Author: luc
Date: Tue Mar 13 13:03:21 2007
New Revision: 517839
URL: http://svn.apache.org/viewvc?view=rev&rev=517839
Log:
added a section for the optimization package in the user guide
Added:
jakarta/commons/proper/math/trunk/xdocs/userguide/optimization.xml (with
props)
Added: jakarta/commons/proper/math/trunk/xdocs/userguide/optimization.xml
URL:
http://svn.apache.org/viewvc/jakarta/commons/proper/math/trunk/xdocs/userguide/optimization.xml?view=auto&rev=517839
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--- jakarta/commons/proper/math/trunk/xdocs/userguide/optimization.xml (added)
+++ jakarta/commons/proper/math/trunk/xdocs/userguide/optimization.xml Tue Mar
13 13:03:21 2007
@@ -0,0 +1,88 @@
+<?xml version="1.0"?>
+
+<!--
+ Licensed to the Apache Software Foundation (ASF) under one or more
+ contributor license agreements. See the NOTICE file distributed with
+ this work for additional information regarding copyright ownership.
+ The ASF licenses this file to You under the Apache License, Version 2.0
+ (the "License"); you may not use this file except in compliance with
+ the License. You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+ Unless required by applicable law or agreed to in writing, software
+ distributed under the License is distributed on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ See the License for the specific language governing permissions and
+ limitations under the License.
+ -->
+
+<?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>
Propchange: jakarta/commons/proper/math/trunk/xdocs/userguide/optimization.xml
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