90 lines
4.0 KiB
XML
90 lines
4.0 KiB
XML
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<!--
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Licensed to the Apache Software Foundation (ASF) under one or more
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contributor license agreements. See the NOTICE file distributed with
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this work for additional information regarding copyright ownership.
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The ASF licenses this file to You under the Apache License, Version 2.0
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(the "License"); you may not use this file except in compliance with
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the License. You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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<?xml-stylesheet type="text/xsl" href="./xdoc.xsl"?>
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<!-- $Revision: 480435 $ $Date: 2006-11-29 08:06:35 +0100 (mer., 29 nov. 2006) $ -->
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<document url="optimization.html">
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<properties>
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<title>The Commons Math User Guide - Optimization</title>
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</properties>
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<body>
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<section name="13 Optimization">
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<subsection name="13.1 Overview" href="overview">
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<p>
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The optimization package provides simplex-based direct search optimization algorithms.
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</p>
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<p>
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The aim of this package is similar to the aim of the estimation package, but the
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algorithms are entirely differents as:
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<ul>
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<li>
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they do not need the partial derivatives of the measurements
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with respect to the free parameters
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</li>
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<li>
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they do not rely on residuals-based quadratic cost functions but
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handle any cost functions, including non-continuous ones!
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</li>
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</ul>
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</p>
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</subsection>
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<subsection name="13.2 Direct Methods" href="direct">
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<p>
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Direct search methods only use cost function values, they don't
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need derivatives and don't either try to compute approximation of
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the derivatives. According to a 1996 paper by Margaret H. Wright
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(<a href="http://cm.bell-labs.com/cm/cs/doc/96/4-02.ps.gz">Direct
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Search Methods: Once Scorned, Now Respectable</a>), they are used
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when either the computation of the derivative is impossible (noisy
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functions, unpredictable dicontinuities) or difficult (complexity,
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computation cost). In the first cases, rather than an optimum, a
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<em>not too bad</em> point is desired. In the latter cases, an
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optimum is desired but cannot be reasonably found. In all cases
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direct search methods can be useful.
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</p>
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<p>
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Simplex-based direct search methods are based on comparison of
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the cost function values at the vertices of a simplex (which is a
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set of n+1 points in dimension n) that is updated by the algorithms
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steps.
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</p>
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<p>
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The instances can be built either in single-start or in
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multi-start mode. Multi-start is a traditional way to try to avoid
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beeing trapped in a local minimum and miss the global minimum of a
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function. It can also be used to verify the convergence of an
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algorithm. In multi-start mode, the <code>minimizes</code>method
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returns the best minimum found after all starts, and the <code>etMinima</code>
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method can be used to retrieve all minima from all starts (including the one
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already provided by the <code>minimizes</code> method).
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</p>
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<p>
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The package provides two solvers. The first one is the classical
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<a href="../apidocs/org/apache/commons/math/optimization/NelderMead.html">
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Nelder-Mead</a> method. The second one is Virginia Torczon's
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<a href="../apidocs/org/apache/commons/math/optimization/MultiDirectional.html">
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multi-directional</a> method.
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</p>
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</subsection>
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</section>
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</body>
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</document>
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