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<title>QuantLib: ArmijoLineSearch Class Reference</title>
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<a class="el" href="namespace_quant_lib.html">QuantLib</a>::<a class="el" href="class_quant_lib_1_1_armijo_line_search.html">ArmijoLineSearch</a></div>
<h1>ArmijoLineSearch Class Reference</h1><!-- doxytag: class="QuantLib::ArmijoLineSearch" --><!-- doxytag: inherits="QuantLib::LineSearch" --><code>#include <ql/math/optimization/armijo.hpp></code>
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Inheritance diagram for ArmijoLineSearch:</div>
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<p><center><img src="class_quant_lib_1_1_armijo_line_search__inherit__graph.png" border="0" usemap="#_armijo_line_search__inherit__map" alt="Inheritance graph"></center>
<map name="_armijo_line_search__inherit__map">
<area shape="rect" href="class_quant_lib_1_1_line_search.html" title="Base class for line search." alt="" coords="25,7,119,33"></map>
<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
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<a href="class_quant_lib_1_1_armijo_line_search-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Armijo line search.
<p>
Let <img class="formulaInl" alt="$ \alpha $" src="form_3.png"> and <img class="formulaInl" alt="$ \beta $" src="form_152.png"> be 2 scalars in <img class="formulaInl" alt="$ [0,1] $" src="form_153.png">. Let <img class="formulaInl" alt="$ x $" src="form_138.png"> be the current value of the unknown, <img class="formulaInl" alt="$ d $" src="form_154.png"> the search direction and <img class="formulaInl" alt="$ t $" src="form_85.png"> the step. Let <img class="formulaInl" alt="$ f $" src="form_41.png"> be the function to minimize. The line search stops when <img class="formulaInl" alt="$ t $" src="form_85.png"> verifies <p class="formulaDsp">
<img class="formulaDsp" alt="\[ f(x + t \cdot d) - f(x) \leq -\alpha t f'(x+t \cdot d) \]" src="form_155.png">
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and <p class="formulaDsp">
<img class="formulaDsp" alt="\[ f(x+\frac{t}{\beta} \cdot d) - f(x) > -\frac{\alpha}{\beta} t f'(x+t \cdot d) \]" src="form_156.png">
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(see Polak, Algorithms and consistent approximations, Optimization, volume 124 of Applied Mathematical Sciences, Springer-Verlag, NY, 1997) <table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a9b7b48a8c23873cce8850ca4c91b983"></a><!-- doxytag: member="QuantLib::ArmijoLineSearch::ArmijoLineSearch" ref="a9b7b48a8c23873cce8850ca4c91b983" args="(Real eps=1e-8, Real alpha=0.05, Real beta=0.65)" -->
</td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_armijo_line_search.html#a9b7b48a8c23873cce8850ca4c91b983">ArmijoLineSearch</a> (<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> eps=1e-8, Real alpha=0.05, Real beta=0.65)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Default constructor. <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5d35ecca8f9fb5e845371eb48e90d3f0"></a><!-- doxytag: member="QuantLib::ArmijoLineSearch::operator()" ref="5d35ecca8f9fb5e845371eb48e90d3f0" args="(Problem &P, EndCriteria::Type &ecType, const EndCriteria &, const Real t_ini)" -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_armijo_line_search.html#5d35ecca8f9fb5e845371eb48e90d3f0">operator()</a> (<a class="el" href="class_quant_lib_1_1_problem.html">Problem</a> &P, EndCriteria::Type &ecType, const <a class="el" href="class_quant_lib_1_1_end_criteria.html">EndCriteria</a> &, const <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> t_ini)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Perform line search. <br></td></tr>
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