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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 | <html><head><meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1"><title>Plugin type: minimizer/singlecost</title><link rel="stylesheet" type="text/css" href="progref.css"><meta name="generator" content="DocBook XSL Stylesheets V1.79.1"><link rel="home" href="index.html" title="Mia Program Reference"><link rel="up" href="plugins.html" title="Chapter 3. Plugin Reference"><link rel="prev" href="SecPlugintypemeshio.html" title="Plugin type: mesh/io"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Plugin type: minimizer/singlecost</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="SecPlugintypemeshio.html">Prev</a> </td><th width="60%" align="center">Chapter 3. Plugin Reference</th><td width="20%" align="right"> </td></tr></table><hr></div><div class="section"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="SecPlugintypeminimizersinglecost"></a>Plugin type: minimizer/singlecost</h2></div></div></div><p class="plugdescr">These plug-ins provide optimizers of many-to-one functions</p><h4><a name="idp20828"></a>Plugins:</h4><p class="pluginlist">
<a class="xref" href="SecPlugintypeminimizersinglecost.html#plugingdasminimizersinglecost" title="gdas">gdas</a>
<a class="xref" href="SecPlugintypeminimizersinglecost.html#plugingdsqminimizersinglecost" title="gdsq">gdsq</a>
<a class="xref" href="SecPlugintypeminimizersinglecost.html#plugingslminimizersinglecost" title="gsl">gsl</a>
<a class="xref" href="SecPlugintypeminimizersinglecost.html#pluginnloptminimizersinglecost" title="nlopt">nlopt</a>
</p><p class="plugin">
</p><div class="sect4"><div class="titlepage"><div><div><h5 class="title"><a name="plugingdasminimizersinglecost"></a>gdas</h5></div></div></div><p class="plugindescr">Gradient descent with automatic step size correction.. Supported parameters are:</p><div class="informaltable"><table class="informaltable" width="100%" border="1"><colgroup><col width="10%" class="c1"><col width="20%" class="c2"><col width="10%" class="c3"></colgroup><thead><tr><th align="center" valign="top">Name</th><th align="center" valign="top">Type</th><th align="center" valign="top">Default</th><th align="center" valign="top">Description</th></tr></thead><tbody><tr><td align="center" valign="top">ftolr</td><td align="center" valign="top">double in [0, inf)</td><td align="center" valign="top">0</td><td align="left" valign="top">Stop if the relative change of the criterion is below.</td></tr><tr><td align="center" valign="top">max-step</td><td align="center" valign="top">double in (0, inf)</td><td align="center" valign="top">2</td><td align="left" valign="top">Maximal absolute step size</td></tr><tr><td align="center" valign="top">maxiter</td><td align="center" valign="top">uint in [1, inf)</td><td align="center" valign="top">200</td><td align="left" valign="top">Stopping criterion: the maximum number of iterations</td></tr><tr><td align="center" valign="top">min-step</td><td align="center" valign="top">double in (0, inf)</td><td align="center" valign="top">0.1</td><td align="left" valign="top">Minimal absolute step size</td></tr><tr><td align="center" valign="top">xtola</td><td align="center" valign="top">double in [0, inf)</td><td align="center" valign="top">0.01</td><td align="left" valign="top">Stop if the inf-norm of the change applied to x is below this value.</td></tr></tbody></table></div></div><p class="plugin">
</p><p class="plugin">
</p><div class="sect4"><div class="titlepage"><div><div><h5 class="title"><a name="plugingdsqminimizersinglecost"></a>gdsq</h5></div></div></div><p class="plugindescr">Gradient descent with quadratic step estimation. Supported parameters are:</p><div class="informaltable"><table class="informaltable" width="100%" border="1"><colgroup><col width="10%" class="c1"><col width="20%" class="c2"><col width="10%" class="c3"></colgroup><thead><tr><th align="center" valign="top">Name</th><th align="center" valign="top">Type</th><th align="center" valign="top">Default</th><th align="center" valign="top">Description</th></tr></thead><tbody><tr><td align="center" valign="top">ftolr</td><td align="center" valign="top">double in [0, inf)</td><td align="center" valign="top">0</td><td align="left" valign="top">Stop if the relative change of the criterion is below.</td></tr><tr><td align="center" valign="top">gtola</td><td align="center" valign="top">double in [0, inf)</td><td align="center" valign="top">0</td><td align="left" valign="top">Stop if the inf-norm of the gradient is below this value.</td></tr><tr><td align="center" valign="top">maxiter</td><td align="center" valign="top">uint in [1, inf)</td><td align="center" valign="top">100</td><td align="left" valign="top">Stopping criterion: the maximum number of iterations</td></tr><tr><td align="center" valign="top">scale</td><td align="center" valign="top">double in (1, inf)</td><td align="center" valign="top">2</td><td align="left" valign="top">Fallback fixed step size scaling</td></tr><tr><td align="center" valign="top">step</td><td align="center" valign="top">double in (0, inf)</td><td align="center" valign="top">0.1</td><td align="left" valign="top">Initial step size</td></tr><tr><td align="center" valign="top">xtola</td><td align="center" valign="top">double in [0, inf)</td><td align="center" valign="top">0</td><td align="left" valign="top">Stop if the inf-norm of x-update is below this value.</td></tr></tbody></table></div></div><p class="plugin">
</p><p class="plugin">
</p><div class="sect4"><div class="titlepage"><div><div><h5 class="title"><a name="plugingslminimizersinglecost"></a>gsl</h5></div></div></div><p class="plugindescr">optimizer plugin based on the multimin optimizers of the GNU Scientific Library (GSL) https://www.gnu.org/software/gsl/. Supported parameters are:</p><div class="informaltable"><table class="informaltable" width="100%" border="1"><colgroup><col width="10%" class="c1"><col width="20%" class="c2"><col width="10%" class="c3"></colgroup><thead><tr><th align="center" valign="top">Name</th><th align="center" valign="top">Type</th><th align="center" valign="top">Default</th><th align="center" valign="top">Description</th></tr></thead><tbody><tr><td align="center" valign="top">eps</td><td align="center" valign="top">double in (0, inf)</td><td align="center" valign="top">0.01</td><td align="left" valign="top">gradient based optimizers: stop when |grad| < eps, simplex: stop when simplex size < eps.</td></tr><tr><td align="center" valign="top">iter</td><td align="center" valign="top">uint in [1, inf)</td><td align="center" valign="top">100</td><td align="left" valign="top">maximum number of iterations</td></tr><tr><td align="center" valign="top">opt</td><td align="center" valign="top">dict</td><td align="center" valign="top">gd</td><td><div class="informaltable"><table class="informaltable" width="100%" border="1"><colgroup><col class="sc0"><col class="sc1"></colgroup><tbody><tr><td colspan="2" align="left" valign="top">Specific optimizer to be used.</td></tr><tr><td align="left" valign="top">bfgs:</td><td align="left" valign="top">Broyden-Fletcher-Goldfarb-Shann</td></tr><tr><td align="left" valign="top">bfgs2:</td><td align="left" valign="top">Broyden-Fletcher-Goldfarb-Shann (most efficient version)</td></tr><tr><td align="left" valign="top">cg-fr:</td><td align="left" valign="top">Flecher-Reeves conjugate gradient algorithm</td></tr><tr><td align="left" valign="top">gd:</td><td align="left" valign="top">Gradient descent.</td></tr><tr><td align="left" valign="top">simplex:</td><td align="left" valign="top">Simplex algorithm of Nelder and Mead</td></tr><tr><td align="left" valign="top">cg-pr:</td><td align="left" valign="top">Polak-Ribiere conjugate gradient algorithm</td></tr></tbody></table></div></td></tr><tr><td align="center" valign="top">step</td><td align="center" valign="top">double in (0, inf)</td><td align="center" valign="top">0.001</td><td align="left" valign="top">initial step size</td></tr><tr><td align="center" valign="top">tol</td><td align="center" valign="top">double in (0, inf)</td><td align="center" valign="top">0.1</td><td align="left" valign="top">some tolerance parameter</td></tr></tbody></table></div></div><p class="plugin">
</p><p class="plugin">
</p><div class="sect4"><div class="titlepage"><div><div><h5 class="title"><a name="pluginnloptminimizersinglecost"></a>nlopt</h5></div></div></div><p class="plugindescr">Minimizer algorithms using the NLOPT library, for a description of the optimizers please see 'http://ab-initio.mit.edu/wiki/index.php/NLopt_Algorithms'. Supported parameters are:</p><div class="informaltable"><table class="informaltable" width="100%" border="1"><colgroup><col width="10%" class="c1"><col width="20%" class="c2"><col width="10%" class="c3"></colgroup><thead><tr><th align="center" valign="top">Name</th><th align="center" valign="top">Type</th><th align="center" valign="top">Default</th><th align="center" valign="top">Description</th></tr></thead><tbody><tr><td align="center" valign="top">ftola</td><td align="center" valign="top">double in [0, inf)</td><td align="center" valign="top">0</td><td align="left" valign="top">Stopping criterion: the absolute change of the objective value is below this value</td></tr><tr><td align="center" valign="top">ftolr</td><td align="center" valign="top">double in [0, inf)</td><td align="center" valign="top">0</td><td align="left" valign="top">Stopping criterion: the relative change of the objective value is below this value</td></tr><tr><td align="center" valign="top">higher</td><td align="center" valign="top">double</td><td align="center" valign="top">inf</td><td align="left" valign="top">Higher boundary (equal for all parameters)</td></tr><tr><td align="center" valign="top">local-opt</td><td align="center" valign="top">dict</td><td align="center" valign="top">none</td><td><div class="informaltable"><table class="informaltable" width="100%" border="1"><colgroup><col class="sc0"><col class="sc1"></colgroup><tbody><tr><td colspan="2" align="left" valign="top">local minimization algorithm that may be required for the main minimization algorithm.</td></tr><tr><td align="left" valign="top">gn-orig-direct-l:</td><td align="left" valign="top">Dividing Rectangles (original implementation, locally biased)</td></tr><tr><td align="left" valign="top">gn-direct-l-noscal:</td><td align="left" valign="top">Dividing Rectangles (unscaled, locally biased)</td></tr><tr><td align="left" valign="top">gn-isres:</td><td align="left" valign="top">Improved Stochastic Ranking Evolution Strategy</td></tr><tr><td align="left" valign="top">ld-tnewton:</td><td align="left" valign="top">Truncated Newton</td></tr><tr><td align="left" valign="top">gn-direct-l-rand:</td><td align="left" valign="top">Dividing Rectangles (locally biased, randomized)</td></tr><tr><td align="left" valign="top">ln-newuoa:</td><td align="left" valign="top">Derivative-free Unconstrained Optimization by Iteratively Constructed Quadratic Approximation</td></tr><tr><td align="left" valign="top">gn-direct-l-rand-noscale:</td><td align="left" valign="top">Dividing Rectangles (unscaled, locally biased, randomized)</td></tr><tr><td align="left" valign="top">gn-orig-direct:</td><td align="left" valign="top">Dividing Rectangles (original implementation)</td></tr><tr><td align="left" valign="top">ld-tnewton-precond:</td><td align="left" valign="top">Preconditioned Truncated Newton</td></tr><tr><td align="left" valign="top">ld-tnewton-restart:</td><td align="left" valign="top">Truncated Newton with steepest-descent restarting</td></tr><tr><td align="left" valign="top">gn-direct:</td><td align="left" valign="top">Dividing Rectangles</td></tr><tr><td align="left" valign="top">ln-neldermead:</td><td align="left" valign="top">Nelder-Mead simplex algorithm</td></tr><tr><td align="left" valign="top">ln-cobyla:</td><td align="left" valign="top">Constrained Optimization BY Linear Approximation</td></tr><tr><td align="left" valign="top">gn-crs2-lm:</td><td align="left" valign="top">Controlled Random Search with Local Mutation</td></tr><tr><td align="left" valign="top">ld-var2:</td><td align="left" valign="top">Shifted Limited-Memory Variable-Metric, Rank 2</td></tr><tr><td align="left" valign="top">ld-var1:</td><td align="left" valign="top">Shifted Limited-Memory Variable-Metric, Rank 1</td></tr><tr><td align="left" valign="top">ld-mma:</td><td align="left" valign="top">Method of Moving Asymptotes</td></tr><tr><td align="left" valign="top">ld-lbfgs-nocedal:</td><td align="left" valign="top"> </td></tr><tr><td align="left" valign="top">ld-lbfgs:</td><td align="left" valign="top">Low-storage BFGS</td></tr><tr><td align="left" valign="top">gn-direct-l:</td><td align="left" valign="top">Dividing Rectangles (locally biased)</td></tr><tr><td align="left" valign="top">none:</td><td align="left" valign="top">don't specify algorithm</td></tr><tr><td align="left" valign="top">ln-bobyqa:</td><td align="left" valign="top">Derivative-free Bound-constrained Optimization</td></tr><tr><td align="left" valign="top">ln-sbplx:</td><td align="left" valign="top">Subplex variant of Nelder-Mead</td></tr><tr><td align="left" valign="top">ln-newuoa-bound:</td><td align="left" valign="top">Derivative-free Bound-constrained Optimization by Iteratively Constructed Quadratic Approximation</td></tr><tr><td align="left" valign="top">ln-praxis:</td><td align="left" valign="top">Gradient-free Local Optimization via the Principal-Axis Method</td></tr><tr><td align="left" valign="top">gn-direct-noscal:</td><td align="left" valign="top">Dividing Rectangles (unscaled)</td></tr><tr><td align="left" valign="top">ld-tnewton-precond-restart:</td><td align="left" valign="top">Preconditioned Truncated Newton with steepest-descent restarting</td></tr></tbody></table></div></td></tr><tr><td align="center" valign="top">lower</td><td align="center" valign="top">double</td><td align="center" valign="top">-inf</td><td align="left" valign="top">Lower boundary (equal for all parameters)</td></tr><tr><td align="center" valign="top">maxiter</td><td align="center" valign="top">int in [1, inf)</td><td align="center" valign="top">100</td><td align="left" valign="top">Stopping criterion: the maximum number of iterations</td></tr><tr><td align="center" valign="top">opt</td><td align="center" valign="top">dict</td><td align="center" valign="top">ld-lbfgs</td><td><div class="informaltable"><table class="informaltable" width="100%" border="1"><colgroup><col class="sc0"><col class="sc1"></colgroup><tbody><tr><td colspan="2" align="left" valign="top">main minimization algorithm</td></tr><tr><td align="left" valign="top">gn-orig-direct-l:</td><td align="left" valign="top">Dividing Rectangles (original implementation, locally biased)</td></tr><tr><td align="left" valign="top">g-mlsl-lds:</td><td align="left" valign="top">Multi-Level Single-Linkage (low-discrepancy-sequence, require local gradient based optimization and bounds)</td></tr><tr><td align="left" valign="top">gn-direct-l-noscal:</td><td align="left" valign="top">Dividing Rectangles (unscaled, locally biased)</td></tr><tr><td align="left" valign="top">gn-isres:</td><td align="left" valign="top">Improved Stochastic Ranking Evolution Strategy</td></tr><tr><td align="left" valign="top">ld-tnewton:</td><td align="left" valign="top">Truncated Newton</td></tr><tr><td align="left" valign="top">gn-direct-l-rand:</td><td align="left" valign="top">Dividing Rectangles (locally biased, randomized)</td></tr><tr><td align="left" valign="top">ln-newuoa:</td><td align="left" valign="top">Derivative-free Unconstrained Optimization by Iteratively Constructed Quadratic Approximation</td></tr><tr><td align="left" valign="top">gn-direct-l-rand-noscale:</td><td align="left" valign="top">Dividing Rectangles (unscaled, locally biased, randomized)</td></tr><tr><td align="left" valign="top">gn-orig-direct:</td><td align="left" valign="top">Dividing Rectangles (original implementation)</td></tr><tr><td align="left" valign="top">ld-tnewton-precond:</td><td align="left" valign="top">Preconditioned Truncated Newton</td></tr><tr><td align="left" valign="top">ld-tnewton-restart:</td><td align="left" valign="top">Truncated Newton with steepest-descent restarting</td></tr><tr><td align="left" valign="top">gn-direct:</td><td align="left" valign="top">Dividing Rectangles</td></tr><tr><td align="left" valign="top">auglag-eq:</td><td align="left" valign="top">Augmented Lagrangian algorithm with equality constraints only</td></tr><tr><td align="left" valign="top">ln-neldermead:</td><td align="left" valign="top">Nelder-Mead simplex algorithm</td></tr><tr><td align="left" valign="top">ln-cobyla:</td><td align="left" valign="top">Constrained Optimization BY Linear Approximation</td></tr><tr><td align="left" valign="top">gn-crs2-lm:</td><td align="left" valign="top">Controlled Random Search with Local Mutation</td></tr><tr><td align="left" valign="top">ld-var2:</td><td align="left" valign="top">Shifted Limited-Memory Variable-Metric, Rank 2</td></tr><tr><td align="left" valign="top">ld-var1:</td><td align="left" valign="top">Shifted Limited-Memory Variable-Metric, Rank 1</td></tr><tr><td align="left" valign="top">ld-mma:</td><td align="left" valign="top">Method of Moving Asymptotes</td></tr><tr><td align="left" valign="top">ld-lbfgs-nocedal:</td><td align="left" valign="top"> </td></tr><tr><td align="left" valign="top">g-mlsl:</td><td align="left" valign="top">Multi-Level Single-Linkage (require local optimization and bounds)</td></tr><tr><td align="left" valign="top">ld-lbfgs:</td><td align="left" valign="top">Low-storage BFGS</td></tr><tr><td align="left" valign="top">gn-direct-l:</td><td align="left" valign="top">Dividing Rectangles (locally biased)</td></tr><tr><td align="left" valign="top">ln-bobyqa:</td><td align="left" valign="top">Derivative-free Bound-constrained Optimization</td></tr><tr><td align="left" valign="top">ln-sbplx:</td><td align="left" valign="top">Subplex variant of Nelder-Mead</td></tr><tr><td align="left" valign="top">ln-newuoa-bound:</td><td align="left" valign="top">Derivative-free Bound-constrained Optimization by Iteratively Constructed Quadratic Approximation</td></tr><tr><td align="left" valign="top">auglag:</td><td align="left" valign="top">Augmented Lagrangian algorithm</td></tr><tr><td align="left" valign="top">ln-praxis:</td><td align="left" valign="top">Gradient-free Local Optimization via the Principal-Axis Method</td></tr><tr><td align="left" valign="top">gn-direct-noscal:</td><td align="left" valign="top">Dividing Rectangles (unscaled)</td></tr><tr><td align="left" valign="top">ld-tnewton-precond-restart:</td><td align="left" valign="top">Preconditioned Truncated Newton with steepest-descent restarting</td></tr><tr><td align="left" valign="top">ld-slsqp:</td><td align="left" valign="top">Sequential Least-Squares Quadratic Programming</td></tr></tbody></table></div></td></tr><tr><td align="center" valign="top">step</td><td align="center" valign="top">double in [0, inf)</td><td align="center" valign="top">0</td><td align="left" valign="top">Initial step size for gradient free methods</td></tr><tr><td align="center" valign="top">stop</td><td align="center" valign="top">double</td><td align="center" valign="top">-inf</td><td align="left" valign="top">Stopping criterion: function value falls below this value</td></tr><tr><td align="center" valign="top">xtola</td><td align="center" valign="top">double in [0, inf)</td><td align="center" valign="top">0</td><td align="left" valign="top">Stopping criterion: the absolute change of all x-values is below this value</td></tr><tr><td align="center" valign="top">xtolr</td><td align="center" valign="top">double in [0, inf)</td><td align="center" valign="top">0</td><td align="left" valign="top">Stopping criterion: the relative change of all x-values is below this value</td></tr></tbody></table></div></div><p class="plugin">
</p><h4><a name="idp21254"></a>Plugin consumers:</h4><p class="consumer">
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