(const ae_int_t n, const ae_int_t m, const real_1d_array &x, minlmstate &state);
void minlmcreatevj(const ae_int_t m, const real_1d_array &x, minlmstate &state);
/*************************************************************************
IMPROVED LEVENBERG-MARQUARDT METHOD FOR
NON-LINEAR LEAST SQUARES OPTIMIZATION
DESCRIPTION:
This function is used to find minimum of function which is represented as
sum of squares:
F(x) = f[0]^2(x[0],...,x[n-1]) + ... + f[m-1]^2(x[0],...,x[n-1])
using value of function vector f[] only. Finite differences are used to
calculate Jacobian.
REQUIREMENTS:
This algorithm will request following information during its operation:
* function vector f[] at given point X
There are several overloaded versions of MinLMOptimize() function which
correspond to different LM-like optimization algorithms provided by this
unit. You should choose version which accepts fvec() callback.
You can try to initialize MinLMState structure with VJ function and then
use incorrect version of MinLMOptimize() (for example, version which
works with general form function and does not accept function vector), but
it will lead to exception being thrown after first attempt to calculate
Jacobian.
USAGE:
1. User initializes algorithm state with MinLMCreateV() call
2. User tunes solver parameters with MinLMSetCond(), MinLMSetStpMax() and
other functions
3. User calls MinLMOptimize() function which takes algorithm state and
callback functions.
4. User calls MinLMResults() to get solution
5. Optionally, user may call MinLMRestartFrom() to solve another problem
with same N/M but another starting point and/or another function.
MinLMRestartFrom() allows to reuse already initialized structure.
INPUT PARAMETERS:
N - dimension, N>1
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
M - number of functions f[i]
X - initial solution, array[0..N-1]
DiffStep- differentiation step, >0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
See also MinLMIteration, MinLMResults.
NOTES:
1. you may tune stopping conditions with MinLMSetCond() function
2. if target function contains exp() or other fast growing functions, and
optimization algorithm makes too large steps which leads to overflow,
use MinLMSetStpMax() function to bound algorithm's steps.
-- ALGLIB --
Copyright 30.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmcreatev(const ae_int_t n, const ae_int_t m, const real_1d_array &x, const double diffstep, minlmstate &state);
void minlmcreatev(const ae_int_t m, const real_1d_array &x, const double diffstep, minlmstate &state);
/*************************************************************************
LEVENBERG-MARQUARDT-LIKE METHOD FOR NON-LINEAR OPTIMIZATION
DESCRIPTION:
This function is used to find minimum of general form (not "sum-of-
-squares") function
F = F(x[0], ..., x[n-1])
using its gradient and Hessian. Levenberg-Marquardt modification with
L-BFGS pre-optimization and internal pre-conditioned L-BFGS optimization
after each Levenberg-Marquardt step is used.
REQUIREMENTS:
This algorithm will request following information during its operation:
* function value F at given point X
* F and gradient G (simultaneously) at given point X
* F, G and Hessian H (simultaneously) at given point X
There are several overloaded versions of MinLMOptimize() function which
correspond to different LM-like optimization algorithms provided by this
unit. You should choose version which accepts func(), grad() and hess()
function pointers. First pointer is used to calculate F at given point,
second one calculates F(x) and grad F(x), third one calculates F(x),
grad F(x), hess F(x).
You can try to initialize MinLMState structure with FGH-function and then
use incorrect version of MinLMOptimize() (for example, version which does
not provide Hessian matrix), but it will lead to exception being thrown
after first attempt to calculate Hessian.
USAGE:
1. User initializes algorithm state with MinLMCreateFGH() call
2. User tunes solver parameters with MinLMSetCond(), MinLMSetStpMax() and
other functions
3. User calls MinLMOptimize() function which takes algorithm state and
pointers (delegates, etc.) to callback functions.
4. User calls MinLMResults() to get solution
5. Optionally, user may call MinLMRestartFrom() to solve another problem
with same N but another starting point and/or another function.
MinLMRestartFrom() allows to reuse already initialized structure.
INPUT PARAMETERS:
N - dimension, N>1
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
X - initial solution, array[0..N-1]
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
1. you may tune stopping conditions with MinLMSetCond() function
2. if target function contains exp() or other fast growing functions, and
optimization algorithm makes too large steps which leads to overflow,
use MinLMSetStpMax() function to bound algorithm's steps.
-- ALGLIB --
Copyright 30.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmcreatefgh(const ae_int_t n, const real_1d_array &x, minlmstate &state);
void minlmcreatefgh(const real_1d_array &x, minlmstate &state);
/*************************************************************************
This function sets stopping conditions for Levenberg-Marquardt optimization
algorithm.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsG - >=0
The subroutine finishes its work if the condition
|v|<EpsG is satisfied, where:
* |.| means Euclidian norm
* v - scaled gradient vector, v[i]=g[i]*s[i]
* g - gradient
* s - scaling coefficients set by MinLMSetScale()
EpsF - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |F(k+1)-F(k)|<=EpsF*max{|F(k)|,|F(k+1)|,1}
is satisfied.
EpsX - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |v|<=EpsX is fulfilled, where:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - ste pvector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinLMSetScale()
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited. Only Levenberg-Marquardt
iterations are counted (L-BFGS/CG iterations are NOT
counted because their cost is very low compared to that of
LM).
Passing EpsG=0, EpsF=0, EpsX=0 and MaxIts=0 (simultaneously) will lead to
automatic stopping criterion selection (small EpsX).
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlmsetcond(const minlmstate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxits);
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
If NeedXRep is True, algorithm will call rep() callback function if it is
provided to MinLMOptimize(). Both Levenberg-Marquardt and internal L-BFGS
iterations are reported.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlmsetxrep(const minlmstate &state, const bool needxrep);
/*************************************************************************
This function sets maximum step length
INPUT PARAMETERS:
State - structure which stores algorithm state
StpMax - maximum step length, >=0. Set StpMax to 0.0, if you don't
want to limit step length.
Use this subroutine when you optimize target function which contains exp()
or other fast growing functions, and optimization algorithm makes too
large steps which leads to overflow. This function allows us to reject
steps that are too large (and therefore expose us to the possible
overflow) without actually calculating function value at the x+stp*d.
NOTE: non-zero StpMax leads to moderate performance degradation because
intermediate step of preconditioned L-BFGS optimization is incompatible
with limits on step size.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlmsetstpmax(const minlmstate &state, const double stpmax);
/*************************************************************************
This function sets scaling coefficients for LM optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Generally, scale is NOT considered to be a form of preconditioner. But LM
optimizer is unique in that it uses scaling matrix both in the stopping
condition tests and as Marquardt damping factor.
Proper scaling is very important for the algorithm performance. It is less
important for the quality of results, but still has some influence (it is
easier to converge when variables are properly scaled, so premature
stopping is possible when very badly scalled variables are combined with
relaxed stopping conditions).
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void minlmsetscale(const minlmstate &state, const real_1d_array &s);
/*************************************************************************
This function sets boundary constraints for LM optimizer
Boundary constraints are inactive by default (after initial creation).
They are preserved until explicitly turned off with another SetBC() call.
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bounds, array[N].
If some (all) variables are unbounded, you may specify
very small number or -INF (latter is recommended because
it will allow solver to use better algorithm).
BndU - upper bounds, array[N].
If some (all) variables are unbounded, you may specify
very large number or +INF (latter is recommended because
it will allow solver to use better algorithm).
NOTE 1: it is possible to specify BndL[i]=BndU[i]. In this case I-th
variable will be "frozen" at X[i]=BndL[i]=BndU[i].
NOTE 2: this solver has following useful properties:
* bound constraints are always satisfied exactly
* function is evaluated only INSIDE area specified by bound constraints
or at its boundary
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void minlmsetbc(const minlmstate &state, const real_1d_array &bndl, const real_1d_array &bndu);
/*************************************************************************
This function is used to change acceleration settings
You can choose between three acceleration strategies:
* AccType=0, no acceleration.
* AccType=1, secant updates are used to update quadratic model after each
iteration. After fixed number of iterations (or after model breakdown)
we recalculate quadratic model using analytic Jacobian or finite
differences. Number of secant-based iterations depends on optimization
settings: about 3 iterations - when we have analytic Jacobian, up to 2*N
iterations - when we use finite differences to calculate Jacobian.
AccType=1 is recommended when Jacobian calculation cost is prohibitive
high (several Mx1 function vector calculations followed by several NxN
Cholesky factorizations are faster than calculation of one M*N Jacobian).
It should also be used when we have no Jacobian, because finite difference
approximation takes too much time to compute.
Table below list optimization protocols (XYZ protocol corresponds to
MinLMCreateXYZ) and acceleration types they support (and use by default).
ACCELERATION TYPES SUPPORTED BY OPTIMIZATION PROTOCOLS:
protocol 0 1 comment
V + +
VJ + +
FGH +
DAFAULT VALUES:
protocol 0 1 comment
V x without acceleration it is so slooooooooow
VJ x
FGH x
NOTE: this function should be called before optimization. Attempt to call
it during algorithm iterations may result in unexpected behavior.
NOTE: attempt to call this function with unsupported protocol/acceleration
combination will result in exception being thrown.
-- ALGLIB --
Copyright 14.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlmsetacctype(const minlmstate &state, const ae_int_t acctype);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool minlmiteration(const minlmstate &state);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
func - callback which calculates function (or merit function)
value func at given point x
grad - callback which calculates function (or merit function)
value func and gradient grad at given point x
hess - callback which calculates function (or merit function)
value func, gradient grad and Hessian hess at given point x
fvec - callback which calculates function vector fi[]
at given point x
jac - callback which calculates function vector fi[]
and Jacobian jac at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
NOTES:
1. Depending on function used to create state structure, this algorithm
may accept Jacobian and/or Hessian and/or gradient. According to the
said above, there ase several versions of this function, which accept
different sets of callbacks.
This flexibility opens way to subtle errors - you may create state with
MinLMCreateFGH() (optimization using Hessian), but call function which
does not accept Hessian. So when algorithm will request Hessian, there
will be no callback to call. In this case exception will be thrown.
Be careful to avoid such errors because there is no way to find them at
compile time - you can see them at runtime only.
-- ALGLIB --
Copyright 10.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmoptimize(minlmstate &state,
void (*fvec)(const real_1d_array &x, real_1d_array &fi, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
void minlmoptimize(minlmstate &state,
void (*fvec)(const real_1d_array &x, real_1d_array &fi, void *ptr),
void (*jac)(const real_1d_array &x, real_1d_array &fi, real_2d_array &jac, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
void minlmoptimize(minlmstate &state,
void (*func)(const real_1d_array &x, double &func, void *ptr),
void (*grad)(const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*hess)(const real_1d_array &x, double &func, real_1d_array &grad, real_2d_array &hess, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
void minlmoptimize(minlmstate &state,
void (*func)(const real_1d_array &x, double &func, void *ptr),
void (*jac)(const real_1d_array &x, real_1d_array &fi, real_2d_array &jac, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
void minlmoptimize(minlmstate &state,
void (*func)(const real_1d_array &x, double &func, void *ptr),
void (*grad)(const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*jac)(const real_1d_array &x, real_1d_array &fi, real_2d_array &jac, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
/*************************************************************************
Levenberg-Marquardt algorithm results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report; includes termination codes and
additional information. Termination codes are listed below,
see comments for this structure for more info.
Termination code is stored in rep.terminationtype field:
* -7 derivative correctness check failed;
see rep.funcidx, rep.varidx for
more information.
* -3 constraints are inconsistent
* 1 relative function improvement is no more than
EpsF.
* 2 relative step is no more than EpsX.
* 4 gradient is no more than EpsG.
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible
* 8 terminated by user who called minlmrequesttermination().
X contains point which was "current accepted" when
termination request was submitted.
-- ALGLIB --
Copyright 10.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmresults(const minlmstate &state, real_1d_array &x, minlmreport &rep);
/*************************************************************************
Levenberg-Marquardt algorithm results
Buffered implementation of MinLMResults(), which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 10.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmresultsbuf(const minlmstate &state, real_1d_array &x, minlmreport &rep);
/*************************************************************************
This subroutine restarts LM algorithm from new point. All optimization
parameters are left unchanged.
This function allows to solve multiple optimization problems (which
must have same number of dimensions) without object reallocation penalty.
INPUT PARAMETERS:
State - structure used for reverse communication previously
allocated with MinLMCreateXXX call.
X - new starting point.
-- ALGLIB --
Copyright 30.07.2010 by Bochkanov Sergey
*************************************************************************/
void minlmrestartfrom(const minlmstate &state, const real_1d_array &x);
/*************************************************************************
This subroutine submits request for termination of running optimizer. It
should be called from user-supplied callback when user decides that it is
time to "smoothly" terminate optimization process. As result, optimizer
stops at point which was "current accepted" when termination request was
submitted and returns error code 8 (successful termination).
INPUT PARAMETERS:
State - optimizer structure
NOTE: after request for termination optimizer may perform several
additional calls to user-supplied callbacks. It does NOT guarantee
to stop immediately - it just guarantees that these additional calls
will be discarded later.
NOTE: calling this function on optimizer which is NOT running will have no
effect.
NOTE: multiple calls to this function are possible. First call is counted,
subsequent calls are silently ignored.
-- ALGLIB --
Copyright 08.10.2014 by Bochkanov Sergey
*************************************************************************/
void minlmrequesttermination(const minlmstate &state);
/*************************************************************************
This is obsolete function.
Since ALGLIB 3.3 it is equivalent to MinLMCreateVJ().
-- ALGLIB --
Copyright 30.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmcreatevgj(const ae_int_t n, const ae_int_t m, const real_1d_array &x, minlmstate &state);
void minlmcreatevgj(const ae_int_t m, const real_1d_array &x, minlmstate &state);
/*************************************************************************
This is obsolete function.
Since ALGLIB 3.3 it is equivalent to MinLMCreateFJ().
-- ALGLIB --
Copyright 30.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmcreatefgj(const ae_int_t n, const ae_int_t m, const real_1d_array &x, minlmstate &state);
void minlmcreatefgj(const ae_int_t m, const real_1d_array &x, minlmstate &state);
/*************************************************************************
This function is considered obsolete since ALGLIB 3.1.0 and is present for
backward compatibility only. We recommend to use MinLMCreateVJ, which
provides similar, but more consistent and feature-rich interface.
-- ALGLIB --
Copyright 30.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmcreatefj(const ae_int_t n, const ae_int_t m, const real_1d_array &x, minlmstate &state);
void minlmcreatefj(const ae_int_t m, const real_1d_array &x, minlmstate &state);
/*************************************************************************
This subroutine turns on verification of the user-supplied analytic
gradient:
* user calls this subroutine before optimization begins
* MinLMOptimize() is called
* prior to actual optimization, for each function Fi and each component
of parameters being optimized X[j] algorithm performs following steps:
* two trial steps are made to X[j]-TestStep*S[j] and X[j]+TestStep*S[j],
where X[j] is j-th parameter and S[j] is a scale of j-th parameter
* if needed, steps are bounded with respect to constraints on X[]
* Fi(X) is evaluated at these trial points
* we perform one more evaluation in the middle point of the interval
* we build cubic model using function values and derivatives at trial
points and we compare its prediction with actual value in the middle
point
* in case difference between prediction and actual value is higher than
some predetermined threshold, algorithm stops with completion code -7;
Rep.VarIdx is set to index of the parameter with incorrect derivative,
Rep.FuncIdx is set to index of the function.
* after verification is over, algorithm proceeds to the actual optimization.
NOTE 1: verification needs N (parameters count) Jacobian evaluations. It
is very costly and you should use it only for low dimensional
problems, when you want to be sure that you've correctly
calculated analytic derivatives. You should not use it in the
production code (unless you want to check derivatives provided
by some third party).
NOTE 2: you should carefully choose TestStep. Value which is too large
(so large that function behaviour is significantly non-cubic) will
lead to false alarms. You may use different step for different
parameters by means of setting scale with MinLMSetScale().
NOTE 3: this function may lead to false positives. In case it reports that
I-th derivative was calculated incorrectly, you may decrease test
step and try one more time - maybe your function changes too
sharply and your step is too large for such rapidly chanding
function.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step:
* TestStep=0 turns verification off
* TestStep>0 activates verification
-- ALGLIB --
Copyright 15.06.2012 by Bochkanov Sergey
*************************************************************************/
void minlmsetgradientcheck(const minlmstate &state, const double teststep);
/*************************************************************************
Obsolete function, use MinLBFGSSetPrecDefault() instead.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetdefaultpreconditioner(const minlbfgsstate &state);
/*************************************************************************
Obsolete function, use MinLBFGSSetCholeskyPreconditioner() instead.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetcholeskypreconditioner(const minlbfgsstate &state, const real_2d_array &p, const bool isupper);
/*************************************************************************
This is obsolete function which was used by previous version of the BLEIC
optimizer. It does nothing in the current version of BLEIC.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetbarrierwidth(const minbleicstate &state, const double mu);
/*************************************************************************
This is obsolete function which was used by previous version of the BLEIC
optimizer. It does nothing in the current version of BLEIC.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetbarrierdecay(const minbleicstate &state, const double mudecay);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 25.03.2010 by Bochkanov Sergey
*************************************************************************/
void minasacreate(const ae_int_t n, const real_1d_array &x, const real_1d_array &bndl, const real_1d_array &bndu, minasastate &state);
void minasacreate(const real_1d_array &x, const real_1d_array &bndl, const real_1d_array &bndu, minasastate &state);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minasasetcond(const minasastate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxits);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minasasetxrep(const minasastate &state, const bool needxrep);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minasasetalgorithm(const minasastate &state, const ae_int_t algotype);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minasasetstpmax(const minasastate &state, const double stpmax);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool minasaiteration(const minasastate &state);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
grad - callback which calculates function (or merit function)
value func and gradient grad at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
void minasaoptimize(minasastate &state,
void (*grad)(const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
void minasaresults(const minasastate &state, real_1d_array &x, minasareport &rep);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
void minasaresultsbuf(const minasastate &state, real_1d_array &x, minasareport &rep);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 30.07.2010 by Bochkanov Sergey
*************************************************************************/
void minasarestartfrom(const minasastate &state, const real_1d_array &x, const real_1d_array &bndl, const real_1d_array &bndu);
/*************************************************************************
NONLINEARLY CONSTRAINED OPTIMIZATION
WITH PRECONDITIONED AUGMENTED LAGRANGIAN ALGORITHM
DESCRIPTION:
The subroutine minimizes function F(x) of N arguments subject to any
combination of:
* bound constraints
* linear inequality constraints
* linear equality constraints
* nonlinear equality constraints Gi(x)=0
* nonlinear inequality constraints Hi(x)<=0
REQUIREMENTS:
* user must provide function value and gradient for F(), H(), G()
* starting point X0 must be feasible or not too far away from the feasible
set
* F(), G(), H() are twice continuously differentiable on the feasible set
and its neighborhood
* nonlinear constraints G() and H() must have non-zero gradient at G(x)=0
and at H(x)=0. Say, constraint like x^2>=1 is supported, but x^2>=0 is
NOT supported.
USAGE:
Constrained optimization if far more complex than the unconstrained one.
Nonlinearly constrained optimization is one of the most esoteric numerical
procedures.
Here we give very brief outline of the MinNLC optimizer. We strongly
recommend you to study examples in the ALGLIB Reference Manual and to read
ALGLIB User Guide on optimization, which is available at
http://www.alglib.net/optimization/
1. User initializes algorithm state with MinNLCCreate() call and chooses
what NLC solver to use. There is some solver which is used by default,
with default settings, but you should NOT rely on default choice. It
may change in future releases of ALGLIB without notice, and no one can
guarantee that new solver will be able to solve your problem with
default settings.
From the other side, if you choose solver explicitly, you can be pretty
sure that it will work with new ALGLIB releases.
In the current release following solvers can be used:
* AUL solver (activated with MinNLCSetAlgoAUL() function)
2. User adds boundary and/or linear and/or nonlinear constraints by means
of calling one of the following functions:
a) MinNLCSetBC() for boundary constraints
b) MinNLCSetLC() for linear constraints
c) MinNLCSetNLC() for nonlinear constraints
You may combine (a), (b) and (c) in one optimization problem.
3. User sets scale of the variables with MinNLCSetScale() function. It is
VERY important to set scale of the variables, because nonlinearly
constrained problems are hard to solve when variables are badly scaled.
4. User sets stopping conditions with MinNLCSetCond(). If NLC solver
uses inner/outer iteration layout, this function sets stopping
conditions for INNER iterations.
5. User chooses one of the preconditioning methods. Preconditioning is
very important for efficient handling of boundary/linear/nonlinear
constraints. Without preconditioning algorithm would require thousands
of iterations even for simple problems. Two preconditioners can be
used:
* approximate LBFGS-based preconditioner which should be used for
problems with almost orthogonal constraints (activated by calling
MinNLCSetPrecInexact)
* exact low-rank preconditiner (activated by MinNLCSetPrecExactLowRank)
which should be used for problems with moderate number of constraints
which do not have to be orthogonal.
6. Finally, user calls MinNLCOptimize() function which takes algorithm
state and pointer (delegate, etc.) to callback function which calculates
F/G/H.
7. User calls MinNLCResults() to get solution
8. Optionally user may call MinNLCRestartFrom() to solve another problem
with same N but another starting point. MinNLCRestartFrom() allows to
reuse already initialized structure.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size ofX
X - starting point, array[N]:
* it is better to set X to a feasible point
* but X can be infeasible, in which case algorithm will try
to find feasible point first, using X as initial
approximation.
OUTPUT PARAMETERS:
State - structure stores algorithm state
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlccreate(const ae_int_t n, const real_1d_array &x, minnlcstate &state);
void minnlccreate(const real_1d_array &x, minnlcstate &state);
/*************************************************************************
This subroutine is a finite difference variant of MinNLCCreate(). It uses
finite differences in order to differentiate target function.
Description below contains information which is specific to this function
only. We recommend to read comments on MinNLCCreate() in order to get more
information about creation of NLC optimizer.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size ofX
X - starting point, array[N]:
* it is better to set X to a feasible point
* but X can be infeasible, in which case algorithm will try
to find feasible point first, using X as initial
approximation.
DiffStep- differentiation step, >0
OUTPUT PARAMETERS:
State - structure stores algorithm state
NOTES:
1. algorithm uses 4-point central formula for differentiation.
2. differentiation step along I-th axis is equal to DiffStep*S[I] where
S[] is scaling vector which can be set by MinNLCSetScale() call.
3. we recommend you to use moderate values of differentiation step. Too
large step will result in too large TRUNCATION errors, while too small
step will result in too large NUMERICAL errors. 1.0E-4 can be good
value to start from.
4. Numerical differentiation is very inefficient - one gradient
calculation needs 4*N function evaluations. This function will work for
any N - either small (1...10), moderate (10...100) or large (100...).
However, performance penalty will be too severe for any N's except for
small ones.
We should also say that code which relies on numerical differentiation
is less robust and precise. Imprecise gradient may slow down
convergence, especially on highly nonlinear problems.
Thus we recommend to use this function for fast prototyping on small-
dimensional problems only, and to implement analytical gradient as soon
as possible.
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlccreatef(const ae_int_t n, const real_1d_array &x, const double diffstep, minnlcstate &state);
void minnlccreatef(const real_1d_array &x, const double diffstep, minnlcstate &state);
/*************************************************************************
This function sets boundary constraints for NLC optimizer.
Boundary constraints are inactive by default (after initial creation).
They are preserved after algorithm restart with MinNLCRestartFrom().
You may combine boundary constraints with general linear ones - and with
nonlinear ones! Boundary constraints are handled more efficiently than
other types. Thus, if your problem has mixed constraints, you may
explicitly specify some of them as boundary and save some time/space.
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bounds, array[N].
If some (all) variables are unbounded, you may specify
very small number or -INF.
BndU - upper bounds, array[N].
If some (all) variables are unbounded, you may specify
very large number or +INF.
NOTE 1: it is possible to specify BndL[i]=BndU[i]. In this case I-th
variable will be "frozen" at X[i]=BndL[i]=BndU[i].
NOTE 2: when you solve your problem with augmented Lagrangian solver,
boundary constraints are satisfied only approximately! It is
possible that algorithm will evaluate function outside of
feasible area!
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetbc(const minnlcstate &state, const real_1d_array &bndl, const real_1d_array &bndu);
/*************************************************************************
This function sets linear constraints for MinNLC optimizer.
Linear constraints are inactive by default (after initial creation). They
are preserved after algorithm restart with MinNLCRestartFrom().
You may combine linear constraints with boundary ones - and with nonlinear
ones! If your problem has mixed constraints, you may explicitly specify
some of them as linear. It may help optimizer to handle them more
efficiently.
INPUT PARAMETERS:
State - structure previously allocated with MinNLCCreate call.
C - linear constraints, array[K,N+1].
Each row of C represents one constraint, either equality
or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of C (including right part) must be finite.
CT - type of constraints, array[K]:
* if CT[i]>0, then I-th constraint is C[i,*]*x >= C[i,n+1]
* if CT[i]=0, then I-th constraint is C[i,*]*x = C[i,n+1]
* if CT[i]<0, then I-th constraint is C[i,*]*x <= C[i,n+1]
K - number of equality/inequality constraints, K>=0:
* if given, only leading K elements of C/CT are used
* if not given, automatically determined from sizes of C/CT
NOTE 1: when you solve your problem with augmented Lagrangian solver,
linear constraints are satisfied only approximately! It is
possible that algorithm will evaluate function outside of
feasible area!
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetlc(const minnlcstate &state, const real_2d_array &c, const integer_1d_array &ct, const ae_int_t k);
void minnlcsetlc(const minnlcstate &state, const real_2d_array &c, const integer_1d_array &ct);
/*************************************************************************
This function sets nonlinear constraints for MinNLC optimizer.
In fact, this function sets NUMBER of nonlinear constraints. Constraints
itself (constraint functions) are passed to MinNLCOptimize() method. This
method requires user-defined vector function F[] and its Jacobian J[],
where:
* first component of F[] and first row of Jacobian J[] corresponds to
function being minimized
* next NLEC components of F[] (and rows of J) correspond to nonlinear
equality constraints G_i(x)=0
* next NLIC components of F[] (and rows of J) correspond to nonlinear
inequality constraints H_i(x)<=0
NOTE: you may combine nonlinear constraints with linear/boundary ones. If
your problem has mixed constraints, you may explicitly specify some
of them as linear ones. It may help optimizer to handle them more
efficiently.
INPUT PARAMETERS:
State - structure previously allocated with MinNLCCreate call.
NLEC - number of Non-Linear Equality Constraints (NLEC), >=0
NLIC - number of Non-Linear Inquality Constraints (NLIC), >=0
NOTE 1: when you solve your problem with augmented Lagrangian solver,
nonlinear constraints are satisfied only approximately! It is
possible that algorithm will evaluate function outside of
feasible area!
NOTE 2: algorithm scales variables according to scale specified by
MinNLCSetScale() function, so it can handle problems with badly
scaled variables (as long as we KNOW their scales).
However, there is no way to automatically scale nonlinear
constraints Gi(x) and Hi(x). Inappropriate scaling of Gi/Hi may
ruin convergence. Solving problem with constraint "1000*G0(x)=0"
is NOT same as solving it with constraint "0.001*G0(x)=0".
It means that YOU are the one who is responsible for correct
scaling of nonlinear constraints Gi(x) and Hi(x). We recommend you
to scale nonlinear constraints in such way that I-th component of
dG/dX (or dH/dx) has approximately unit magnitude (for problems
with unit scale) or has magnitude approximately equal to 1/S[i]
(where S is a scale set by MinNLCSetScale() function).
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetnlc(const minnlcstate &state, const ae_int_t nlec, const ae_int_t nlic);
/*************************************************************************
This function sets stopping conditions for inner iterations of optimizer.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsG - >=0
The subroutine finishes its work if the condition
|v|<EpsG is satisfied, where:
* |.| means Euclidian norm
* v - scaled gradient vector, v[i]=g[i]*s[i]
* g - gradient
* s - scaling coefficients set by MinNLCSetScale()
EpsF - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |F(k+1)-F(k)|<=EpsF*max{|F(k)|,|F(k+1)|,1}
is satisfied.
EpsX - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |v|<=EpsX is fulfilled, where:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - step vector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinNLCSetScale()
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited.
Passing EpsG=0, EpsF=0 and EpsX=0 and MaxIts=0 (simultaneously) will lead
to automatic stopping criterion selection.
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetcond(const minnlcstate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxits);
/*************************************************************************
This function sets scaling coefficients for NLC optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Scaling is also used by finite difference variant of the optimizer - step
along I-th axis is equal to DiffStep*S[I].
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetscale(const minnlcstate &state, const real_1d_array &s);
/*************************************************************************
This function sets preconditioner to "inexact LBFGS-based" mode.
Preconditioning is very important for convergence of Augmented Lagrangian
algorithm because presence of penalty term makes problem ill-conditioned.
Difference between performance of preconditioned and unpreconditioned
methods can be as large as 100x!
MinNLC optimizer may utilize two preconditioners, each with its own
benefits and drawbacks: a) inexact LBFGS-based, and b) exact low rank one.
It also provides special unpreconditioned mode of operation which can be
used for test purposes. Comments below discuss LBFGS-based preconditioner.
Inexact LBFGS-based preconditioner uses L-BFGS formula combined with
orthogonality assumption to perform very fast updates. For a N-dimensional
problem with K general linear or nonlinear constraints (boundary ones are
not counted) it has O(N*K) cost per iteration. This preconditioner has
best quality (less iterations) when general linear and nonlinear
constraints are orthogonal to each other (orthogonality with respect to
boundary constraints is not required). Number of iterations increases when
constraints are non-orthogonal, because algorithm assumes orthogonality,
but still it is better than no preconditioner at all.
INPUT PARAMETERS:
State - structure stores algorithm state
-- ALGLIB --
Copyright 26.09.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetprecinexact(const minnlcstate &state);
/*************************************************************************
This function sets preconditioner to "exact low rank" mode.
Preconditioning is very important for convergence of Augmented Lagrangian
algorithm because presence of penalty term makes problem ill-conditioned.
Difference between performance of preconditioned and unpreconditioned
methods can be as large as 100x!
MinNLC optimizer may utilize two preconditioners, each with its own
benefits and drawbacks: a) inexact LBFGS-based, and b) exact low rank one.
It also provides special unpreconditioned mode of operation which can be
used for test purposes. Comments below discuss low rank preconditioner.
Exact low-rank preconditioner uses Woodbury matrix identity to build
quadratic model of the penalized function. It has no special assumptions
about orthogonality, so it is quite general. However, for a N-dimensional
problem with K general linear or nonlinear constraints (boundary ones are
not counted) it has O(N*K^2) cost per iteration (for comparison: inexact
LBFGS-based preconditioner has O(N*K) cost).
INPUT PARAMETERS:
State - structure stores algorithm state
UpdateFreq- update frequency. Preconditioner is rebuilt after every
UpdateFreq iterations. Recommended value: 10 or higher.
Zero value means that good default value will be used.
-- ALGLIB --
Copyright 26.09.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetprecexactlowrank(const minnlcstate &state, const ae_int_t updatefreq);
/*************************************************************************
This function sets preconditioner to "turned off" mode.
Preconditioning is very important for convergence of Augmented Lagrangian
algorithm because presence of penalty term makes problem ill-conditioned.
Difference between performance of preconditioned and unpreconditioned
methods can be as large as 100x!
MinNLC optimizer may utilize two preconditioners, each with its own
benefits and drawbacks: a) inexact LBFGS-based, and b) exact low rank one.
It also provides special unpreconditioned mode of operation which can be
used for test purposes.
This function activates this test mode. Do not use it in production code
to solve real-life problems.
INPUT PARAMETERS:
State - structure stores algorithm state
-- ALGLIB --
Copyright 26.09.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetprecnone(const minnlcstate &state);
/*************************************************************************
This function tells MinNLC unit to use Augmented Lagrangian algorithm
for nonlinearly constrained optimization. This algorithm is a slight
modification of one described in "A Modified Barrier-Augmented Lagrangian
Method for Constrained Minimization (1999)" by D.GOLDFARB, R.POLYAK,
K. SCHEINBERG, I.YUZEFOVICH.
Augmented Lagrangian algorithm works by converting problem of minimizing
F(x) subject to equality/inequality constraints to unconstrained problem
of the form
min[ f(x) +
+ Rho*PENALTY_EQ(x) + SHIFT_EQ(x,Nu1) +
+ Rho*PENALTY_INEQ(x) + SHIFT_INEQ(x,Nu2) ]
where:
* Rho is a fixed penalization coefficient
* PENALTY_EQ(x) is a penalty term, which is used to APPROXIMATELY enforce
equality constraints
* SHIFT_EQ(x) is a special "shift" term which is used to "fine-tune"
equality constraints, greatly increasing precision
* PENALTY_INEQ(x) is a penalty term which is used to approximately enforce
inequality constraints
* SHIFT_INEQ(x) is a special "shift" term which is used to "fine-tune"
inequality constraints, greatly increasing precision
* Nu1/Nu2 are vectors of Lagrange coefficients which are fine-tuned during
outer iterations of algorithm
This version of AUL algorithm uses preconditioner, which greatly
accelerates convergence. Because this algorithm is similar to penalty
methods, it may perform steps into infeasible area. All kinds of
constraints (boundary, linear and nonlinear ones) may be violated in
intermediate points - and in the solution. However, properly configured
AUL method is significantly better at handling constraints than barrier
and/or penalty methods.
The very basic outline of algorithm is given below:
1) first outer iteration is performed with "default" values of Lagrange
multipliers Nu1/Nu2. Solution quality is low (candidate point can be
too far away from true solution; large violation of constraints is
possible) and is comparable with that of penalty methods.
2) subsequent outer iterations refine Lagrange multipliers and improve
quality of the solution.
INPUT PARAMETERS:
State - structure which stores algorithm state
Rho - penalty coefficient, Rho>0:
* large enough that algorithm converges with desired
precision. Minimum value is 10*max(S'*diag(H)*S), where
S is a scale matrix (set by MinNLCSetScale) and H is a
Hessian of the function being minimized. If you can not
easily estimate Hessian norm, see our recommendations
below.
* not TOO large to prevent ill-conditioning
* for unit-scale problems (variables and Hessian have unit
magnitude), Rho=100 or Rho=1000 can be used.
* it is important to note that Rho is internally multiplied
by scaling matrix, i.e. optimum value of Rho depends on
scale of variables specified by MinNLCSetScale().
ItsCnt - number of outer iterations:
* ItsCnt=0 means that small number of outer iterations is
automatically chosen (10 iterations in current version).
* ItsCnt=1 means that AUL algorithm performs just as usual
barrier method.
* ItsCnt>1 means that AUL algorithm performs specified
number of outer iterations
HOW TO CHOOSE PARAMETERS
Nonlinear optimization is a tricky area and Augmented Lagrangian algorithm
is sometimes hard to tune. Good values of Rho and ItsCnt are problem-
specific. In order to help you we prepared following set of
recommendations:
* for unit-scale problems (variables and Hessian have unit magnitude),
Rho=100 or Rho=1000 can be used.
* start from some small value of Rho and solve problem with just one
outer iteration (ItcCnt=1). In this case algorithm behaves like penalty
method. Increase Rho in 2x or 10x steps until you see that one outer
iteration returns point which is "rough approximation to solution".
It is very important to have Rho so large that penalty term becomes
constraining i.e. modified function becomes highly convex in constrained
directions.
From the other side, too large Rho may prevent you from converging to
the solution. You can diagnose it by studying number of inner iterations
performed by algorithm: too few (5-10 on 1000-dimensional problem) or
too many (orders of magnitude more than dimensionality) usually means
that Rho is too large.
* with just one outer iteration you usually have low-quality solution.
Some constraints can be violated with very large margin, while other
ones (which are NOT violated in the true solution) can push final point
too far in the inner area of the feasible set.
For example, if you have constraint x0>=0 and true solution x0=1, then
merely a presence of "x0>=0" will introduce a bias towards larger values
of x0. Say, algorithm may stop at x0=1.5 instead of 1.0.
* after you found good Rho, you may increase number of outer iterations.
ItsCnt=10 is a good value. Subsequent outer iteration will refine values
of Lagrange multipliers. Constraints which were violated will be
enforced, inactive constraints will be dropped (corresponding multipliers
will be decreased). Ideally, you should see 10-1000x improvement in
constraint handling (constraint violation is reduced).
* if you see that algorithm converges to vicinity of solution, but
additional outer iterations do not refine solution, it may mean that
algorithm is unstable - it wanders around true solution, but can not
approach it. Sometimes algorithm may be stabilized by increasing Rho one
more time, making it 5x or 10x larger.
SCALING OF CONSTRAINTS [IMPORTANT]
AUL optimizer scales variables according to scale specified by
MinNLCSetScale() function, so it can handle problems with badly scaled
variables (as long as we KNOW their scales). However, because function
being optimized is a mix of original function and constraint-dependent
penalty functions, it is important to rescale both variables AND
constraints.
Say, if you minimize f(x)=x^2 subject to 1000000*x>=0, then you have
constraint whose scale is different from that of target function (another
example is 0.000001*x>=0). It is also possible to have constraints whose
scales are misaligned: 1000000*x0>=0, 0.000001*x1<=0. Inappropriate
scaling may ruin convergence because minimizing x^2 subject to x>=0 is NOT
same as minimizing it subject to 1000000*x>=0.
Because we know coefficients of boundary/linear constraints, we can
automatically rescale and normalize them. However, there is no way to
automatically rescale nonlinear constraints Gi(x) and Hi(x) - they are
black boxes.
It means that YOU are the one who is responsible for correct scaling of
nonlinear constraints Gi(x) and Hi(x). We recommend you to rescale
nonlinear constraints in such way that I-th component of dG/dX (or dH/dx)
has magnitude approximately equal to 1/S[i] (where S is a scale set by
MinNLCSetScale() function).
WHAT IF IT DOES NOT CONVERGE?
It is possible that AUL algorithm fails to converge to precise values of
Lagrange multipliers. It stops somewhere around true solution, but candidate
point is still too far from solution, and some constraints are violated.
Such kind of failure is specific for Lagrangian algorithms - technically,
they stop at some point, but this point is not constrained solution.
There are exist several reasons why algorithm may fail to converge:
a) too loose stopping criteria for inner iteration
b) degenerate, redundant constraints
c) target function has unconstrained extremum exactly at the boundary of
some constraint
d) numerical noise in the target function
In all these cases algorithm is unstable - each outer iteration results in
large and almost random step which improves handling of some constraints,
but violates other ones (ideally outer iterations should form a sequence
of progressively decreasing steps towards solution).
First reason possible is that too loose stopping criteria for inner
iteration were specified. Augmented Lagrangian algorithm solves a sequence
of intermediate problems, and requries each of them to be solved with high
precision. Insufficient precision results in incorrect update of Lagrange
multipliers.
Another reason is that you may have specified degenerate constraints: say,
some constraint was repeated twice. In most cases AUL algorithm gracefully
handles such situations, but sometimes it may spend too much time figuring
out subtle degeneracies in constraint matrix.
Third reason is tricky and hard to diagnose. Consider situation when you
minimize f=x^2 subject to constraint x>=0. Unconstrained extremum is
located exactly at the boundary of constrained area. In this case
algorithm will tend to oscillate between negative and positive x. Each
time it stops at x<0 it "reinforces" constraint x>=0, and each time it is
bounced to x>0 it "relaxes" constraint (and is attracted to x<0).
Such situation sometimes happens in problems with hidden symetries.
Algorithm is got caught in a loop with Lagrange multipliers being
continuously increased/decreased. Luckily, such loop forms after at least
three iterations, so this problem can be solved by DECREASING number of
outer iterations down to 1-2 and increasing penalty coefficient Rho as
much as possible.
Final reason is numerical noise. AUL algorithm is robust against moderate
noise (more robust than, say, active set methods), but large noise may
destabilize algorithm.
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetalgoaul(const minnlcstate &state, const double rho, const ae_int_t itscnt);
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
If NeedXRep is True, algorithm will call rep() callback function if it is
provided to MinNLCOptimize().
NOTE: algorithm passes two parameters to rep() callback - current point
and penalized function value at current point. Important - function
value which is returned is NOT function being minimized. It is sum
of the value of the function being minimized - and penalty term.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minnlcsetxrep(const minnlcstate &state, const bool needxrep);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool minnlciteration(const minnlcstate &state);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
fvec - callback which calculates function vector fi[]
at given point x
jac - callback which calculates function vector fi[]
and Jacobian jac at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
NOTES:
1. This function has two different implementations: one which uses exact
(analytical) user-supplied Jacobian, and one which uses only function
vector and numerically differentiates function in order to obtain
gradient.
Depending on the specific function used to create optimizer object
you should choose appropriate variant of MinNLCOptimize() - one which
accepts function AND Jacobian or one which accepts ONLY function.
Be careful to choose variant of MinNLCOptimize() which corresponds to
your optimization scheme! Table below lists different combinations of
callback (function/gradient) passed to MinNLCOptimize() and specific
function used to create optimizer.
| USER PASSED TO MinNLCOptimize()
CREATED WITH | function only | function and gradient
------------------------------------------------------------
MinNLCCreateF() | works FAILS
MinNLCCreate() | FAILS works
Here "FAILS" denotes inappropriate combinations of optimizer creation
function and MinNLCOptimize() version. Attemps to use such
combination will lead to exception. Either you did not pass gradient
when it WAS needed or you passed gradient when it was NOT needed.
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcoptimize(minnlcstate &state,
void (*fvec)(const real_1d_array &x, real_1d_array &fi, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
void minnlcoptimize(minnlcstate &state,
void (*jac)(const real_1d_array &x, real_1d_array &fi, real_2d_array &jac, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
/*************************************************************************
MinNLC results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report. You should check Rep.TerminationType
in order to distinguish successful termination from
unsuccessful one:
* -8 internal integrity control detected infinite or
NAN values in function/gradient. Abnormal
termination signalled.
* -7 gradient verification failed.
See MinNLCSetGradientCheck() for more information.
* 1 relative function improvement is no more than EpsF.
* 2 scaled step is no more than EpsX.
* 4 scaled gradient norm is no more than EpsG.
* 5 MaxIts steps was taken
More information about fields of this structure can be
found in the comments on MinNLCReport datatype.
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcresults(const minnlcstate &state, real_1d_array &x, minnlcreport &rep);
/*************************************************************************
NLC results
Buffered implementation of MinNLCResults() which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minnlcresultsbuf(const minnlcstate &state, real_1d_array &x, minnlcreport &rep);
/*************************************************************************
This subroutine restarts algorithm from new point.
All optimization parameters (including constraints) are left unchanged.
This function allows to solve multiple optimization problems (which
must have same number of dimensions) without object reallocation penalty.
INPUT PARAMETERS:
State - structure previously allocated with MinNLCCreate call.
X - new starting point.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minnlcrestartfrom(const minnlcstate &state, const real_1d_array &x);
/*************************************************************************
This subroutine turns on verification of the user-supplied analytic
gradient:
* user calls this subroutine before optimization begins
* MinNLCOptimize() is called
* prior to actual optimization, for each component of parameters being
optimized X[i] algorithm performs following steps:
* two trial steps are made to X[i]-TestStep*S[i] and X[i]+TestStep*S[i],
where X[i] is i-th component of the initial point and S[i] is a scale
of i-th parameter
* F(X) is evaluated at these trial points
* we perform one more evaluation in the middle point of the interval
* we build cubic model using function values and derivatives at trial
points and we compare its prediction with actual value in the middle
point
* in case difference between prediction and actual value is higher than
some predetermined threshold, algorithm stops with completion code -7;
Rep.VarIdx is set to index of the parameter with incorrect derivative,
and Rep.FuncIdx is set to index of the function.
* after verification is over, algorithm proceeds to the actual optimization.
NOTE 1: verification needs N (parameters count) gradient evaluations. It
is very costly and you should use it only for low dimensional
problems, when you want to be sure that you've correctly
calculated analytic derivatives. You should not use it in the
production code (unless you want to check derivatives provided by
some third party).
NOTE 2: you should carefully choose TestStep. Value which is too large
(so large that function behaviour is significantly non-cubic) will
lead to false alarms. You may use different step for different
parameters by means of setting scale with MinNLCSetScale().
NOTE 3: this function may lead to false positives. In case it reports that
I-th derivative was calculated incorrectly, you may decrease test
step and try one more time - maybe your function changes too
sharply and your step is too large for such rapidly chanding
function.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step:
* TestStep=0 turns verification off
* TestStep>0 activates verification
-- ALGLIB --
Copyright 15.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetgradientcheck(const minnlcstate &state, const double teststep);
/*************************************************************************
NONSMOOTH NONCONVEX OPTIMIZATION
SUBJECT TO BOX/LINEAR/NONLINEAR-NONSMOOTH CONSTRAINTS
DESCRIPTION:
The subroutine minimizes function F(x) of N arguments subject to any
combination of:
* bound constraints
* linear inequality constraints
* linear equality constraints
* nonlinear equality constraints Gi(x)=0
* nonlinear inequality constraints Hi(x)<=0
IMPORTANT: see MinNSSetAlgoAGS for important information on performance
restrictions of AGS solver.
REQUIREMENTS:
* starting point X0 must be feasible or not too far away from the feasible
set
* F(), G(), H() are continuous, locally Lipschitz and continuously (but
not necessarily twice) differentiable in an open dense subset of R^N.
Functions F(), G() and H() may be nonsmooth and non-convex.
Informally speaking, it means that functions are composed of large
differentiable "patches" with nonsmoothness having place only at the
boundaries between these "patches".
Most real-life nonsmooth functions satisfy these requirements. Say,
anything which involves finite number of abs(), min() and max() is very
likely to pass the test.
Say, it is possible to optimize anything of the following:
* f=abs(x0)+2*abs(x1)
* f=max(x0,x1)
* f=sin(max(x0,x1)+abs(x2))
* for nonlinearly constrained problems: F() must be bounded from below
without nonlinear constraints (this requirement is due to the fact that,
contrary to box and linear constraints, nonlinear ones require special
handling).
* user must provide function value and gradient for F(), H(), G() at all
points where function/gradient can be calculated. If optimizer requires
value exactly at the boundary between "patches" (say, at x=0 for f=abs(x)),
where gradient is not defined, user may resolve tie arbitrarily (in our
case - return +1 or -1 at its discretion).
* NS solver supports numerical differentiation, i.e. it may differentiate
your function for you, but it results in 2N increase of function
evaluations. Not recommended unless you solve really small problems. See
minnscreatef() for more information on this functionality.
USAGE:
1. User initializes algorithm state with MinNSCreate() call and chooses
what NLC solver to use. There is some solver which is used by default,
with default settings, but you should NOT rely on default choice. It
may change in future releases of ALGLIB without notice, and no one can
guarantee that new solver will be able to solve your problem with
default settings.
From the other side, if you choose solver explicitly, you can be pretty
sure that it will work with new ALGLIB releases.
In the current release following solvers can be used:
* AGS solver (activated with MinNSSetAlgoAGS() function)
2. User adds boundary and/or linear and/or nonlinear constraints by means
of calling one of the following functions:
a) MinNSSetBC() for boundary constraints
b) MinNSSetLC() for linear constraints
c) MinNSSetNLC() for nonlinear constraints
You may combine (a), (b) and (c) in one optimization problem.
3. User sets scale of the variables with MinNSSetScale() function. It is
VERY important to set scale of the variables, because nonlinearly
constrained problems are hard to solve when variables are badly scaled.
4. User sets stopping conditions with MinNSSetCond().
5. Finally, user calls MinNSOptimize() function which takes algorithm
state and pointer (delegate, etc) to callback function which calculates
F/G/H.
7. User calls MinNSResults() to get solution
8. Optionally user may call MinNSRestartFrom() to solve another problem
with same N but another starting point. MinNSRestartFrom() allows to
reuse already initialized structure.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
X - starting point, array[N]:
* it is better to set X to a feasible point
* but X can be infeasible, in which case algorithm will try
to find feasible point first, using X as initial
approximation.
OUTPUT PARAMETERS:
State - structure stores algorithm state
NOTE: minnscreatef() function may be used if you do not have analytic
gradient. This function creates solver which uses numerical
differentiation with user-specified step.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnscreate(const ae_int_t n, const real_1d_array &x, minnsstate &state);
void minnscreate(const real_1d_array &x, minnsstate &state);
/*************************************************************************
Version of minnscreatef() which uses numerical differentiation. I.e., you
do not have to calculate derivatives yourself. However, this version needs
2N times more function evaluations.
2-point differentiation formula is used, because more precise 4-point
formula is unstable when used on non-smooth functions.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
X - starting point, array[N]:
* it is better to set X to a feasible point
* but X can be infeasible, in which case algorithm will try
to find feasible point first, using X as initial
approximation.
DiffStep- differentiation step, DiffStep>0. Algorithm performs
numerical differentiation with step for I-th variable
being equal to DiffStep*S[I] (here S[] is a scale vector,
set by minnssetscale() function).
Do not use too small steps, because it may lead to
catastrophic cancellation during intermediate calculations.
OUTPUT PARAMETERS:
State - structure stores algorithm state
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnscreatef(const ae_int_t n, const real_1d_array &x, const double diffstep, minnsstate &state);
void minnscreatef(const real_1d_array &x, const double diffstep, minnsstate &state);
/*************************************************************************
This function sets boundary constraints.
Boundary constraints are inactive by default (after initial creation).
They are preserved after algorithm restart with minnsrestartfrom().
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bounds, array[N].
If some (all) variables are unbounded, you may specify
very small number or -INF.
BndU - upper bounds, array[N].
If some (all) variables are unbounded, you may specify
very large number or +INF.
NOTE 1: it is possible to specify BndL[i]=BndU[i]. In this case I-th
variable will be "frozen" at X[i]=BndL[i]=BndU[i].
NOTE 2: AGS solver has following useful properties:
* bound constraints are always satisfied exactly
* function is evaluated only INSIDE area specified by bound constraints,
even when numerical differentiation is used (algorithm adjusts nodes
according to boundary constraints)
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnssetbc(const minnsstate &state, const real_1d_array &bndl, const real_1d_array &bndu);
/*************************************************************************
This function sets linear constraints.
Linear constraints are inactive by default (after initial creation).
They are preserved after algorithm restart with minnsrestartfrom().
INPUT PARAMETERS:
State - structure previously allocated with minnscreate() call.
C - linear constraints, array[K,N+1].
Each row of C represents one constraint, either equality
or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of C (including right part) must be finite.
CT - type of constraints, array[K]:
* if CT[i]>0, then I-th constraint is C[i,*]*x >= C[i,n+1]
* if CT[i]=0, then I-th constraint is C[i,*]*x = C[i,n+1]
* if CT[i]<0, then I-th constraint is C[i,*]*x <= C[i,n+1]
K - number of equality/inequality constraints, K>=0:
* if given, only leading K elements of C/CT are used
* if not given, automatically determined from sizes of C/CT
NOTE: linear (non-bound) constraints are satisfied only approximately:
* there always exists some minor violation (about current sampling radius
in magnitude during optimization, about EpsX in the solution) due to use
of penalty method to handle constraints.
* numerical differentiation, if used, may lead to function evaluations
outside of the feasible area, because algorithm does NOT change
numerical differentiation formula according to linear constraints.
If you want constraints to be satisfied exactly, try to reformulate your
problem in such manner that all constraints will become boundary ones
(this kind of constraints is always satisfied exactly, both in the final
solution and in all intermediate points).
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnssetlc(const minnsstate &state, const real_2d_array &c, const integer_1d_array &ct, const ae_int_t k);
void minnssetlc(const minnsstate &state, const real_2d_array &c, const integer_1d_array &ct);
/*************************************************************************
This function sets nonlinear constraints.
In fact, this function sets NUMBER of nonlinear constraints. Constraints
itself (constraint functions) are passed to minnsoptimize() method. This
method requires user-defined vector function F[] and its Jacobian J[],
where:
* first component of F[] and first row of Jacobian J[] correspond to
function being minimized
* next NLEC components of F[] (and rows of J) correspond to nonlinear
equality constraints G_i(x)=0
* next NLIC components of F[] (and rows of J) correspond to nonlinear
inequality constraints H_i(x)<=0
NOTE: you may combine nonlinear constraints with linear/boundary ones. If
your problem has mixed constraints, you may explicitly specify some
of them as linear ones. It may help optimizer to handle them more
efficiently.
INPUT PARAMETERS:
State - structure previously allocated with minnscreate() call.
NLEC - number of Non-Linear Equality Constraints (NLEC), >=0
NLIC - number of Non-Linear Inquality Constraints (NLIC), >=0
NOTE 1: nonlinear constraints are satisfied only approximately! It is
possible that algorithm will evaluate function outside of
the feasible area!
NOTE 2: algorithm scales variables according to scale specified by
minnssetscale() function, so it can handle problems with badly
scaled variables (as long as we KNOW their scales).
However, there is no way to automatically scale nonlinear
constraints Gi(x) and Hi(x). Inappropriate scaling of Gi/Hi may
ruin convergence. Solving problem with constraint "1000*G0(x)=0"
is NOT same as solving it with constraint "0.001*G0(x)=0".
It means that YOU are the one who is responsible for correct
scaling of nonlinear constraints Gi(x) and Hi(x). We recommend you
to scale nonlinear constraints in such way that I-th component of
dG/dX (or dH/dx) has approximately unit magnitude (for problems
with unit scale) or has magnitude approximately equal to 1/S[i]
(where S is a scale set by minnssetscale() function).
NOTE 3: nonlinear constraints are always hard to handle, no matter what
algorithm you try to use. Even basic box/linear constraints modify
function curvature by adding valleys and ridges. However,
nonlinear constraints add valleys which are very hard to follow
due to their "curved" nature.
It means that optimization with single nonlinear constraint may be
significantly slower than optimization with multiple linear ones.
It is normal situation, and we recommend you to carefully choose
Rho parameter of minnssetalgoags(), because too large value may
slow down convergence.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnssetnlc(const minnsstate &state, const ae_int_t nlec, const ae_int_t nlic);
/*************************************************************************
This function sets stopping conditions for iterations of optimizer.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsX - >=0
The AGS solver finishes its work if on k+1-th iteration
sampling radius decreases below EpsX.
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited.
Passing EpsX=0 and MaxIts=0 (simultaneously) will lead to automatic
stopping criterion selection. We do not recommend you to rely on default
choice in production code.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnssetcond(const minnsstate &state, const double epsx, const ae_int_t maxits);
/*************************************************************************
This function sets scaling coefficients for NLC optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Scaling is also used by finite difference variant of the optimizer - step
along I-th axis is equal to DiffStep*S[I].
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnssetscale(const minnsstate &state, const real_1d_array &s);
/*************************************************************************
This function tells MinNS unit to use AGS (adaptive gradient sampling)
algorithm for nonsmooth constrained optimization. This algorithm is a
slight modification of one described in "An Adaptive Gradient Sampling
Algorithm for Nonsmooth Optimization" by Frank E. Curtisy and Xiaocun Quez.
This optimizer has following benefits and drawbacks:
+ robustness; it can be used with nonsmooth and nonconvex functions.
+ relatively easy tuning; most of the metaparameters are easy to select.
- it has convergence of steepest descent, slower than CG/LBFGS.
- each iteration involves evaluation of ~2N gradient values and solution
of 2Nx2N quadratic programming problem, which limits applicability of
algorithm by small-scale problems (up to 50-100).
IMPORTANT: this algorithm has convergence guarantees, i.e. it will
steadily move towards some stationary point of the function.
However, "stationary point" does not always mean "solution".
Nonsmooth problems often have "flat spots", i.e. areas where
function do not change at all. Such "flat spots" are stationary
points by definition, and algorithm may be caught here.
Nonsmooth CONVEX tasks are not prone to this problem. Say, if
your function has form f()=MAX(f0,f1,...), and f_i are convex,
then f() is convex too and you have guaranteed convergence to
solution.
INPUT PARAMETERS:
State - structure which stores algorithm state
Radius - initial sampling radius, >=0.
Internally multiplied by vector of per-variable scales
specified by minnssetscale()).
You should select relatively large sampling radius, roughly
proportional to scaled length of the first steps of the
algorithm. Something close to 0.1 in magnitude should be
good for most problems.
AGS solver can automatically decrease radius, so too large
radius is not a problem (assuming that you won't choose
so large radius that algorithm will sample function in
too far away points, where gradient value is irrelevant).
Too small radius won't cause algorithm to fail, but it may
slow down algorithm (it may have to perform too short
steps).
Penalty - penalty coefficient for nonlinear constraints:
* for problem with nonlinear constraints should be some
problem-specific positive value, large enough that
penalty term changes shape of the function.
Starting from some problem-specific value penalty
coefficient becomes large enough to exactly enforce
nonlinear constraints; larger values do not improve
precision.
Increasing it too much may slow down convergence, so you
should choose it carefully.
* can be zero for problems WITHOUT nonlinear constraints
(i.e. for unconstrained ones or ones with just box or
linear constraints)
* if you specify zero value for problem with at least one
nonlinear constraint, algorithm will terminate with
error code -1.
ALGORITHM OUTLINE
The very basic outline of unconstrained AGS algorithm is given below:
0. If sampling radius is below EpsX or we performed more then MaxIts
iterations - STOP.
1. sample O(N) gradient values at random locations around current point;
informally speaking, this sample is an implicit piecewise linear model
of the function, although algorithm formulation does not mention that
explicitly
2. solve quadratic programming problem in order to find descent direction
3. if QP solver tells us that we are near solution, decrease sampling
radius and move to (0)
4. perform backtracking line search
5. after moving to new point, goto (0)
As for the constraints:
* box constraints are handled exactly by modification of the function
being minimized
* linear/nonlinear constraints are handled by adding L1 penalty. Because
our solver can handle nonsmoothness, we can use L1 penalty function,
which is an exact one (i.e. exact solution is returned under such
penalty).
* penalty coefficient for linear constraints is chosen automatically;
however, penalty coefficient for nonlinear constraints must be specified
by user.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnssetalgoags(const minnsstate &state, const double radius, const double penalty);
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
If NeedXRep is True, algorithm will call rep() callback function if it is
provided to minnsoptimize().
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minnssetxrep(const minnsstate &state, const bool needxrep);
/*************************************************************************
This subroutine submits request for termination of running optimizer. It
should be called from user-supplied callback when user decides that it is
time to "smoothly" terminate optimization process. As result, optimizer
stops at point which was "current accepted" when termination request was
submitted and returns error code 8 (successful termination).
INPUT PARAMETERS:
State - optimizer structure
NOTE: after request for termination optimizer may perform several
additional calls to user-supplied callbacks. It does NOT guarantee
to stop immediately - it just guarantees that these additional calls
will be discarded later.
NOTE: calling this function on optimizer which is NOT running will have no
effect.
NOTE: multiple calls to this function are possible. First call is counted,
subsequent calls are silently ignored.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnsrequesttermination(const minnsstate &state);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool minnsiteration(const minnsstate &state);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
fvec - callback which calculates function vector fi[]
at given point x
jac - callback which calculates function vector fi[]
and Jacobian jac at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
NOTES:
1. This function has two different implementations: one which uses exact
(analytical) user-supplied Jacobian, and one which uses only function
vector and numerically differentiates function in order to obtain
gradient.
Depending on the specific function used to create optimizer object
you should choose appropriate variant of minnsoptimize() - one which
accepts function AND Jacobian or one which accepts ONLY function.
Be careful to choose variant of minnsoptimize() which corresponds to
your optimization scheme! Table below lists different combinations of
callback (function/gradient) passed to minnsoptimize() and specific
function used to create optimizer.
| USER PASSED TO minnsoptimize()
CREATED WITH | function only | function and gradient
------------------------------------------------------------
minnscreatef() | works FAILS
minnscreate() | FAILS works
Here "FAILS" denotes inappropriate combinations of optimizer creation
function and minnsoptimize() version. Attemps to use such
combination will lead to exception. Either you did not pass gradient
when it WAS needed or you passed gradient when it was NOT needed.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnsoptimize(minnsstate &state,
void (*fvec)(const real_1d_array &x, real_1d_array &fi, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
void minnsoptimize(minnsstate &state,
void (*jac)(const real_1d_array &x, real_1d_array &fi, real_2d_array &jac, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL);
/*************************************************************************
MinNS results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report. You should check Rep.TerminationType
in order to distinguish successful termination from
unsuccessful one:
* -8 internal integrity control detected infinite or
NAN values in function/gradient. Abnormal
termination signalled.
* -3 box constraints are inconsistent
* -1 inconsistent parameters were passed:
* penalty parameter for minnssetalgoags() is zero,
but we have nonlinear constraints set by minnssetnlc()
* 2 sampling radius decreased below epsx
* 7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
* 8 User requested termination via minnsrequesttermination()
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnsresults(const minnsstate &state, real_1d_array &x, minnsreport &rep);
/*************************************************************************
Buffered implementation of minnsresults() which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnsresultsbuf(const minnsstate &state, real_1d_array &x, minnsreport &rep);
/*************************************************************************
This subroutine restarts algorithm from new point.
All optimization parameters (including constraints) are left unchanged.
This function allows to solve multiple optimization problems (which
must have same number of dimensions) without object reallocation penalty.
INPUT PARAMETERS:
State - structure previously allocated with minnscreate() call.
X - new starting point.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnsrestartfrom(const minnsstate &state, const real_1d_array &x);
}
/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS COMPUTATIONAL CORE DECLARATIONS (FUNCTIONS)
//
/////////////////////////////////////////////////////////////////////////
namespace alglib_impl
{
void trimprepare(double f, double* threshold, ae_state *_state);
void trimfunction(double* f,
/* Real */ ae_vector* g,
ae_int_t n,
double threshold,
ae_state *_state);
ae_bool enforceboundaryconstraints(/* Real */ ae_vector* x,
/* Real */ ae_vector* bl,
/* Boolean */ ae_vector* havebl,
/* Real */ ae_vector* bu,
/* Boolean */ ae_vector* havebu,
ae_int_t nmain,
ae_int_t nslack,
ae_state *_state);
void projectgradientintobc(/* Real */ ae_vector* x,
/* Real */ ae_vector* g,
/* Real */ ae_vector* bl,
/* Boolean */ ae_vector* havebl,
/* Real */ ae_vector* bu,
/* Boolean */ ae_vector* havebu,
ae_int_t nmain,
ae_int_t nslack,
ae_state *_state);
void calculatestepbound(/* Real */ ae_vector* x,
/* Real */ ae_vector* d,
double alpha,
/* Real */ ae_vector* bndl,
/* Boolean */ ae_vector* havebndl,
/* Real */ ae_vector* bndu,
/* Boolean */ ae_vector* havebndu,
ae_int_t nmain,
ae_int_t nslack,
ae_int_t* variabletofreeze,
double* valuetofreeze,
double* maxsteplen,
ae_state *_state);
ae_int_t postprocessboundedstep(/* Real */ ae_vector* x,
/* Real */ ae_vector* xprev,
/* Real */ ae_vector* bndl,
/* Boolean */ ae_vector* havebndl,
/* Real */ ae_vector* bndu,
/* Boolean */ ae_vector* havebndu,
ae_int_t nmain,
ae_int_t nslack,
ae_int_t variabletofreeze,
double valuetofreeze,
double steptaken,
double maxsteplen,
ae_state *_state);
void filterdirection(/* Real */ ae_vector* d,
/* Real */ ae_vector* x,
/* Real */ ae_vector* bndl,
/* Boolean */ ae_vector* havebndl,
/* Real */ ae_vector* bndu,
/* Boolean */ ae_vector* havebndu,
/* Real */ ae_vector* s,
ae_int_t nmain,
ae_int_t nslack,
double droptol,
ae_state *_state);
ae_int_t numberofchangedconstraints(/* Real */ ae_vector* x,
/* Real */ ae_vector* xprev,
/* Real */ ae_vector* bndl,
/* Boolean */ ae_vector* havebndl,
/* Real */ ae_vector* bndu,
/* Boolean */ ae_vector* havebndu,
ae_int_t nmain,
ae_int_t nslack,
ae_state *_state);
ae_bool findfeasiblepoint(/* Real */ ae_vector* x,
/* Real */ ae_vector* bndl,
/* Boolean */ ae_vector* havebndl,
/* Real */ ae_vector* bndu,
/* Boolean */ ae_vector* havebndu,
ae_int_t nmain,
ae_int_t nslack,
/* Real */ ae_matrix* ce,
ae_int_t k,
double epsi,
ae_int_t* qpits,
ae_int_t* gpaits,
ae_state *_state);
ae_bool derivativecheck(double f0,
double df0,
double f1,
double df1,
double f,
double df,
double width,
ae_state *_state);
void estimateparabolicmodel(double absasum,
double absasum2,
double mx,
double mb,
double md,
double d1,
double d2,
ae_int_t* d1est,
ae_int_t* d2est,
ae_state *_state);
void inexactlbfgspreconditioner(/* Real */ ae_vector* s,
ae_int_t n,
/* Real */ ae_vector* d,
/* Real */ ae_vector* c,
/* Real */ ae_matrix* w,
ae_int_t k,
precbuflbfgs* buf,
ae_state *_state);
void preparelowrankpreconditioner(/* Real */ ae_vector* d,
/* Real */ ae_vector* c,
/* Real */ ae_matrix* w,
ae_int_t n,
ae_int_t k,
precbuflowrank* buf,
ae_state *_state);
void applylowrankpreconditioner(/* Real */ ae_vector* s,
precbuflowrank* buf,
ae_state *_state);
void _precbuflbfgs_init(void* _p, ae_state *_state);
void _precbuflbfgs_init_copy(void* _dst, void* _src, ae_state *_state);
void _precbuflbfgs_clear(void* _p);
void _precbuflbfgs_destroy(void* _p);
void _precbuflowrank_init(void* _p, ae_state *_state);
void _precbuflowrank_init_copy(void* _dst, void* _src, ae_state *_state);
void _precbuflowrank_clear(void* _p);
void _precbuflowrank_destroy(void* _p);
void cqminit(ae_int_t n, convexquadraticmodel* s, ae_state *_state);
void cqmseta(convexquadraticmodel* s,
/* Real */ ae_matrix* a,
ae_bool isupper,
double alpha,
ae_state *_state);
void cqmgeta(convexquadraticmodel* s,
/* Real */ ae_matrix* a,
ae_state *_state);
void cqmrewritedensediagonal(convexquadraticmodel* s,
/* Real */ ae_vector* z,
ae_state *_state);
void cqmsetd(convexquadraticmodel* s,
/* Real */ ae_vector* d,
double tau,
ae_state *_state);
void cqmdropa(convexquadraticmodel* s, ae_state *_state);
void cqmsetb(convexquadraticmodel* s,
/* Real */ ae_vector* b,
ae_state *_state);
void cqmsetq(convexquadraticmodel* s,
/* Real */ ae_matrix* q,
/* Real */ ae_vector* r,
ae_int_t k,
double theta,
ae_state *_state);
void cqmsetactiveset(convexquadraticmodel* s,
/* Real */ ae_vector* x,
/* Boolean */ ae_vector* activeset,
ae_state *_state);
double cqmeval(convexquadraticmodel* s,
/* Real */ ae_vector* x,
ae_state *_state);
void cqmevalx(convexquadraticmodel* s,
/* Real */ ae_vector* x,
double* r,
double* noise,
ae_state *_state);
void cqmgradunconstrained(convexquadraticmodel* s,
/* Real */ ae_vector* x,
/* Real */ ae_vector* g,
ae_state *_state);
double cqmxtadx2(convexquadraticmodel* s,
/* Real */ ae_vector* x,
ae_state *_state);
void cqmadx(convexquadraticmodel* s,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state);
ae_bool cqmconstrainedoptimum(convexquadraticmodel* s,
/* Real */ ae_vector* x,
ae_state *_state);
void cqmscalevector(convexquadraticmodel* s,
/* Real */ ae_vector* x,
ae_state *_state);
double cqmdebugconstrainedevalt(convexquadraticmodel* s,
/* Real */ ae_vector* x,
ae_state *_state);
double cqmdebugconstrainedevale(convexquadraticmodel* s,
/* Real */ ae_vector* x,
ae_state *_state);
void _convexquadraticmodel_init(void* _p, ae_state *_state);
void _convexquadraticmodel_init_copy(void* _dst, void* _src, ae_state *_state);
void _convexquadraticmodel_clear(void* _p);
void _convexquadraticmodel_destroy(void* _p);
void snnlsinit(ae_int_t nsmax,
ae_int_t ndmax,
ae_int_t nrmax,
snnlssolver* s,
ae_state *_state);
void snnlssetproblem(snnlssolver* s,
/* Real */ ae_matrix* a,
/* Real */ ae_vector* b,
ae_int_t ns,
ae_int_t nd,
ae_int_t nr,
ae_state *_state);
void snnlsdropnnc(snnlssolver* s, ae_int_t idx, ae_state *_state);
void snnlssolve(snnlssolver* s,
/* Real */ ae_vector* x,
ae_state *_state);
void _snnlssolver_init(void* _p, ae_state *_state);
void _snnlssolver_init_copy(void* _dst, void* _src, ae_state *_state);
void _snnlssolver_clear(void* _p);
void _snnlssolver_destroy(void* _p);
void sasinit(ae_int_t n, sactiveset* s, ae_state *_state);
void sassetscale(sactiveset* state,
/* Real */ ae_vector* s,
ae_state *_state);
void sassetprecdiag(sactiveset* state,
/* Real */ ae_vector* d,
ae_state *_state);
void sassetbc(sactiveset* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void sassetlc(sactiveset* state,
/* Real */ ae_matrix* c,
/* Integer */ ae_vector* ct,
ae_int_t k,
ae_state *_state);
void sassetlcx(sactiveset* state,
/* Real */ ae_matrix* cleic,
ae_int_t nec,
ae_int_t nic,
ae_state *_state);
ae_bool sasstartoptimization(sactiveset* state,
/* Real */ ae_vector* x,
ae_state *_state);
void sasexploredirection(sactiveset* state,
/* Real */ ae_vector* d,
double* stpmax,
ae_int_t* cidx,
double* vval,
ae_state *_state);
ae_int_t sasmoveto(sactiveset* state,
/* Real */ ae_vector* xn,
ae_bool needact,
ae_int_t cidx,
double cval,
ae_state *_state);
void sasimmediateactivation(sactiveset* state,
ae_int_t cidx,
double cval,
ae_state *_state);
void sasconstraineddescent(sactiveset* state,
/* Real */ ae_vector* g,
/* Real */ ae_vector* d,
ae_state *_state);
void sasconstraineddescentprec(sactiveset* state,
/* Real */ ae_vector* g,
/* Real */ ae_vector* d,
ae_state *_state);
void sasconstraineddirection(sactiveset* state,
/* Real */ ae_vector* d,
ae_state *_state);
void sasconstraineddirectionprec(sactiveset* state,
/* Real */ ae_vector* d,
ae_state *_state);
void sascorrection(sactiveset* state,
/* Real */ ae_vector* x,
double* penalty,
ae_state *_state);
double sasactivelcpenalty1(sactiveset* state,
/* Real */ ae_vector* x,
ae_state *_state);
double sasscaledconstrainednorm(sactiveset* state,
/* Real */ ae_vector* d,
ae_state *_state);
void sasstopoptimization(sactiveset* state, ae_state *_state);
void sasreactivateconstraints(sactiveset* state,
/* Real */ ae_vector* gc,
ae_state *_state);
void sasreactivateconstraintsprec(sactiveset* state,
/* Real */ ae_vector* gc,
ae_state *_state);
void sasrebuildbasis(sactiveset* state, ae_state *_state);
void _sactiveset_init(void* _p, ae_state *_state);
void _sactiveset_init_copy(void* _dst, void* _src, ae_state *_state);
void _sactiveset_clear(void* _p);
void _sactiveset_destroy(void* _p);
void mincgcreate(ae_int_t n,
/* Real */ ae_vector* x,
mincgstate* state,
ae_state *_state);
void mincgcreatef(ae_int_t n,
/* Real */ ae_vector* x,
double diffstep,
mincgstate* state,
ae_state *_state);
void mincgsetcond(mincgstate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxits,
ae_state *_state);
void mincgsetscale(mincgstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void mincgsetxrep(mincgstate* state, ae_bool needxrep, ae_state *_state);
void mincgsetdrep(mincgstate* state, ae_bool needdrep, ae_state *_state);
void mincgsetcgtype(mincgstate* state, ae_int_t cgtype, ae_state *_state);
void mincgsetstpmax(mincgstate* state, double stpmax, ae_state *_state);
void mincgsuggeststep(mincgstate* state, double stp, ae_state *_state);
double mincglastgoodstep(mincgstate* state, ae_state *_state);
void mincgsetprecdefault(mincgstate* state, ae_state *_state);
void mincgsetprecdiag(mincgstate* state,
/* Real */ ae_vector* d,
ae_state *_state);
void mincgsetprecscale(mincgstate* state, ae_state *_state);
ae_bool mincgiteration(mincgstate* state, ae_state *_state);
void mincgresults(mincgstate* state,
/* Real */ ae_vector* x,
mincgreport* rep,
ae_state *_state);
void mincgresultsbuf(mincgstate* state,
/* Real */ ae_vector* x,
mincgreport* rep,
ae_state *_state);
void mincgrestartfrom(mincgstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void mincgrequesttermination(mincgstate* state, ae_state *_state);
void mincgsetprecdiagfast(mincgstate* state,
/* Real */ ae_vector* d,
ae_state *_state);
void mincgsetpreclowrankfast(mincgstate* state,
/* Real */ ae_vector* d1,
/* Real */ ae_vector* c,
/* Real */ ae_matrix* v,
ae_int_t vcnt,
ae_state *_state);
void mincgsetprecvarpart(mincgstate* state,
/* Real */ ae_vector* d2,
ae_state *_state);
void mincgsetgradientcheck(mincgstate* state,
double teststep,
ae_state *_state);
void _mincgstate_init(void* _p, ae_state *_state);
void _mincgstate_init_copy(void* _dst, void* _src, ae_state *_state);
void _mincgstate_clear(void* _p);
void _mincgstate_destroy(void* _p);
void _mincgreport_init(void* _p, ae_state *_state);
void _mincgreport_init_copy(void* _dst, void* _src, ae_state *_state);
void _mincgreport_clear(void* _p);
void _mincgreport_destroy(void* _p);
void minbleiccreate(ae_int_t n,
/* Real */ ae_vector* x,
minbleicstate* state,
ae_state *_state);
void minbleiccreatef(ae_int_t n,
/* Real */ ae_vector* x,
double diffstep,
minbleicstate* state,
ae_state *_state);
void minbleicsetbc(minbleicstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void minbleicsetlc(minbleicstate* state,
/* Real */ ae_matrix* c,
/* Integer */ ae_vector* ct,
ae_int_t k,
ae_state *_state);
void minbleicsetcond(minbleicstate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minbleicsetscale(minbleicstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minbleicsetprecdefault(minbleicstate* state, ae_state *_state);
void minbleicsetprecdiag(minbleicstate* state,
/* Real */ ae_vector* d,
ae_state *_state);
void minbleicsetprecscale(minbleicstate* state, ae_state *_state);
void minbleicsetxrep(minbleicstate* state,
ae_bool needxrep,
ae_state *_state);
void minbleicsetdrep(minbleicstate* state,
ae_bool needdrep,
ae_state *_state);
void minbleicsetstpmax(minbleicstate* state,
double stpmax,
ae_state *_state);
ae_bool minbleiciteration(minbleicstate* state, ae_state *_state);
void minbleicresults(minbleicstate* state,
/* Real */ ae_vector* x,
minbleicreport* rep,
ae_state *_state);
void minbleicresultsbuf(minbleicstate* state,
/* Real */ ae_vector* x,
minbleicreport* rep,
ae_state *_state);
void minbleicrestartfrom(minbleicstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void minbleicrequesttermination(minbleicstate* state, ae_state *_state);
void minbleicemergencytermination(minbleicstate* state, ae_state *_state);
void minbleicsetgradientcheck(minbleicstate* state,
double teststep,
ae_state *_state);
void _minbleicstate_init(void* _p, ae_state *_state);
void _minbleicstate_init_copy(void* _dst, void* _src, ae_state *_state);
void _minbleicstate_clear(void* _p);
void _minbleicstate_destroy(void* _p);
void _minbleicreport_init(void* _p, ae_state *_state);
void _minbleicreport_init_copy(void* _dst, void* _src, ae_state *_state);
void _minbleicreport_clear(void* _p);
void _minbleicreport_destroy(void* _p);
void minlbfgscreate(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
minlbfgsstate* state,
ae_state *_state);
void minlbfgscreatef(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
double diffstep,
minlbfgsstate* state,
ae_state *_state);
void minlbfgssetcond(minlbfgsstate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minlbfgssetxrep(minlbfgsstate* state,
ae_bool needxrep,
ae_state *_state);
void minlbfgssetstpmax(minlbfgsstate* state,
double stpmax,
ae_state *_state);
void minlbfgssetscale(minlbfgsstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minlbfgscreatex(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
ae_int_t flags,
double diffstep,
minlbfgsstate* state,
ae_state *_state);
void minlbfgssetprecdefault(minlbfgsstate* state, ae_state *_state);
void minlbfgssetpreccholesky(minlbfgsstate* state,
/* Real */ ae_matrix* p,
ae_bool isupper,
ae_state *_state);
void minlbfgssetprecdiag(minlbfgsstate* state,
/* Real */ ae_vector* d,
ae_state *_state);
void minlbfgssetprecscale(minlbfgsstate* state, ae_state *_state);
void minlbfgssetprecrankklbfgsfast(minlbfgsstate* state,
/* Real */ ae_vector* d,
/* Real */ ae_vector* c,
/* Real */ ae_matrix* w,
ae_int_t cnt,
ae_state *_state);
void minlbfgssetpreclowrankexact(minlbfgsstate* state,
/* Real */ ae_vector* d,
/* Real */ ae_vector* c,
/* Real */ ae_matrix* w,
ae_int_t cnt,
ae_state *_state);
ae_bool minlbfgsiteration(minlbfgsstate* state, ae_state *_state);
void minlbfgsresults(minlbfgsstate* state,
/* Real */ ae_vector* x,
minlbfgsreport* rep,
ae_state *_state);
void minlbfgsresultsbuf(minlbfgsstate* state,
/* Real */ ae_vector* x,
minlbfgsreport* rep,
ae_state *_state);
void minlbfgsrestartfrom(minlbfgsstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void minlbfgsrequesttermination(minlbfgsstate* state, ae_state *_state);
void minlbfgssetgradientcheck(minlbfgsstate* state,
double teststep,
ae_state *_state);
void _minlbfgsstate_init(void* _p, ae_state *_state);
void _minlbfgsstate_init_copy(void* _dst, void* _src, ae_state *_state);
void _minlbfgsstate_clear(void* _p);
void _minlbfgsstate_destroy(void* _p);
void _minlbfgsreport_init(void* _p, ae_state *_state);
void _minlbfgsreport_init_copy(void* _dst, void* _src, ae_state *_state);
void _minlbfgsreport_clear(void* _p);
void _minlbfgsreport_destroy(void* _p);
void qqploaddefaults(ae_int_t nmain, qqpsettings* s, ae_state *_state);
void qqpcopysettings(qqpsettings* src, qqpsettings* dst, ae_state *_state);
void qqpoptimize(convexquadraticmodel* ac,
sparsematrix* sparseac,
ae_int_t akind,
ae_bool sparseupper,
/* Real */ ae_vector* bc,
/* Real */ ae_vector* bndlc,
/* Real */ ae_vector* bnduc,
/* Real */ ae_vector* sc,
/* Real */ ae_vector* xoriginc,
ae_int_t nc,
/* Real */ ae_matrix* cleicc,
ae_int_t nec,
ae_int_t nic,
qqpsettings* settings,
qqpbuffers* sstate,
/* Real */ ae_vector* xs,
ae_int_t* terminationtype,
ae_state *_state);
void _qqpsettings_init(void* _p, ae_state *_state);
void _qqpsettings_init_copy(void* _dst, void* _src, ae_state *_state);
void _qqpsettings_clear(void* _p);
void _qqpsettings_destroy(void* _p);
void _qqpbuffers_init(void* _p, ae_state *_state);
void _qqpbuffers_init_copy(void* _dst, void* _src, ae_state *_state);
void _qqpbuffers_clear(void* _p);
void _qqpbuffers_destroy(void* _p);
void qpbleicloaddefaults(ae_int_t nmain,
qpbleicsettings* s,
ae_state *_state);
void qpbleiccopysettings(qpbleicsettings* src,
qpbleicsettings* dst,
ae_state *_state);
void qpbleicoptimize(convexquadraticmodel* a,
sparsematrix* sparsea,
ae_int_t akind,
ae_bool sparseaupper,
double absasum,
double absasum2,
/* Real */ ae_vector* b,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
/* Real */ ae_vector* s,
/* Real */ ae_vector* xorigin,
ae_int_t n,
/* Real */ ae_matrix* cleic,
ae_int_t nec,
ae_int_t nic,
qpbleicsettings* settings,
qpbleicbuffers* sstate,
ae_bool* firstcall,
/* Real */ ae_vector* xs,
ae_int_t* terminationtype,
ae_state *_state);
void _qpbleicsettings_init(void* _p, ae_state *_state);
void _qpbleicsettings_init_copy(void* _dst, void* _src, ae_state *_state);
void _qpbleicsettings_clear(void* _p);
void _qpbleicsettings_destroy(void* _p);
void _qpbleicbuffers_init(void* _p, ae_state *_state);
void _qpbleicbuffers_init_copy(void* _dst, void* _src, ae_state *_state);
void _qpbleicbuffers_clear(void* _p);
void _qpbleicbuffers_destroy(void* _p);
void qpcholeskyloaddefaults(ae_int_t nmain,
qpcholeskysettings* s,
ae_state *_state);
void qpcholeskycopysettings(qpcholeskysettings* src,
qpcholeskysettings* dst,
ae_state *_state);
void qpcholeskyoptimize(convexquadraticmodel* a,
double anorm,
/* Real */ ae_vector* b,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
/* Real */ ae_vector* s,
/* Real */ ae_vector* xorigin,
ae_int_t n,
/* Real */ ae_matrix* cleic,
ae_int_t nec,
ae_int_t nic,
qpcholeskybuffers* sstate,
/* Real */ ae_vector* xsc,
ae_int_t* terminationtype,
ae_state *_state);
void _qpcholeskysettings_init(void* _p, ae_state *_state);
void _qpcholeskysettings_init_copy(void* _dst, void* _src, ae_state *_state);
void _qpcholeskysettings_clear(void* _p);
void _qpcholeskysettings_destroy(void* _p);
void _qpcholeskybuffers_init(void* _p, ae_state *_state);
void _qpcholeskybuffers_init_copy(void* _dst, void* _src, ae_state *_state);
void _qpcholeskybuffers_clear(void* _p);
void _qpcholeskybuffers_destroy(void* _p);
void minqpcreate(ae_int_t n, minqpstate* state, ae_state *_state);
void minqpsetlinearterm(minqpstate* state,
/* Real */ ae_vector* b,
ae_state *_state);
void minqpsetquadraticterm(minqpstate* state,
/* Real */ ae_matrix* a,
ae_bool isupper,
ae_state *_state);
void minqpsetquadratictermsparse(minqpstate* state,
sparsematrix* a,
ae_bool isupper,
ae_state *_state);
void minqpsetstartingpoint(minqpstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void minqpsetorigin(minqpstate* state,
/* Real */ ae_vector* xorigin,
ae_state *_state);
void minqpsetscale(minqpstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minqpsetalgocholesky(minqpstate* state, ae_state *_state);
void minqpsetalgobleic(minqpstate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minqpsetalgoquickqp(minqpstate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxouterits,
ae_bool usenewton,
ae_state *_state);
void minqpsetbc(minqpstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void minqpsetlc(minqpstate* state,
/* Real */ ae_matrix* c,
/* Integer */ ae_vector* ct,
ae_int_t k,
ae_state *_state);
void minqpoptimize(minqpstate* state, ae_state *_state);
void minqpresults(minqpstate* state,
/* Real */ ae_vector* x,
minqpreport* rep,
ae_state *_state);
void minqpresultsbuf(minqpstate* state,
/* Real */ ae_vector* x,
minqpreport* rep,
ae_state *_state);
void minqpsetlineartermfast(minqpstate* state,
/* Real */ ae_vector* b,
ae_state *_state);
void minqpsetquadratictermfast(minqpstate* state,
/* Real */ ae_matrix* a,
ae_bool isupper,
double s,
ae_state *_state);
void minqprewritediagonal(minqpstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minqpsetstartingpointfast(minqpstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void minqpsetoriginfast(minqpstate* state,
/* Real */ ae_vector* xorigin,
ae_state *_state);
void _minqpstate_init(void* _p, ae_state *_state);
void _minqpstate_init_copy(void* _dst, void* _src, ae_state *_state);
void _minqpstate_clear(void* _p);
void _minqpstate_destroy(void* _p);
void _minqpreport_init(void* _p, ae_state *_state);
void _minqpreport_init_copy(void* _dst, void* _src, ae_state *_state);
void _minqpreport_clear(void* _p);
void _minqpreport_destroy(void* _p);
void minlmcreatevj(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
minlmstate* state,
ae_state *_state);
void minlmcreatev(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
double diffstep,
minlmstate* state,
ae_state *_state);
void minlmcreatefgh(ae_int_t n,
/* Real */ ae_vector* x,
minlmstate* state,
ae_state *_state);
void minlmsetcond(minlmstate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minlmsetxrep(minlmstate* state, ae_bool needxrep, ae_state *_state);
void minlmsetstpmax(minlmstate* state, double stpmax, ae_state *_state);
void minlmsetscale(minlmstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minlmsetbc(minlmstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void minlmsetacctype(minlmstate* state,
ae_int_t acctype,
ae_state *_state);
ae_bool minlmiteration(minlmstate* state, ae_state *_state);
void minlmresults(minlmstate* state,
/* Real */ ae_vector* x,
minlmreport* rep,
ae_state *_state);
void minlmresultsbuf(minlmstate* state,
/* Real */ ae_vector* x,
minlmreport* rep,
ae_state *_state);
void minlmrestartfrom(minlmstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void minlmrequesttermination(minlmstate* state, ae_state *_state);
void minlmcreatevgj(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
minlmstate* state,
ae_state *_state);
void minlmcreatefgj(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
minlmstate* state,
ae_state *_state);
void minlmcreatefj(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
minlmstate* state,
ae_state *_state);
void minlmsetgradientcheck(minlmstate* state,
double teststep,
ae_state *_state);
void _minlmstate_init(void* _p, ae_state *_state);
void _minlmstate_init_copy(void* _dst, void* _src, ae_state *_state);
void _minlmstate_clear(void* _p);
void _minlmstate_destroy(void* _p);
void _minlmreport_init(void* _p, ae_state *_state);
void _minlmreport_init_copy(void* _dst, void* _src, ae_state *_state);
void _minlmreport_clear(void* _p);
void _minlmreport_destroy(void* _p);
void minlbfgssetdefaultpreconditioner(minlbfgsstate* state,
ae_state *_state);
void minlbfgssetcholeskypreconditioner(minlbfgsstate* state,
/* Real */ ae_matrix* p,
ae_bool isupper,
ae_state *_state);
void minbleicsetbarrierwidth(minbleicstate* state,
double mu,
ae_state *_state);
void minbleicsetbarrierdecay(minbleicstate* state,
double mudecay,
ae_state *_state);
void minasacreate(ae_int_t n,
/* Real */ ae_vector* x,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
minasastate* state,
ae_state *_state);
void minasasetcond(minasastate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minasasetxrep(minasastate* state, ae_bool needxrep, ae_state *_state);
void minasasetalgorithm(minasastate* state,
ae_int_t algotype,
ae_state *_state);
void minasasetstpmax(minasastate* state, double stpmax, ae_state *_state);
ae_bool minasaiteration(minasastate* state, ae_state *_state);
void minasaresults(minasastate* state,
/* Real */ ae_vector* x,
minasareport* rep,
ae_state *_state);
void minasaresultsbuf(minasastate* state,
/* Real */ ae_vector* x,
minasareport* rep,
ae_state *_state);
void minasarestartfrom(minasastate* state,
/* Real */ ae_vector* x,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void _minasastate_init(void* _p, ae_state *_state);
void _minasastate_init_copy(void* _dst, void* _src, ae_state *_state);
void _minasastate_clear(void* _p);
void _minasastate_destroy(void* _p);
void _minasareport_init(void* _p, ae_state *_state);
void _minasareport_init_copy(void* _dst, void* _src, ae_state *_state);
void _minasareport_clear(void* _p);
void _minasareport_destroy(void* _p);
void minnlccreate(ae_int_t n,
/* Real */ ae_vector* x,
minnlcstate* state,
ae_state *_state);
void minnlccreatef(ae_int_t n,
/* Real */ ae_vector* x,
double diffstep,
minnlcstate* state,
ae_state *_state);
void minnlcsetbc(minnlcstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void minnlcsetlc(minnlcstate* state,
/* Real */ ae_matrix* c,
/* Integer */ ae_vector* ct,
ae_int_t k,
ae_state *_state);
void minnlcsetnlc(minnlcstate* state,
ae_int_t nlec,
ae_int_t nlic,
ae_state *_state);
void minnlcsetcond(minnlcstate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minnlcsetscale(minnlcstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minnlcsetprecinexact(minnlcstate* state, ae_state *_state);
void minnlcsetprecexactlowrank(minnlcstate* state,
ae_int_t updatefreq,
ae_state *_state);
void minnlcsetprecnone(minnlcstate* state, ae_state *_state);
void minnlcsetalgoaul(minnlcstate* state,
double rho,
ae_int_t itscnt,
ae_state *_state);
void minnlcsetxrep(minnlcstate* state, ae_bool needxrep, ae_state *_state);
ae_bool minnlciteration(minnlcstate* state, ae_state *_state);
void minnlcresults(minnlcstate* state,
/* Real */ ae_vector* x,
minnlcreport* rep,
ae_state *_state);
void minnlcresultsbuf(minnlcstate* state,
/* Real */ ae_vector* x,
minnlcreport* rep,
ae_state *_state);
void minnlcrestartfrom(minnlcstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void minnlcsetgradientcheck(minnlcstate* state,
double teststep,
ae_state *_state);
void minnlcequalitypenaltyfunction(double alpha,
double* f,
double* df,
double* d2f,
ae_state *_state);
void minnlcinequalitypenaltyfunction(double alpha,
double stabilizingpoint,
double* f,
double* df,
double* d2f,
ae_state *_state);
void minnlcinequalityshiftfunction(double alpha,
double* f,
double* df,
double* d2f,
ae_state *_state);
void _minnlcstate_init(void* _p, ae_state *_state);
void _minnlcstate_init_copy(void* _dst, void* _src, ae_state *_state);
void _minnlcstate_clear(void* _p);
void _minnlcstate_destroy(void* _p);
void _minnlcreport_init(void* _p, ae_state *_state);
void _minnlcreport_init_copy(void* _dst, void* _src, ae_state *_state);
void _minnlcreport_clear(void* _p);
void _minnlcreport_destroy(void* _p);
void minnscreate(ae_int_t n,
/* Real */ ae_vector* x,
minnsstate* state,
ae_state *_state);
void minnscreatef(ae_int_t n,
/* Real */ ae_vector* x,
double diffstep,
minnsstate* state,
ae_state *_state);
void minnssetbc(minnsstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void minnssetlc(minnsstate* state,
/* Real */ ae_matrix* c,
/* Integer */ ae_vector* ct,
ae_int_t k,
ae_state *_state);
void minnssetnlc(minnsstate* state,
ae_int_t nlec,
ae_int_t nlic,
ae_state *_state);
void minnssetcond(minnsstate* state,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minnssetscale(minnsstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minnssetalgoags(minnsstate* state,
double radius,
double penalty,
ae_state *_state);
void minnssetxrep(minnsstate* state, ae_bool needxrep, ae_state *_state);
void minnsrequesttermination(minnsstate* state, ae_state *_state);
ae_bool minnsiteration(minnsstate* state, ae_state *_state);
void minnsresults(minnsstate* state,
/* Real */ ae_vector* x,
minnsreport* rep,
ae_state *_state);
void minnsresultsbuf(minnsstate* state,
/* Real */ ae_vector* x,
minnsreport* rep,
ae_state *_state);
void minnsrestartfrom(minnsstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void _minnsqp_init(void* _p, ae_state *_state);
void _minnsqp_init_copy(void* _dst, void* _src, ae_state *_state);
void _minnsqp_clear(void* _p);
void _minnsqp_destroy(void* _p);
void _minnsstate_init(void* _p, ae_state *_state);
void _minnsstate_init_copy(void* _dst, void* _src, ae_state *_state);
void _minnsstate_clear(void* _p);
void _minnsstate_destroy(void* _p);
void _minnsreport_init(void* _p, ae_state *_state);
void _minnsreport_init_copy(void* _dst, void* _src, ae_state *_state);
void _minnsreport_clear(void* _p);
void _minnsreport_destroy(void* _p);
}
#endif
|