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<div id="projectbrief">A free/open-source library for quantitative finance</div>
<div id="projectnumber">Reference manual - version 1.20</div>
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<li class="navelem"><a class="el" href="namespace_quant_lib.html">QuantLib</a></li><li class="navelem"><a class="el" href="class_quant_lib_1_1_armijo_line_search.html">ArmijoLineSearch</a></li> </ul>
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<div class="header">
<div class="summary">
<a href="#pub-methods">Public Member Functions</a> |
<a href="class_quant_lib_1_1_armijo_line_search-members.html">List of all members</a> </div>
<div class="headertitle">
<div class="title">ArmijoLineSearch Class Reference</div> </div>
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<div class="contents">
<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>
<div id="dynsection-0" onclick="return toggleVisibility(this)" class="dynheader closed" style="cursor:pointer;">
<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for ArmijoLineSearch:</div>
<div id="dynsection-0-summary" class="dynsummary" style="display:block;">
</div>
<div id="dynsection-0-content" class="dyncontent" style="display:none;">
<div class="center"><img src="class_quant_lib_1_1_armijo_line_search__inherit__graph.png" border="0" usemap="#a_armijo_line_search_inherit__map" alt="Inheritance graph"/></div>
<map name="_armijo_line_search_inherit__map" id="a_armijo_line_search_inherit__map">
<area shape="rect" title="Armijo line search." alt="" coords="5,80,129,107"/>
<area shape="rect" href="class_quant_lib_1_1_line_search.html" title="Base class for line search." alt="" coords="24,5,111,32"/>
</map>
<center><span class="legend">[<a href="graph_legend.html">legend</a>]</span></center></div>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:aa9b7b48a8c23873cce8850ca4c91b983"><td class="memItemLeft" align="right" valign="top"><a id="aa9b7b48a8c23873cce8850ca4c91b983"></a>
 </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, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> alpha=0.05, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> beta=0.65)</td></tr>
<tr class="memdesc:aa9b7b48a8c23873cce8850ca4c91b983"><td class="mdescLeft"> </td><td class="mdescRight">Default constructor. <br /></td></tr>
<tr class="separator:aa9b7b48a8c23873cce8850ca4c91b983"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af20e38c359ea31c395a8ce7cc336635a"><td class="memItemLeft" align="right" valign="top"><a id="af20e38c359ea31c395a8ce7cc336635a"></a>
<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#af20e38c359ea31c395a8ce7cc336635a">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> &, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> t_ini)</td></tr>
<tr class="memdesc:af20e38c359ea31c395a8ce7cc336635a"><td class="mdescLeft"> </td><td class="mdescRight">Perform line search. <br /></td></tr>
<tr class="separator:af20e38c359ea31c395a8ce7cc336635a"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_methods_class_quant_lib_1_1_line_search"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_class_quant_lib_1_1_line_search')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="class_quant_lib_1_1_line_search.html">LineSearch</a></td></tr>
<tr class="memitem:abf6329e7e510004f936417b572cd3feb inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="abf6329e7e510004f936417b572cd3feb"></a>
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_line_search.html#abf6329e7e510004f936417b572cd3feb">LineSearch</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>=0.0)</td></tr>
<tr class="memdesc:abf6329e7e510004f936417b572cd3feb inherit pub_methods_class_quant_lib_1_1_line_search"><td class="mdescLeft"> </td><td class="mdescRight">Default constructor. <br /></td></tr>
<tr class="separator:abf6329e7e510004f936417b572cd3feb inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa1525d9d1f8f851f1371337be8d9a587 inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="aa1525d9d1f8f851f1371337be8d9a587"></a>
virtual </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_line_search.html#aa1525d9d1f8f851f1371337be8d9a587">~LineSearch</a> ()</td></tr>
<tr class="memdesc:aa1525d9d1f8f851f1371337be8d9a587 inherit pub_methods_class_quant_lib_1_1_line_search"><td class="mdescLeft"> </td><td class="mdescRight">Destructor. <br /></td></tr>
<tr class="separator:aa1525d9d1f8f851f1371337be8d9a587 inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a73029249454596185357bd919ecc66e7 inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="a73029249454596185357bd919ecc66e7"></a>
const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_line_search.html#a73029249454596185357bd919ecc66e7">lastX</a> ()</td></tr>
<tr class="memdesc:a73029249454596185357bd919ecc66e7 inherit pub_methods_class_quant_lib_1_1_line_search"><td class="mdescLeft"> </td><td class="mdescRight">return last x value <br /></td></tr>
<tr class="separator:a73029249454596185357bd919ecc66e7 inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:acb191c566a812e3e7d1406977c0fb9dd inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="acb191c566a812e3e7d1406977c0fb9dd"></a>
<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_line_search.html#acb191c566a812e3e7d1406977c0fb9dd">lastFunctionValue</a> () const</td></tr>
<tr class="memdesc:acb191c566a812e3e7d1406977c0fb9dd inherit pub_methods_class_quant_lib_1_1_line_search"><td class="mdescLeft"> </td><td class="mdescRight">return last cost function value <br /></td></tr>
<tr class="separator:acb191c566a812e3e7d1406977c0fb9dd inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a0a99d489f61c963d573fb9eb2a404c1d inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="a0a99d489f61c963d573fb9eb2a404c1d"></a>
const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_line_search.html#a0a99d489f61c963d573fb9eb2a404c1d">lastGradient</a> ()</td></tr>
<tr class="memdesc:a0a99d489f61c963d573fb9eb2a404c1d inherit pub_methods_class_quant_lib_1_1_line_search"><td class="mdescLeft"> </td><td class="mdescRight">return last gradient <br /></td></tr>
<tr class="separator:a0a99d489f61c963d573fb9eb2a404c1d inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aaaca9b17704b9a7356e394a6e56be66a inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="aaaca9b17704b9a7356e394a6e56be66a"></a>
<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_line_search.html#aaaca9b17704b9a7356e394a6e56be66a">lastGradientNorm2</a> () const</td></tr>
<tr class="memdesc:aaaca9b17704b9a7356e394a6e56be66a inherit pub_methods_class_quant_lib_1_1_line_search"><td class="mdescLeft"> </td><td class="mdescRight">return square norm of last gradient <br /></td></tr>
<tr class="separator:aaaca9b17704b9a7356e394a6e56be66a inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:acf96853903414c5ad66169f291938f4c inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="acf96853903414c5ad66169f291938f4c"></a>
bool </td><td class="memItemRight" valign="bottom"><b>succeed</b> () const</td></tr>
<tr class="separator:acf96853903414c5ad66169f291938f4c inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a5014094d4595b63fad08d361f70bea98 inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="a5014094d4595b63fad08d361f70bea98"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>update</b> (<a class="el" href="class_quant_lib_1_1_array.html">Array</a> &params, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &direction, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> beta, const <a class="el" href="class_quant_lib_1_1_constraint.html">Constraint</a> &constraint)</td></tr>
<tr class="separator:a5014094d4595b63fad08d361f70bea98 inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa84d8a98a895f6cf2dce4fd113140c60 inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="aa84d8a98a895f6cf2dce4fd113140c60"></a>
const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_line_search.html#aa84d8a98a895f6cf2dce4fd113140c60">searchDirection</a> () const</td></tr>
<tr class="memdesc:aa84d8a98a895f6cf2dce4fd113140c60 inherit pub_methods_class_quant_lib_1_1_line_search"><td class="mdescLeft"> </td><td class="mdescRight">current value of the search direction <br /></td></tr>
<tr class="separator:aa84d8a98a895f6cf2dce4fd113140c60 inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a8925a1dc9b83be8f1181b1c638804a1f inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="a8925a1dc9b83be8f1181b1c638804a1f"></a>
<a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td><td class="memItemRight" valign="bottom"><b>searchDirection</b> ()</td></tr>
<tr class="separator:a8925a1dc9b83be8f1181b1c638804a1f inherit pub_methods_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="inherited"></a>
Additional Inherited Members</h2></td></tr>
<tr class="inherit_header pro_attribs_class_quant_lib_1_1_line_search"><td colspan="2" onclick="javascript:toggleInherit('pro_attribs_class_quant_lib_1_1_line_search')"><img src="closed.png" alt="-"/> Protected Attributes inherited from <a class="el" href="class_quant_lib_1_1_line_search.html">LineSearch</a></td></tr>
<tr class="memitem:a2279b9a5a0693be810780a356ce2593f inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="a2279b9a5a0693be810780a356ce2593f"></a>
<a class="el" href="class_quant_lib_1_1_array.html">Array</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_line_search.html#a2279b9a5a0693be810780a356ce2593f">searchDirection_</a></td></tr>
<tr class="memdesc:a2279b9a5a0693be810780a356ce2593f inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="mdescLeft"> </td><td class="mdescRight">current values of the search direction <br /></td></tr>
<tr class="separator:a2279b9a5a0693be810780a356ce2593f inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a633de5cce68edbe62dcc0104c92e69c1 inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="a633de5cce68edbe62dcc0104c92e69c1"></a>
<a class="el" href="class_quant_lib_1_1_array.html">Array</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_line_search.html#a633de5cce68edbe62dcc0104c92e69c1">xtd_</a></td></tr>
<tr class="memdesc:a633de5cce68edbe62dcc0104c92e69c1 inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="mdescLeft"> </td><td class="mdescRight">new x and its gradient <br /></td></tr>
<tr class="separator:a633de5cce68edbe62dcc0104c92e69c1 inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a28dad9f0113c33c5641f4c87b6c5208c inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="a28dad9f0113c33c5641f4c87b6c5208c"></a>
<a class="el" href="class_quant_lib_1_1_array.html">Array</a> </td><td class="memItemRight" valign="bottom"><b>gradient_</b></td></tr>
<tr class="separator:a28dad9f0113c33c5641f4c87b6c5208c inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af784d8fad068c2fcb91696bd7a7346c3 inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="af784d8fad068c2fcb91696bd7a7346c3"></a>
<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_line_search.html#af784d8fad068c2fcb91696bd7a7346c3">qt_</a></td></tr>
<tr class="memdesc:af784d8fad068c2fcb91696bd7a7346c3 inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="mdescLeft"> </td><td class="mdescRight">cost function value and gradient norm corresponding to xtd_ <br /></td></tr>
<tr class="separator:af784d8fad068c2fcb91696bd7a7346c3 inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aca10938722a51a63857d6bc7bc1f4717 inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="aca10938722a51a63857d6bc7bc1f4717"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>qpt_</b></td></tr>
<tr class="separator:aca10938722a51a63857d6bc7bc1f4717 inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a1bdb6aaa82b6a980db5312bcc3c86c3a inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="memItemLeft" align="right" valign="top"><a id="a1bdb6aaa82b6a980db5312bcc3c86c3a"></a>
bool </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_line_search.html#a1bdb6aaa82b6a980db5312bcc3c86c3a">succeed_</a></td></tr>
<tr class="memdesc:a1bdb6aaa82b6a980db5312bcc3c86c3a inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="mdescLeft"> </td><td class="mdescRight">flag to know if linesearch succeed <br /></td></tr>
<tr class="separator:a1bdb6aaa82b6a980db5312bcc3c86c3a inherit pro_attribs_class_quant_lib_1_1_line_search"><td class="memSeparator" colspan="2"> </td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Armijo line search. </p>
<p>Let \( \alpha \) and \( \beta \) be 2 scalars in \( [0,1] \). Let \( x \) be the current value of the unknown, \( d \) the search direction and \( t \) the step. Let \( f \) be the function to minimize. The line search stops when \( t \) verifies </p><p class="formulaDsp">
\[ f(x + t \cdot d) - f(x) \leq -\alpha t f'(x+t \cdot d) \]
</p>
<p> and </p><p class="formulaDsp">
\[ f(x+\frac{t}{\beta} \cdot d) - f(x) > -\frac{\alpha}{\beta} t f'(x+t \cdot d) \]
</p>
<p>(see Polak, Algorithms and consistent approximations, Optimization, volume 124 of Applied Mathematical Sciences, Springer-Verlag, NY, 1997) </p>
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