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added a section for the optimization package in the user guide 

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<?xml version="1.0"?>
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<?xml-stylesheet type="text/xsl" href="./xdoc.xsl"?>
<!-- $Revision: 480435 $ $Date: 2006-11-29 08:06:35 +0100 (mer., 29 nov. 2006) $ -->
<document url="optimization.html">
<properties>
<title>The Commons Math User Guide - Optimization</title>
</properties>
<body>
<section name="13 Optimization">
<subsection name="13.1 Overview" href="overview">
<p>
The optimization package provides simplex-based direct search optimization algorithms.
</p>
<p>
The aim of this package is similar to the aim of the estimation package, but the
algorithms are entirely differents as:
<ul>
<li>
they do not need the partial derivatives of the measurements
with respect to the free parameters
</li>
<li>
they do not rely on residuals-based quadratic cost functions but
handle any cost functions, including non-continuous ones!
</ul>
</p>
</subsection>
<subsection name="13.2 Direct Methods" href="direct">
<p>
Direct search methods only use cost function values, they don't
need derivatives and don't either try to compute approximation of
the derivatives. According to a 1996 paper by Margaret H. Wright
(<a href="http://cm.bell-labs.com/cm/cs/doc/96/4-02.ps.gz">Direct
Search Methods: Once Scorned, Now Respectable</a>), they are used
when either the computation of the derivative is impossible (noisy
functions, unpredictable dicontinuities) or difficult (complexity,
computation cost). In the first cases, rather than an optimum, a
<em>not too bad</em> point is desired. In the latter cases, an
optimum is desired but cannot be reasonably found. In all cases
direct search methods can be useful.
</p>
<p>
Simplex-based direct search methods are based on comparison of
the cost function values at the vertices of a simplex (which is a
set of n+1 points in dimension n) that is updated by the algorithms
steps.
</p>
<p>
The instances can be built either in single-start or in
multi-start mode. Multi-start is a traditional way to try to avoid
beeing trapped in a local minimum and miss the global minimum of a
function. It can also be used to verify the convergence of an
algorithm. In multi-start mode, the <code>minimizes</code>method
returns the best minimum found after all starts, and the <code>etMinima</code>
method can be used to retrieve all minima from all starts (including the one
already provided by the <code>minimizes</code> method).
</p>
<p>
The package provides two solvers. The first one is the classical
<a href="../apidocs/org/apache/commons/math/optimization/NelderMead.html">
Nelder-Mead</a> method. The second one is Virginia Torczon's
<a href="../apidocs/org/apache/commons/math/optimization/MultiDirectional.html">
multi-directional</a> method.
</p>
</subsection>
</section>
</body>
</document>