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<h3 class="subtitle">A free/open-source library for quantitative finance</h3>
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<li class="navelem"><b>QuantLib</b> </li>
<li class="navelem"><a class="el" href="class_quant_lib_1_1_armijo_line_search.html">ArmijoLineSearch</a> </li>
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<a href="#pub-methods">Public Member Functions</a> </div>
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<div class="title">ArmijoLineSearch Class Reference</div> </div>
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<!-- doxytag: class="QuantLib::ArmijoLineSearch" --><!-- doxytag: inherits="QuantLib::LineSearch" -->
<p>Armijo line search.
<a href="class_quant_lib_1_1_armijo_line_search.html#details">More...</a></p>
<p><code>#include <ql/math/optimization/armijo.hpp></code></p>
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Inheritance diagram for ArmijoLineSearch:</div>
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<div class="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"/></div>
<map name="_armijo_line_search_inherit__map" id="_armijo_line_search_inherit__map">
<area shape="rect" id="node2" href="class_quant_lib_1_1_line_search.html" title="Base class for line search." alt="" coords="24,6,109,37"/></map>
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<p><a href="class_quant_lib_1_1_armijo_line_search-members.html">List of all members.</a></p>
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Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aa9b7b48a8c23873cce8850ca4c91b983"></a><!-- doxytag: member="QuantLib::ArmijoLineSearch::ArmijoLineSearch" ref="aa9b7b48a8c23873cce8850ca4c91b983" 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#aa9b7b48a8c23873cce8850ca4c91b983">ArmijoLineSearch</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">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" align="right" valign="top"><a class="anchor" id="a5d35ecca8f9fb5e845371eb48e90d3f0"></a><!-- doxytag: member="QuantLib::ArmijoLineSearch::operator()" ref="a5d35ecca8f9fb5e845371eb48e90d3f0" args="(Problem &P, EndCriteria::Type &ecType, const EndCriteria &, const Real t_ini)" -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_armijo_line_search.html#a5d35ecca8f9fb5e845371eb48e90d3f0">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#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> t_ini)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Perform line search. <br/></td></tr>
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<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Armijo line search. </p>
<p>Let <img class="formulaInl" alt="$ \alpha $" src="form_3.png"/> and <img class="formulaInl" alt="$ \beta $" src="form_220.png"/> be 2 scalars in <img class="formulaInl" alt="$ [0,1] $" src="form_221.png"/>. Let <img class="formulaInl" alt="$ x $" src="form_134.png"/> be the current value of the unknown, <img class="formulaInl" alt="$ d $" src="form_222.png"/> the search direction and <img class="formulaInl" alt="$ t $" src="form_147.png"/> the step. Let <img class="formulaInl" alt="$ f $" src="form_37.png"/> be the function to minimize. The line search stops when <img class="formulaInl" alt="$ t $" src="form_147.png"/> verifies </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ f(x + t \cdot d) - f(x) \leq -\alpha t f'(x+t \cdot d) \]" src="form_223.png"/>
</p>
<p> and </p>
<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_224.png"/>
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<p>(see Polak, Algorithms and consistent approximations, Optimization, volume 124 of Applied Mathematical Sciences, Springer-Verlag, NY, 1997) </p>
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