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3<title>mixpp: Numerical Optimization Module</title>
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61<h1>Numerical Optimization Module</h1>Numerical optimization routines. 
62<a href="#_details">More...</a>
63<p>
64<table border="0" cellpadding="0" cellspacing="0">
65<tr><td></td></tr>
66<tr><td colspan="2"><br><h2>Classes</h2></td></tr>
67<tr><td class="memItemLeft" nowrap align="right" valign="top">class &nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html">itpp::Newton_Search</a></td></tr>
68
69<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Newton Search.  <a href="classitpp_1_1Newton__Search.html#_details">More...</a><br></td></tr>
70<tr><td class="memItemLeft" nowrap align="right" valign="top">class &nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Line__Search.html">itpp::Line_Search</a></td></tr>
71
72<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Line Search.  <a href="classitpp_1_1Line__Search.html#_details">More...</a><br></td></tr>
73<tr><td colspan="2"><br><h2>Enumerations</h2></td></tr>
74<tr><td class="memItemLeft" nowrap align="right" valign="top">enum &nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__optimization.html#g08746316b0b24694973fcb008de0f0e1">itpp::Newton_Search_Method</a> { <b>BFGS</b>
75 }</td></tr>
76
77<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Newton Search method. <br></td></tr>
78<tr><td class="memItemLeft" nowrap align="right" valign="top">enum &nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__optimization.html#g1f546a6d17b2c74304b3624bc7b7e9e9">itpp::Line_Search_Method</a> { <b>Soft</b>,
79<b>Exact</b>
80 }</td></tr>
81
82<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Line Search method. <br></td></tr>
83<tr><td colspan="2"><br><h2>Functions</h2></td></tr>
84<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__optimization.html#g1d1cf6b1f01e40c563123289658ddc8d">itpp::fminunc</a> (double(*function)(const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;), <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>(*gradient)(const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;), const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;x0)</td></tr>
85
86<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Unconstrained minimization.  <a href="#g1d1cf6b1f01e40c563123289658ddc8d"></a><br></td></tr>
87</table>
88<hr><a name="_details"></a><h2>Detailed Description</h2>
89Numerical optimization routines. <hr><h2>Function Documentation</h2>
90<a class="anchor" name="g1d1cf6b1f01e40c563123289658ddc8d"></a><!-- doxytag: member="itpp::fminunc" ref="g1d1cf6b1f01e40c563123289658ddc8d" args="(double(*function)(const vec &amp;), vec(*gradient)(const vec &amp;), const vec &amp;x0)" -->
91<div class="memitem">
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93      <table class="memname">
94        <tr>
95          <td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::fminunc           </td>
96          <td>(</td>
97          <td class="paramtype">double(*)(const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;)&nbsp;</td>
98          <td class="paramname"> <em>function</em>, </td>
99        </tr>
100        <tr>
101          <td class="paramkey"></td>
102          <td></td>
103          <td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>(*)(const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;)&nbsp;</td>
104          <td class="paramname"> <em>gradient</em>, </td>
105        </tr>
106        <tr>
107          <td class="paramkey"></td>
108          <td></td>
109          <td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;&nbsp;</td>
110          <td class="paramname"> <em>x0</em></td><td>&nbsp;</td>
111        </tr>
112        <tr>
113          <td></td>
114          <td>)</td>
115          <td></td><td></td><td></td>
116        </tr>
117      </table>
118</div>
119<div class="memdoc">
120
121<p>
122Unconstrained minimization.
123<p>
124Unconstrained minimization using a Newton or Quasi-Newton optimization method that try to minimize the objective function <img class="formulaInl" alt="$f(\mathbf{x})$" src="form_323.png"> given an initial guess <img class="formulaInl" alt="$\mathbf{x}$" src="form_324.png">.<p>
125The function and the gradient need to be known and supplied.<p>
126The default algorithm is a Quasi-Newton search using BFGS updates of the inverse Hessian matrix.
127<p>References <a class="el" href="newton__search_8cpp-source.html#l00090">itpp::Newton_Search::search()</a>, and <a class="el" href="newton__search_8h-source.html#l00084">itpp::Newton_Search::set_functions()</a>.</p>
128
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