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<h1 align="left"><u>Introduction to lp_solve 5.5.0.13</u></h1>
<p>What is lp_solve and what is it not?
The simple answer is, lp_solve is a Mixed Integer Linear Programming (MILP) solver.</p>
<p>And what is Linear Programming?
See <a href="http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html#Q1">"What is Linear Programming?"</a>
and <a href="http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html#Q3">"Oh, and we also want to solve it as an integer program."</a>
for a brief description.
Also see <a href="formulate.htm">Formulation of an lp problem in lpsolve</a>.</p>
<p>lp_solve is a <b>free</b> (see <a href="LGPL.htm">LGPL</a> for the GNU lesser general public license)
linear (integer) programming solver based on the revised simplex method and the Branch-and-bound method
for the integers.<br>
It contains <b>full source, examples and manuals</b>.<br>
lp_solve solves pure linear, (mixed) integer/binary, semi-continuous and special ordered sets (SOS) models.
Note the word linear. This means that equations must be of the first order. 5 * x - 3 * y is an example. However
x * y is not linear and cannot be handled by lp_solve. Both the objective function and the
constraints have this restriction. Also see <a href="ratio.htm">Ratios</a>.<br>
Via the Branch-and-bound algorithm, it can handle integer variables
(see <a href="integer.htm">integer variables</a>), semi-continuous variables (see <a href="semi-cont.htm">semi-continuous variables</a>)
and Special Ordered Sets (see <a href="SOS.htm">Special Ordered Sets (SOS)</a>).<br>
lp_solve has no limit on model size and accepts standard both lp or mps input files, but even that can be extended.
Note however that some models could give lp_solve a hard time and will even fail to solve. The larger the model
the likely the chance for that. But even commercial solvers have problems with that.<br>
It can also be called as a library from different languages like C, VB, .NET, Delphi, Excel, Java, ...<br>
It can also be called from AMPL, MATLAB, O-Matrix, Scilab, Octave, R via a driver program.
lp_solve is written in ANSI C and can be compiled on many different platforms like linux and WINDOWS.</p>
<p>lp_solve has its own community via the Yahoo group <a href="http://groups.yahoo.com/group/lp_solve">http://groups.yahoo.com/group/lp_solve/</a>.
There you can find the latest sources, executables for the common platforms, examples, manuals and a message
board where people can share their thoughts on lp_solve.</p>
<p>lp_solve was originally developed by <a href="mailto:michel@magma-da.com">Michel Berkelaar</a> at Eindhoven University of Technology.
The work of <a href="mailto:jeroen.dirks@sympatico.ca">Jeroen Dirks</a> made the transition from the basic version 1.5 to the full version 2.0 possible.
He contributed the procedural interface, a built-in MPS reader, and many fixes and enhancements to the code.
At that point there was also a Java port of lp_solve 2.0. This was not a Java native interface (JNI) to the C
library, but rather a translation of the algorithm (ver 2.0) from C into Java. It was also very limited
This meant that it did not keep up with lp_solve as it evolved.
Starting at version 3.0, lp_solve is released under the LGPL license. Before the code could only be used for
non-commercial purposes. Many other people also contributed to lp_solve, but there was no track of them. Sorry
if you are not mentioned.
Development was stagnated for some time at version 3.2, but now it is again alive and well via the new
developers <a href="mailto:kjell.eikland@broadpark.no">Kjell Eikland</a> and <a href="mailto:lpsolve@peno.be">Peter Notebaert</a>.
But also other people help to improve the product.
For example the new Java interface to lp_solve was made by <a href="mailto:juergen.ebert@web.de">Juergen Ebert</a>.
It is a JNI interface that supports the full functionality of lp_solve. He did a great job. We encourage other people to participate in the development of lp_solve.<br>
First a version 4 was introduced that had already several enhancements
and improvements and now with version 5 this enhancement continues resulting is faster solving times,
more stability and able to solver larger models and new functionality.
See <a href="changes5.htm">Changes from version 4 to version 5.1</a> for the changes done to version 5
and <a href="changes55.htm">Changes from version 5.1 to version 5.5</a> for the changes done to version 5.5.</p>
<p>Basically, lp_solve is a library, a set of routines, called the API that can be called from almost
any programming language to solve MILP problems. There are several ways to pass the data to the library:</p>
<ul>
<li>Via the API
<li>Via input files</li>
<li>Via an IDE</li>
</ul>
<h4>Via the API</h4>
The API is a set of routines that can be called from a programming language to build the model
in memory, solve it and return the results. There are many API routines to perform many possible
tasks and set several options. See <a href="lp_solveAPIreference.htm">lp_solve API reference</a> for an overview.<br><br>
<h4>Via input files</h4>
<p>Standard, lp_solve supports several input files types.
The common known MPS format (see <a href="mps-format.htm">mps-format</a>) is supported by most solvers, but
it is not very readable for humans. Another format is the lp format (see <a href="lp-format.htm">lp-format</a>)
that is more readable. lp_solve has the unique ability to use user-written routines to input the model
(see <a href="XLI.htm">External Language Interface</a>).
See <a href="read_mps.htm">read_mps, read_freemps, read_MPS, read_freeMPS</a> and <a href="read_lp.htm">read_lp, read_LP</a> for
the API calls to read the model from file.<br>
<br>
There is also a driver program called lp_solve that uses the API to provide a command line application
to solve models. See <a href="lp_solve.htm">lp_solve</a> for its usage. With this program you don't
have to know anything of API or computer programming languages. You can just provide your model
via file to the program and it will solve the model and give you the result.</p>
<h4>Via an IDE</h4>
<p>Thanks to <a href="mailto:hgourvest@progdigy.com">Henri Gourvest</a>, there is now also an IDE program called LPSolve IDE that uses the API to provide a Windows application
to solve models. See <a href="IDE.htm">LPSolve IDE</a> for its usage. With this program you don't
have to know anything of API or computer programming languages. You can just provide your model
to the program and it will solve the model and give you the result.</p>
<p>As already stated, lp_solve can be called from many programming language. Among them are
C, C++, Pascal, Delphi, Java, VB, C#, VB.NET, Excel. But let this list not be a limitation.
Any programming language capable of calling external libraries (DLLs under Windows, Shared libraries (.so) under Unix/Linux)
can call lp_solve.</p>
<p>Here is a list of some key features of lp_solve:</p>
<ul>
<li>Mixed Integer Linear Programming (MILP) solver
<li>Basically no limit on model size
<li>It is free and with sources
<li>Supports Integer variables, Semi-continuous
variables and Special Ordered Sets
<li>Can read model from MPS, LP or user written
format
<li>Models can be build in-memory without the use of
files
<li>Has a powerful API interface
<li>Easy callable from other programming languages
<li>Advanced pricing using Devex and Steepest Edge
for both primal and dual simplexes
<li>Provides different scaling methods to make the
model more numerical stable
<li>Has presolve capabilities to tighten
constraints/make the model smaller and faster to solve
<li>Has a base crashing routine to determine a
starting point
<li>Allows restart after making changes to the
model. Solve continues from the last found solution
<li>Possible to select desired combinations of
primal and dual phases 1 and 2
<li>Possible to set several solver parameters like
tolerances
<li>Alternative (and faster) inverse/re-factorisation libraries are provided for. See <A href="BFP.htm">Basis Factorization Packages</A>
<li>Alternative model readers and writers possible via the XLI implementation. See <A href="XLI.htm">External Language Interfaces</A>
<li>Has the possibility to convert one model format
to another format
<li>Provides post-optimal sensitivity analysis. See <A href="sensitivity.htm">Sensitivity</A>
<li>...</li>
</ul>
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