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8 org.apache.commons.math.optimization (Commons Math 2.1 API)
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83 <H2>
84 Package org.apache.commons.math.optimization
85 </H2>
86
87 This package provides common interfaces for the optimization algorithms
88 provided in sub-packages.
89 <P>
90 <B>See:</B>
91 <BR>
92 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<A HREF="#package_description"><B>Description</B></A>
93 <P>
94
95 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
96 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
97 <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
98 <B>Interface Summary</B></FONT></TH>
99 </TR>
100 <TR BGCOLOR="white" CLASS="TableRowColor">
101 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/DifferentiableMultivariateRealOptimizer.html" title="interface in org.apache.commons.math.optimization">DifferentiableMultivariateRealOptimizer</A></B></TD>
102 <TD>This interface represents an optimization algorithm for <A HREF="../../../../../org/apache/commons/math/analysis/DifferentiableMultivariateRealFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>scalar differentiable objective functions</CODE></A>.</TD>
103 </TR>
104 <TR BGCOLOR="white" CLASS="TableRowColor">
105 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/DifferentiableMultivariateVectorialOptimizer.html" title="interface in org.apache.commons.math.optimization">DifferentiableMultivariateVectorialOptimizer</A></B></TD>
106 <TD>This interface represents an optimization algorithm for <A HREF="../../../../../org/apache/commons/math/analysis/DifferentiableMultivariateVectorialFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>vectorial differentiable objective functions</CODE></A>.</TD>
107 </TR>
108 <TR BGCOLOR="white" CLASS="TableRowColor">
109 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/MultivariateRealOptimizer.html" title="interface in org.apache.commons.math.optimization">MultivariateRealOptimizer</A></B></TD>
110 <TD>This interface represents an optimization algorithm for <A HREF="../../../../../org/apache/commons/math/analysis/MultivariateRealFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>scalar objective functions</CODE></A>.</TD>
111 </TR>
112 <TR BGCOLOR="white" CLASS="TableRowColor">
113 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/RealConvergenceChecker.html" title="interface in org.apache.commons.math.optimization">RealConvergenceChecker</A></B></TD>
114 <TD>This interface specifies how to check if an <A HREF="../../../../../org/apache/commons/math/optimization/MultivariateRealOptimizer.html" title="interface in org.apache.commons.math.optimization"><CODE>optimization
115 algorithm</CODE></A> has converged.</TD>
116 </TR>
117 <TR BGCOLOR="white" CLASS="TableRowColor">
118 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/UnivariateRealOptimizer.html" title="interface in org.apache.commons.math.optimization">UnivariateRealOptimizer</A></B></TD>
119 <TD>Interface for (univariate real) optimization algorithms.</TD>
120 </TR>
121 <TR BGCOLOR="white" CLASS="TableRowColor">
122 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/VectorialConvergenceChecker.html" title="interface in org.apache.commons.math.optimization">VectorialConvergenceChecker</A></B></TD>
123 <TD>This interface specifies how to check if a <A HREF="../../../../../org/apache/commons/math/optimization/DifferentiableMultivariateVectorialOptimizer.html" title="interface in org.apache.commons.math.optimization"><CODE>optimization algorithm</CODE></A> has converged.</TD>
124 </TR>
125 </TABLE>
126 &nbsp;
127
128 <P>
129
130 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
131 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
132 <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
133 <B>Class Summary</B></FONT></TH>
134 </TR>
135 <TR BGCOLOR="white" CLASS="TableRowColor">
136 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/LeastSquaresConverter.html" title="class in org.apache.commons.math.optimization">LeastSquaresConverter</A></B></TD>
137 <TD>This class converts <A HREF="../../../../../org/apache/commons/math/analysis/MultivariateVectorialFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>vectorial
138 objective functions</CODE></A> to <A HREF="../../../../../org/apache/commons/math/analysis/MultivariateRealFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>scalar objective functions</CODE></A>
139 when the goal is to minimize them.</TD>
140 </TR>
141 <TR BGCOLOR="white" CLASS="TableRowColor">
142 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/MultiStartDifferentiableMultivariateRealOptimizer.html" title="class in org.apache.commons.math.optimization">MultiStartDifferentiableMultivariateRealOptimizer</A></B></TD>
143 <TD>Special implementation of the <A HREF="../../../../../org/apache/commons/math/optimization/DifferentiableMultivariateRealOptimizer.html" title="interface in org.apache.commons.math.optimization"><CODE>DifferentiableMultivariateRealOptimizer</CODE></A> interface adding
144 multi-start features to an existing optimizer.</TD>
145 </TR>
146 <TR BGCOLOR="white" CLASS="TableRowColor">
147 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/MultiStartDifferentiableMultivariateVectorialOptimizer.html" title="class in org.apache.commons.math.optimization">MultiStartDifferentiableMultivariateVectorialOptimizer</A></B></TD>
148 <TD>Special implementation of the <A HREF="../../../../../org/apache/commons/math/optimization/DifferentiableMultivariateVectorialOptimizer.html" title="interface in org.apache.commons.math.optimization"><CODE>DifferentiableMultivariateVectorialOptimizer</CODE></A> interface adding
149 multi-start features to an existing optimizer.</TD>
150 </TR>
151 <TR BGCOLOR="white" CLASS="TableRowColor">
152 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/MultiStartMultivariateRealOptimizer.html" title="class in org.apache.commons.math.optimization">MultiStartMultivariateRealOptimizer</A></B></TD>
153 <TD>Special implementation of the <A HREF="../../../../../org/apache/commons/math/optimization/MultivariateRealOptimizer.html" title="interface in org.apache.commons.math.optimization"><CODE>MultivariateRealOptimizer</CODE></A> interface adding
154 multi-start features to an existing optimizer.</TD>
155 </TR>
156 <TR BGCOLOR="white" CLASS="TableRowColor">
157 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/MultiStartUnivariateRealOptimizer.html" title="class in org.apache.commons.math.optimization">MultiStartUnivariateRealOptimizer</A></B></TD>
158 <TD>Special implementation of the <A HREF="../../../../../org/apache/commons/math/optimization/UnivariateRealOptimizer.html" title="interface in org.apache.commons.math.optimization"><CODE>UnivariateRealOptimizer</CODE></A> interface adding
159 multi-start features to an existing optimizer.</TD>
160 </TR>
161 <TR BGCOLOR="white" CLASS="TableRowColor">
162 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/RealPointValuePair.html" title="class in org.apache.commons.math.optimization">RealPointValuePair</A></B></TD>
163 <TD>This class holds a point and the value of an objective function at this point.</TD>
164 </TR>
165 <TR BGCOLOR="white" CLASS="TableRowColor">
166 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/SimpleRealPointChecker.html" title="class in org.apache.commons.math.optimization">SimpleRealPointChecker</A></B></TD>
167 <TD>Simple implementation of the <A HREF="../../../../../org/apache/commons/math/optimization/RealConvergenceChecker.html" title="interface in org.apache.commons.math.optimization"><CODE>RealConvergenceChecker</CODE></A> interface using
168 only point coordinates.</TD>
169 </TR>
170 <TR BGCOLOR="white" CLASS="TableRowColor">
171 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/SimpleScalarValueChecker.html" title="class in org.apache.commons.math.optimization">SimpleScalarValueChecker</A></B></TD>
172 <TD>Simple implementation of the <A HREF="../../../../../org/apache/commons/math/optimization/RealConvergenceChecker.html" title="interface in org.apache.commons.math.optimization"><CODE>RealConvergenceChecker</CODE></A> interface using
173 only objective function values.</TD>
174 </TR>
175 <TR BGCOLOR="white" CLASS="TableRowColor">
176 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/SimpleVectorialPointChecker.html" title="class in org.apache.commons.math.optimization">SimpleVectorialPointChecker</A></B></TD>
177 <TD>Simple implementation of the <A HREF="../../../../../org/apache/commons/math/optimization/VectorialConvergenceChecker.html" title="interface in org.apache.commons.math.optimization"><CODE>VectorialConvergenceChecker</CODE></A> interface using
178 only point coordinates.</TD>
179 </TR>
180 <TR BGCOLOR="white" CLASS="TableRowColor">
181 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/SimpleVectorialValueChecker.html" title="class in org.apache.commons.math.optimization">SimpleVectorialValueChecker</A></B></TD>
182 <TD>Simple implementation of the <A HREF="../../../../../org/apache/commons/math/optimization/VectorialConvergenceChecker.html" title="interface in org.apache.commons.math.optimization"><CODE>VectorialConvergenceChecker</CODE></A> interface using
183 only objective function values.</TD>
184 </TR>
185 <TR BGCOLOR="white" CLASS="TableRowColor">
186 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/VectorialPointValuePair.html" title="class in org.apache.commons.math.optimization">VectorialPointValuePair</A></B></TD>
187 <TD>This class holds a point and the vectorial value of an objective function at this point.</TD>
188 </TR>
189 </TABLE>
190 &nbsp;
191
192 <P>
193
194 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
195 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
196 <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
197 <B>Enum Summary</B></FONT></TH>
198 </TR>
199 <TR BGCOLOR="white" CLASS="TableRowColor">
200 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/GoalType.html" title="enum in org.apache.commons.math.optimization">GoalType</A></B></TD>
201 <TD>Goal type for an optimization problem.</TD>
202 </TR>
203 </TABLE>
204 &nbsp;
205
206 <P>
207
208 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
209 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
210 <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
211 <B>Exception Summary</B></FONT></TH>
212 </TR>
213 <TR BGCOLOR="white" CLASS="TableRowColor">
214 <TD WIDTH="15%"><B><A HREF="../../../../../org/apache/commons/math/optimization/OptimizationException.html" title="class in org.apache.commons.math.optimization">OptimizationException</A></B></TD>
215 <TD>This class represents exceptions thrown by optimizers.</TD>
216 </TR>
217 </TABLE>
218 &nbsp;
219
220 <P>
221 <A NAME="package_description"><!-- --></A><H2>
222 Package org.apache.commons.math.optimization Description
223 </H2>
224
225 <P>
226 <p>
227 This package provides common interfaces for the optimization algorithms
228 provided in sub-packages. The main interfaces defines optimizers and convergence
229 checkers. The functions that are optimized by the algorithms provided by this
230 package and its sub-packages are a subset of the one defined in the <code>analysis</code>
231 package, namely the real and vector valued functions. These functions are called
232 objective function here. When the goal is to minimize, the functions are often called
233 cost function, this name is not used in this package.
234 </p>
235
236 <p>
237 Optimizers are the algorithms that will either minimize or maximize, the objective function
238 by changing its input variables set until an optimal set is found. There are only four
239 interfaces defining the common behavior of optimizers, one for each supported type of objective
240 function:
241 <ul>
242 <li><A HREF="../../../../../org/apache/commons/math/optimization/UnivariateRealOptimizer.html" title="interface in org.apache.commons.math.optimization"><CODE>UnivariateRealOptimizer</CODE></A> for <A HREF="../../../../../org/apache/commons/math/analysis/UnivariateRealFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>univariate real functions</CODE></A></li>
243 <li><A HREF="../../../../../org/apache/commons/math/optimization/MultivariateRealOptimizer.html" title="interface in org.apache.commons.math.optimization"><CODE>MultivariateRealOptimizer</CODE></A> for <A HREF="../../../../../org/apache/commons/math/analysis/MultivariateRealFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>multivariate real functions</CODE></A></li>
244 <li><A HREF="../../../../../org/apache/commons/math/optimization/DifferentiableMultivariateRealOptimizer.html" title="interface in org.apache.commons.math.optimization"><CODE>DifferentiableMultivariateRealOptimizer</CODE></A> for <A HREF="../../../../../org/apache/commons/math/analysis/DifferentiableMultivariateRealFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>differentiable multivariate real functions</CODE></A></li>
245 <li><A HREF="../../../../../org/apache/commons/math/optimization/DifferentiableMultivariateVectorialOptimizer.html" title="interface in org.apache.commons.math.optimization"><CODE>DifferentiableMultivariateVectorialOptimizer</CODE></A> for <A HREF="../../../../../org/apache/commons/math/analysis/DifferentiableMultivariateVectorialFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>differentiable multivariate vectorial functions</CODE></A></li>
246 </ul>
247 </p>
248
249 <p>
250 Despite there are only four types of supported optimizers, it is possible to optimize a
251 transform a <A HREF="../../../../../org/apache/commons/math/analysis/MultivariateVectorialFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>non-differentiable multivariate vectorial function</CODE></A> by converting it to a <A HREF="../../../../../org/apache/commons/math/analysis/MultivariateRealFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>non-differentiable multivariate
252 real function</CODE></A> thanks to the <A HREF="../../../../../org/apache/commons/math/optimization/LeastSquaresConverter.html" title="class in org.apache.commons.math.optimization"><CODE>LeastSquaresConverter</CODE></A> helper class.
253 The transformed function can be optimized using any implementation of the <A HREF="../../../../../org/apache/commons/math/optimization/MultivariateRealOptimizer.html" title="interface in org.apache.commons.math.optimization"><CODE>MultivariateRealOptimizer</CODE></A> interface.
254 </p>
255
256 <p>
257 For each of the four types of supported optimizers, there is a special implementation which
258 wraps a classical optimizer in order to add it a multi-start feature. This feature call the
259 underlying optimizer several times in sequence with different starting points and returns
260 the best optimum found or all optima if desired. This is a classical way to prevent being
261 trapped into a local extremum when looking for a global one.
262 </p>
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