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<div class="subTitle">org.apache.commons.math3.optimization.direct</div>
<h2 title="Class SimplexOptimizer" class="title">Class SimplexOptimizer</h2>
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<ul class="inheritance">
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<ul class="inheritance">
<li><a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html" title="class in org.apache.commons.math3.optimization.direct">org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateOptimizer</a>&lt;<a href="../../../../../../org/apache/commons/math3/analysis/MultivariateFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateFunction</a>&gt;</li>
<li>
<ul class="inheritance">
<li>org.apache.commons.math3.optimization.direct.SimplexOptimizer</li>
</ul>
</li>
</ul>
</li>
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<div class="description">
<ul class="blockList">
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<dl>
<dt>All Implemented Interfaces:</dt>
<dd><a href="../../../../../../org/apache/commons/math3/optimization/BaseMultivariateOptimizer.html" title="interface in org.apache.commons.math3.optimization">BaseMultivariateOptimizer</a>&lt;<a href="../../../../../../org/apache/commons/math3/analysis/MultivariateFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateFunction</a>&gt;, <a href="../../../../../../org/apache/commons/math3/optimization/BaseOptimizer.html" title="interface in org.apache.commons.math3.optimization">BaseOptimizer</a>&lt;<a href="../../../../../../org/apache/commons/math3/optimization/PointValuePair.html" title="class in org.apache.commons.math3.optimization">PointValuePair</a>&gt;, <a href="../../../../../../org/apache/commons/math3/optimization/MultivariateOptimizer.html" title="interface in org.apache.commons.math3.optimization">MultivariateOptimizer</a></dd>
</dl>
<hr>
<div class="block"><strong>Deprecated.</strong>&nbsp;
<div class="block"><i>As of 3.1 (to be removed in 4.0).</i></div>
</div>
<br>
<pre><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a>
public class <span class="strong">SimplexOptimizer</span>
extends <a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html" title="class in org.apache.commons.math3.optimization.direct">BaseAbstractMultivariateOptimizer</a>&lt;<a href="../../../../../../org/apache/commons/math3/analysis/MultivariateFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateFunction</a>&gt;
implements <a href="../../../../../../org/apache/commons/math3/optimization/MultivariateOptimizer.html" title="interface in org.apache.commons.math3.optimization">MultivariateOptimizer</a></pre>
<div class="block">This class implements simplex-based direct search optimization.
<p>
Direct search methods only use objective function values, they do
not 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 discontinuities) 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 objective 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 <a href="../../../../../../org/apache/commons/math3/optimization/direct/SimplexOptimizer.html#setSimplex(org.apache.commons.math3.optimization.direct.AbstractSimplex)"><code>setSimplex</code></a> method <em>must</em>
be called prior to calling the <code>optimize</code> method.
</p>
<p>
Each call to <a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#optimize(int, FUNC, org.apache.commons.math3.optimization.GoalType, double[])"><code>optimize</code></a> will re-use the start configuration of the current simplex and
move it such that its first vertex is at the provided start point of the
optimization. If the <code>optimize</code> method is called to solve a different
problem and the number of parameters change, the simplex must be
re-initialized to one with the appropriate dimensions.
</p>
<p>
Convergence is checked by providing the <em>worst</em> points of
previous and current simplex to the convergence checker, not the best
ones.
</p>
<p>
This simplex optimizer implementation does not directly support constrained
optimization with simple bounds, so for such optimizations, either a more
dedicated method must be used like <a href="../../../../../../org/apache/commons/math3/optimization/direct/CMAESOptimizer.html" title="class in org.apache.commons.math3.optimization.direct"><code>CMAESOptimizer</code></a> or <a href="../../../../../../org/apache/commons/math3/optimization/direct/BOBYQAOptimizer.html" title="class in org.apache.commons.math3.optimization.direct"><code>BOBYQAOptimizer</code></a>, or the optimized method must be wrapped in an adapter like
<a href="../../../../../../org/apache/commons/math3/optimization/direct/MultivariateFunctionMappingAdapter.html" title="class in org.apache.commons.math3.optimization.direct"><code>MultivariateFunctionMappingAdapter</code></a> or <a href="../../../../../../org/apache/commons/math3/optimization/direct/MultivariateFunctionPenaltyAdapter.html" title="class in org.apache.commons.math3.optimization.direct"><code>MultivariateFunctionPenaltyAdapter</code></a>.
</p></div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>3.0</dd>
<dt><span class="strong">Version:</span></dt>
<dd>$Id: SimplexOptimizer.java 1504724 2013-07-18 23:41:20Z sebb $</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/optimization/direct/AbstractSimplex.html" title="class in org.apache.commons.math3.optimization.direct"><code>AbstractSimplex</code></a>,
<a href="../../../../../../org/apache/commons/math3/optimization/direct/MultivariateFunctionMappingAdapter.html" title="class in org.apache.commons.math3.optimization.direct"><code>MultivariateFunctionMappingAdapter</code></a>,
<a href="../../../../../../org/apache/commons/math3/optimization/direct/MultivariateFunctionPenaltyAdapter.html" title="class in org.apache.commons.math3.optimization.direct"><code>MultivariateFunctionPenaltyAdapter</code></a>,
<a href="../../../../../../org/apache/commons/math3/optimization/direct/CMAESOptimizer.html" title="class in org.apache.commons.math3.optimization.direct"><code>CMAESOptimizer</code></a>,
<a href="../../../../../../org/apache/commons/math3/optimization/direct/BOBYQAOptimizer.html" title="class in org.apache.commons.math3.optimization.direct"><code>BOBYQAOptimizer</code></a></dd></dl>
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<h3>Fields inherited from class&nbsp;org.apache.commons.math3.optimization.direct.<a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html" title="class in org.apache.commons.math3.optimization.direct">BaseAbstractMultivariateOptimizer</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#evaluations">evaluations</a></code></li>
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<caption><span>Constructors</span><span class="tabEnd">&nbsp;</span></caption>
<tr>
<th class="colOne" scope="col">Constructor and Description</th>
</tr>
<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/optimization/direct/SimplexOptimizer.html#SimplexOptimizer()">SimplexOptimizer</a></strong>()</code>
<div class="block"><strong>Deprecated.</strong>&nbsp;
<div class="block"><i>See <a href="../../../../../../org/apache/commons/math3/optimization/SimpleValueChecker.html#SimpleValueChecker()"><code>SimpleValueChecker.SimpleValueChecker()</code></a></i></div>
</div>
</td>
</tr>
<tr class="rowColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/optimization/direct/SimplexOptimizer.html#SimplexOptimizer(org.apache.commons.math3.optimization.ConvergenceChecker)">SimplexOptimizer</a></strong>(<a href="../../../../../../org/apache/commons/math3/optimization/ConvergenceChecker.html" title="interface in org.apache.commons.math3.optimization">ConvergenceChecker</a>&lt;<a href="../../../../../../org/apache/commons/math3/optimization/PointValuePair.html" title="class in org.apache.commons.math3.optimization">PointValuePair</a>&gt;&nbsp;checker)</code>
<div class="block"><strong>Deprecated.</strong>&nbsp;</div>
&nbsp;</td>
</tr>
<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/optimization/direct/SimplexOptimizer.html#SimplexOptimizer(double, double)">SimplexOptimizer</a></strong>(double&nbsp;rel,
double&nbsp;abs)</code>
<div class="block"><strong>Deprecated.</strong>&nbsp;</div>
&nbsp;</td>
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<caption><span>Methods</span><span class="tabEnd">&nbsp;</span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
</tr>
<tr class="altColor">
<td class="colFirst"><code>protected <a href="../../../../../../org/apache/commons/math3/optimization/PointValuePair.html" title="class in org.apache.commons.math3.optimization">PointValuePair</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/optimization/direct/SimplexOptimizer.html#doOptimize()">doOptimize</a></strong>()</code>
<div class="block"><strong>Deprecated.</strong>&nbsp;</div>
<div class="block">Perform the bulk of the optimization algorithm.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected <a href="../../../../../../org/apache/commons/math3/optimization/PointValuePair.html" title="class in org.apache.commons.math3.optimization">PointValuePair</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/optimization/direct/SimplexOptimizer.html#optimizeInternal(int, org.apache.commons.math3.analysis.MultivariateFunction, org.apache.commons.math3.optimization.GoalType, org.apache.commons.math3.optimization.OptimizationData...)">optimizeInternal</a></strong>(int&nbsp;maxEval,
<a href="../../../../../../org/apache/commons/math3/analysis/MultivariateFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateFunction</a>&nbsp;f,
<a href="../../../../../../org/apache/commons/math3/optimization/GoalType.html" title="enum in org.apache.commons.math3.optimization">GoalType</a>&nbsp;goalType,
<a href="../../../../../../org/apache/commons/math3/optimization/OptimizationData.html" title="interface in org.apache.commons.math3.optimization">OptimizationData</a>...&nbsp;optData)</code>
<div class="block"><strong>Deprecated.</strong>&nbsp;</div>
<div class="block">Optimize an objective function.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/optimization/direct/SimplexOptimizer.html#setSimplex(org.apache.commons.math3.optimization.direct.AbstractSimplex)">setSimplex</a></strong>(<a href="../../../../../../org/apache/commons/math3/optimization/direct/AbstractSimplex.html" title="class in org.apache.commons.math3.optimization.direct">AbstractSimplex</a>&nbsp;simplex)</code>
<div class="block"><strong>Deprecated.</strong>&nbsp;
<div class="block"><i>As of 3.1. The initial simplex can now be passed as an
argument of the <a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#optimize(int, FUNC, org.apache.commons.math3.optimization.GoalType, org.apache.commons.math3.optimization.OptimizationData...)"><code>BaseAbstractMultivariateOptimizer.optimize(int,MultivariateFunction,GoalType,OptimizationData[])</code></a>
method.</i></div>
</div>
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<h3>Methods inherited from class&nbsp;org.apache.commons.math3.optimization.direct.<a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html" title="class in org.apache.commons.math3.optimization.direct">BaseAbstractMultivariateOptimizer</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#computeObjectiveValue(double[])">computeObjectiveValue</a>, <a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#getConvergenceChecker()">getConvergenceChecker</a>, <a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#getEvaluations()">getEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#getGoalType()">getGoalType</a>, <a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#getLowerBound()">getLowerBound</a>, <a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#getMaxEvaluations()">getMaxEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#getStartPoint()">getStartPoint</a>, <a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#getUpperBound()">getUpperBound</a>, <a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#optimize(int, FUNC, org.apache.commons.math3.optimization.GoalType, double[])">optimize</a>, <a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#optimize(int, FUNC, org.apache.commons.math3.optimization.GoalType, org.apache.commons.math3.optimization.OptimizationData...)">optimize</a>, <a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#optimizeInternal(int, FUNC, org.apache.commons.math3.optimization.GoalType, double[])">optimizeInternal</a></code></li>
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<h3>Methods inherited from class&nbsp;java.lang.<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
<code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li>
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<h3>Methods inherited from interface&nbsp;org.apache.commons.math3.optimization.<a href="../../../../../../org/apache/commons/math3/optimization/BaseMultivariateOptimizer.html" title="interface in org.apache.commons.math3.optimization">BaseMultivariateOptimizer</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/optimization/BaseMultivariateOptimizer.html#optimize(int, FUNC, org.apache.commons.math3.optimization.GoalType, double[])">optimize</a></code></li>
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<code><a href="../../../../../../org/apache/commons/math3/optimization/BaseOptimizer.html#getConvergenceChecker()">getConvergenceChecker</a>, <a href="../../../../../../org/apache/commons/math3/optimization/BaseOptimizer.html#getEvaluations()">getEvaluations</a>, <a href="../../../../../../org/apache/commons/math3/optimization/BaseOptimizer.html#getMaxEvaluations()">getMaxEvaluations</a></code></li>
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<a name="SimplexOptimizer()">
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<h4>SimplexOptimizer</h4>
<pre><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a>
public&nbsp;SimplexOptimizer()</pre>
<div class="block"><span class="strong">Deprecated.</span>&nbsp;<i>See <a href="../../../../../../org/apache/commons/math3/optimization/SimpleValueChecker.html#SimpleValueChecker()"><code>SimpleValueChecker.SimpleValueChecker()</code></a></i></div>
<div class="block">Constructor using a default <a href="../../../../../../org/apache/commons/math3/optimization/SimpleValueChecker.html" title="class in org.apache.commons.math3.optimization"><code>convergence
checker</code></a>.</div>
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<h4>SimplexOptimizer</h4>
<pre>public&nbsp;SimplexOptimizer(<a href="../../../../../../org/apache/commons/math3/optimization/ConvergenceChecker.html" title="interface in org.apache.commons.math3.optimization">ConvergenceChecker</a>&lt;<a href="../../../../../../org/apache/commons/math3/optimization/PointValuePair.html" title="class in org.apache.commons.math3.optimization">PointValuePair</a>&gt;&nbsp;checker)</pre>
<div class="block"><span class="strong">Deprecated.</span>&nbsp;</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>checker</code> - Convergence checker.</dd></dl>
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<h4>SimplexOptimizer</h4>
<pre>public&nbsp;SimplexOptimizer(double&nbsp;rel,
double&nbsp;abs)</pre>
<div class="block"><span class="strong">Deprecated.</span>&nbsp;</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>rel</code> - Relative threshold.</dd><dd><code>abs</code> - Absolute threshold.</dd></dl>
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<a name="setSimplex(org.apache.commons.math3.optimization.direct.AbstractSimplex)">
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<h4>setSimplex</h4>
<pre><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a>
public&nbsp;void&nbsp;setSimplex(<a href="../../../../../../org/apache/commons/math3/optimization/direct/AbstractSimplex.html" title="class in org.apache.commons.math3.optimization.direct">AbstractSimplex</a>&nbsp;simplex)</pre>
<div class="block"><span class="strong">Deprecated.</span>&nbsp;<i>As of 3.1. The initial simplex can now be passed as an
argument of the <a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#optimize(int, FUNC, org.apache.commons.math3.optimization.GoalType, org.apache.commons.math3.optimization.OptimizationData...)"><code>BaseAbstractMultivariateOptimizer.optimize(int,MultivariateFunction,GoalType,OptimizationData[])</code></a>
method.</i></div>
<div class="block">Set the simplex algorithm.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>simplex</code> - Simplex.</dd></dl>
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<a name="optimizeInternal(int, org.apache.commons.math3.analysis.MultivariateFunction, org.apache.commons.math3.optimization.GoalType, org.apache.commons.math3.optimization.OptimizationData...)">
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<h4>optimizeInternal</h4>
<pre>protected&nbsp;<a href="../../../../../../org/apache/commons/math3/optimization/PointValuePair.html" title="class in org.apache.commons.math3.optimization">PointValuePair</a>&nbsp;optimizeInternal(int&nbsp;maxEval,
<a href="../../../../../../org/apache/commons/math3/analysis/MultivariateFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateFunction</a>&nbsp;f,
<a href="../../../../../../org/apache/commons/math3/optimization/GoalType.html" title="enum in org.apache.commons.math3.optimization">GoalType</a>&nbsp;goalType,
<a href="../../../../../../org/apache/commons/math3/optimization/OptimizationData.html" title="interface in org.apache.commons.math3.optimization">OptimizationData</a>...&nbsp;optData)</pre>
<div class="block"><span class="strong">Deprecated.</span>&nbsp;</div>
<div class="block">Optimize an objective function.</div>
<dl>
<dt><strong>Overrides:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#optimizeInternal(int, FUNC, org.apache.commons.math3.optimization.GoalType, org.apache.commons.math3.optimization.OptimizationData...)">optimizeInternal</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html" title="class in org.apache.commons.math3.optimization.direct">BaseAbstractMultivariateOptimizer</a>&lt;<a href="../../../../../../org/apache/commons/math3/analysis/MultivariateFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateFunction</a>&gt;</code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>maxEval</code> - Allowed number of evaluations of the objective function.</dd><dd><code>f</code> - Objective function.</dd><dd><code>goalType</code> - Optimization type.</dd><dd><code>optData</code> - Optimization data. The following data will be looked for:
<ul>
<li><a href="../../../../../../org/apache/commons/math3/optimization/InitialGuess.html" title="class in org.apache.commons.math3.optimization"><code>InitialGuess</code></a></li>
<li><a href="../../../../../../org/apache/commons/math3/optimization/direct/AbstractSimplex.html" title="class in org.apache.commons.math3.optimization.direct"><code>AbstractSimplex</code></a></li>
</ul></dd>
<dt><span class="strong">Returns:</span></dt><dd>the point/value pair giving the optimal value for objective
function.</dd></dl>
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<a name="doOptimize()">
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<h4>doOptimize</h4>
<pre>protected&nbsp;<a href="../../../../../../org/apache/commons/math3/optimization/PointValuePair.html" title="class in org.apache.commons.math3.optimization">PointValuePair</a>&nbsp;doOptimize()</pre>
<div class="block"><span class="strong">Deprecated.</span>&nbsp;</div>
<div class="block">Perform the bulk of the optimization algorithm.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html#doOptimize()">doOptimize</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../../org/apache/commons/math3/optimization/direct/BaseAbstractMultivariateOptimizer.html" title="class in org.apache.commons.math3.optimization.direct">BaseAbstractMultivariateOptimizer</a>&lt;<a href="../../../../../../org/apache/commons/math3/analysis/MultivariateFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateFunction</a>&gt;</code></dd>
<dt><span class="strong">Returns:</span></dt><dd>the point/value pair giving the optimal value of the
objective function.</dd></dl>
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