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<li class="navelem"><a class="el" href="namespacemlpack.html">mlpack</a></li><li class="navelem"><a class="el" href="namespacemlpack_1_1optimization.html">optimization</a></li><li class="navelem"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html">GradientDescent</a></li> </ul>
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<div class="title">mlpack::optimization::GradientDescent&lt; FunctionType &gt; Class Template Reference</div> </div>
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<p>Gradient Descent is a technique to minimize a function.
<a href="classmlpack_1_1optimization_1_1GradientDescent.html#details">More...</a></p>
<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:a4755e084ee5cde85897e241cd1117a85"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a4755e084ee5cde85897e241cd1117a85">GradientDescent</a> (FunctionType &amp;<a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a86773ecb5168d7cb08e36cda3d336b55">function</a>, const double <a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a715079a2cf3184cae181d47afe4cbd42">stepSize</a>=0.01, const size_t <a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a7bf45f14dbde579be1c4ecb934d2984f">maxIterations</a>=100000, const double <a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a3e84efdf47853d628655a1750fb8523a">tolerance</a>=1e-5)</td></tr>
<tr class="memdesc:a4755e084ee5cde85897e241cd1117a85"><td class="mdescLeft">&#160;</td><td class="mdescRight">Construct the Gradient Descent optimizer with the given function and parameters. <a href="#a4755e084ee5cde85897e241cd1117a85">More...</a><br /></td></tr>
<tr class="separator:a4755e084ee5cde85897e241cd1117a85"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aaa6285f395314801d8822d7553719fb4"><td class="memItemLeft" align="right" valign="top">const FunctionType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#aaa6285f395314801d8822d7553719fb4">Function</a> () const </td></tr>
<tr class="memdesc:aaa6285f395314801d8822d7553719fb4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the instantiated function to be optimized. <a href="#aaa6285f395314801d8822d7553719fb4">More...</a><br /></td></tr>
<tr class="separator:aaa6285f395314801d8822d7553719fb4"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3850668f2220842895a6b1a3eb567259"><td class="memItemLeft" align="right" valign="top">FunctionType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a3850668f2220842895a6b1a3eb567259">Function</a> ()</td></tr>
<tr class="memdesc:a3850668f2220842895a6b1a3eb567259"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modify the instantiated function. <a href="#a3850668f2220842895a6b1a3eb567259">More...</a><br /></td></tr>
<tr class="separator:a3850668f2220842895a6b1a3eb567259"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab8cf876f67ec1dea34b86eaf4ecfc725"><td class="memItemLeft" align="right" valign="top">size_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#ab8cf876f67ec1dea34b86eaf4ecfc725">MaxIterations</a> () const </td></tr>
<tr class="memdesc:ab8cf876f67ec1dea34b86eaf4ecfc725"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the maximum number of iterations (0 indicates no limit). <a href="#ab8cf876f67ec1dea34b86eaf4ecfc725">More...</a><br /></td></tr>
<tr class="separator:ab8cf876f67ec1dea34b86eaf4ecfc725"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3dcebe67040ad2ca5d93ab3084686e6e"><td class="memItemLeft" align="right" valign="top">size_t &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a3dcebe67040ad2ca5d93ab3084686e6e">MaxIterations</a> ()</td></tr>
<tr class="memdesc:a3dcebe67040ad2ca5d93ab3084686e6e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modify the maximum number of iterations (0 indicates no limit). <a href="#a3dcebe67040ad2ca5d93ab3084686e6e">More...</a><br /></td></tr>
<tr class="separator:a3dcebe67040ad2ca5d93ab3084686e6e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a781e2e83082a14ce71a2bfc8a36f41e0"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a781e2e83082a14ce71a2bfc8a36f41e0">Optimize</a> (arma::mat &amp;iterate)</td></tr>
<tr class="memdesc:a781e2e83082a14ce71a2bfc8a36f41e0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Optimize the given function using gradient descent. <a href="#a781e2e83082a14ce71a2bfc8a36f41e0">More...</a><br /></td></tr>
<tr class="separator:a781e2e83082a14ce71a2bfc8a36f41e0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6073395f5d8c020ea20d8d5d519a257d"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a6073395f5d8c020ea20d8d5d519a257d">StepSize</a> () const </td></tr>
<tr class="memdesc:a6073395f5d8c020ea20d8d5d519a257d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the step size. <a href="#a6073395f5d8c020ea20d8d5d519a257d">More...</a><br /></td></tr>
<tr class="separator:a6073395f5d8c020ea20d8d5d519a257d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3a55d15d3e55a40b1428b2248392dd00"><td class="memItemLeft" align="right" valign="top">double &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a3a55d15d3e55a40b1428b2248392dd00">StepSize</a> ()</td></tr>
<tr class="memdesc:a3a55d15d3e55a40b1428b2248392dd00"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modify the step size. <a href="#a3a55d15d3e55a40b1428b2248392dd00">More...</a><br /></td></tr>
<tr class="separator:a3a55d15d3e55a40b1428b2248392dd00"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a04f7740c385eb35d65ffdce08b3f581a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a04f7740c385eb35d65ffdce08b3f581a">Tolerance</a> () const </td></tr>
<tr class="memdesc:a04f7740c385eb35d65ffdce08b3f581a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the tolerance for termination. <a href="#a04f7740c385eb35d65ffdce08b3f581a">More...</a><br /></td></tr>
<tr class="separator:a04f7740c385eb35d65ffdce08b3f581a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a16c47ee04e37a438ab9be28e971b04b4"><td class="memItemLeft" align="right" valign="top">double &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a16c47ee04e37a438ab9be28e971b04b4">Tolerance</a> ()</td></tr>
<tr class="memdesc:a16c47ee04e37a438ab9be28e971b04b4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Modify the tolerance for termination. <a href="#a16c47ee04e37a438ab9be28e971b04b4">More...</a><br /></td></tr>
<tr class="separator:a16c47ee04e37a438ab9be28e971b04b4"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-attribs"></a>
Private Attributes</h2></td></tr>
<tr class="memitem:a86773ecb5168d7cb08e36cda3d336b55"><td class="memItemLeft" align="right" valign="top">FunctionType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a86773ecb5168d7cb08e36cda3d336b55">function</a></td></tr>
<tr class="memdesc:a86773ecb5168d7cb08e36cda3d336b55"><td class="mdescLeft">&#160;</td><td class="mdescRight">The instantiated function. <a href="#a86773ecb5168d7cb08e36cda3d336b55">More...</a><br /></td></tr>
<tr class="separator:a86773ecb5168d7cb08e36cda3d336b55"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7bf45f14dbde579be1c4ecb934d2984f"><td class="memItemLeft" align="right" valign="top">size_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a7bf45f14dbde579be1c4ecb934d2984f">maxIterations</a></td></tr>
<tr class="memdesc:a7bf45f14dbde579be1c4ecb934d2984f"><td class="mdescLeft">&#160;</td><td class="mdescRight">The maximum number of allowed iterations. <a href="#a7bf45f14dbde579be1c4ecb934d2984f">More...</a><br /></td></tr>
<tr class="separator:a7bf45f14dbde579be1c4ecb934d2984f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a715079a2cf3184cae181d47afe4cbd42"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a715079a2cf3184cae181d47afe4cbd42">stepSize</a></td></tr>
<tr class="memdesc:a715079a2cf3184cae181d47afe4cbd42"><td class="mdescLeft">&#160;</td><td class="mdescRight">The step size for each example. <a href="#a715079a2cf3184cae181d47afe4cbd42">More...</a><br /></td></tr>
<tr class="separator:a715079a2cf3184cae181d47afe4cbd42"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3e84efdf47853d628655a1750fb8523a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html#a3e84efdf47853d628655a1750fb8523a">tolerance</a></td></tr>
<tr class="memdesc:a3e84efdf47853d628655a1750fb8523a"><td class="mdescLeft">&#160;</td><td class="mdescRight">The tolerance for termination. <a href="#a3e84efdf47853d628655a1750fb8523a">More...</a><br /></td></tr>
<tr class="separator:a3e84efdf47853d628655a1750fb8523a"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename FunctionType&gt;<br />
class mlpack::optimization::GradientDescent&lt; FunctionType &gt;</h3>
<p>Gradient Descent is a technique to minimize a function. </p>
<p>To find a local minimum of a function using gradient descent, one takes steps proportional to the negative of the gradient of the function at the current point, producing the following update scheme:</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ A_{j + 1} = A_j + \alpha \nabla F(A) \]" src="form_34.png"/>
</p>
<p>where <img class="formulaInl" alt="$ \alpha $" src="form_35.png"/> is a parameter which specifies the step size. <img class="formulaInl" alt="$ F $" src="form_36.png"/> is the function being optimized. The algorithm continues until <img class="formulaInl" alt="$ j $" src="form_37.png"/> reaches the maximum number of iterations&mdash;or when an update produces an improvement within a certain tolerance <img class="formulaInl" alt="$ \epsilon $" src="form_38.png"/>. That is,</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ | F(A_{j + 1}) - F(A_j) | &lt; \epsilon. \]" src="form_39.png"/>
</p>
<p>The parameter <img class="formulaInl" alt="$\epsilon$" src="form_40.png"/> is specified by the tolerance parameter to the constructor.</p>
<p>For Gradient Descent to work, a FunctionType template parameter is required. This class must implement the following function:</p>
<p>double Evaluate(const arma::mat&amp; coordinates); void Gradient(const arma::mat&amp; coordinates, arma::mat&amp; gradient);</p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">FunctionType</td><td>Decomposable objective function type to be minimized. </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="gradient__descent_8hpp_source.html#l00053">53</a> of file <a class="el" href="gradient__descent_8hpp_source.html">gradient_descent.hpp</a>.</p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a class="anchor" id="a4755e084ee5cde85897e241cd1117a85"></a>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename FunctionType &gt; </div>
<table class="memname">
<tr>
<td class="memname"><a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html">mlpack::optimization::GradientDescent</a>&lt; FunctionType &gt;::<a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html">GradientDescent</a> </td>
<td>(</td>
<td class="paramtype">FunctionType &amp;&#160;</td>
<td class="paramname"><em>function</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const double&#160;</td>
<td class="paramname"><em>stepSize</em> = <code>0.01</code>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const size_t&#160;</td>
<td class="paramname"><em>maxIterations</em> = <code>100000</code>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const double&#160;</td>
<td class="paramname"><em>tolerance</em> = <code>1e-5</code>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Construct the Gradient Descent optimizer with the given function and parameters. </p>
<p>The defaults here are not necessarily good for the given problem, so it is suggested that the values used be tailored to the task at hand.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">function</td><td>Function to be optimized (minimized). </td></tr>
<tr><td class="paramname">stepSize</td><td>Step size for each iteration. </td></tr>
<tr><td class="paramname">maxIterations</td><td>Maximum number of iterations allowed (0 means no limit). </td></tr>
<tr><td class="paramname">tolerance</td><td>Maximum absolute tolerance to terminate algorithm. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<h2 class="groupheader">Member Function Documentation</h2>
<a class="anchor" id="aaa6285f395314801d8822d7553719fb4"></a>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename FunctionType &gt; </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">const FunctionType&amp; <a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html">mlpack::optimization::GradientDescent</a>&lt; FunctionType &gt;::Function </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p>Get the instantiated function to be optimized. </p>
<p>Definition at line <a class="el" href="gradient__descent_8hpp_source.html#l00084">84</a> of file <a class="el" href="gradient__descent_8hpp_source.html">gradient_descent.hpp</a>.</p>
</div>
</div>
<a class="anchor" id="a3850668f2220842895a6b1a3eb567259"></a>
<div class="memitem">
<div class="memproto">
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template&lt;typename FunctionType &gt; </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
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<tr>
<td class="memname">FunctionType&amp; <a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html">mlpack::optimization::GradientDescent</a>&lt; FunctionType &gt;::Function </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span></span> </td>
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<p>Modify the instantiated function. </p>
<p>Definition at line <a class="el" href="gradient__descent_8hpp_source.html#l00086">86</a> of file <a class="el" href="gradient__descent_8hpp_source.html">gradient_descent.hpp</a>.</p>
</div>
</div>
<a class="anchor" id="ab8cf876f67ec1dea34b86eaf4ecfc725"></a>
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template&lt;typename FunctionType &gt; </div>
<table class="mlabels">
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<td class="mlabels-left">
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<td class="memname">size_t <a class="el" href="classmlpack_1_1optimization_1_1GradientDescent.html">mlpack::optimization::GradientDescent</a>&lt; FunctionType &gt;::MaxIterations </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span></span> </td>
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<p>Get the maximum number of iterations (0 indicates no limit). </p>
<p>Definition at line <a class="el" href="gradient__descent_8hpp_source.html#l00094">94</a> of file <a class="el" href="gradient__descent_8hpp_source.html">gradient_descent.hpp</a>.</p>
<p>References <a class="el" href="gradient__descent_8hpp_source.html#l00111">mlpack::optimization::GradientDescent&lt; FunctionType &gt;::maxIterations</a>.</p>
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<p>Modify the maximum number of iterations (0 indicates no limit). </p>
<p>Definition at line <a class="el" href="gradient__descent_8hpp_source.html#l00096">96</a> of file <a class="el" href="gradient__descent_8hpp_source.html">gradient_descent.hpp</a>.</p>
<p>References <a class="el" href="gradient__descent_8hpp_source.html#l00111">mlpack::optimization::GradientDescent&lt; FunctionType &gt;::maxIterations</a>.</p>
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<p>Optimize the given function using gradient descent. </p>
<p>The given starting point will be modified to store the finishing point of the algorithm, and the final objective value is returned.</p>
<dl class="params"><dt>Parameters</dt><dd>
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<dl class="section return"><dt>Returns</dt><dd>Objective value of the final point. </dd></dl>
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<p>Get the step size. </p>
<p>Definition at line <a class="el" href="gradient__descent_8hpp_source.html#l00089">89</a> of file <a class="el" href="gradient__descent_8hpp_source.html">gradient_descent.hpp</a>.</p>
<p>References <a class="el" href="gradient__descent_8hpp_source.html#l00108">mlpack::optimization::GradientDescent&lt; FunctionType &gt;::stepSize</a>.</p>
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<p>Modify the step size. </p>
<p>Definition at line <a class="el" href="gradient__descent_8hpp_source.html#l00091">91</a> of file <a class="el" href="gradient__descent_8hpp_source.html">gradient_descent.hpp</a>.</p>
<p>References <a class="el" href="gradient__descent_8hpp_source.html#l00108">mlpack::optimization::GradientDescent&lt; FunctionType &gt;::stepSize</a>.</p>
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<p>Get the tolerance for termination. </p>
<p>Definition at line <a class="el" href="gradient__descent_8hpp_source.html#l00099">99</a> of file <a class="el" href="gradient__descent_8hpp_source.html">gradient_descent.hpp</a>.</p>
<p>References <a class="el" href="gradient__descent_8hpp_source.html#l00114">mlpack::optimization::GradientDescent&lt; FunctionType &gt;::tolerance</a>.</p>
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<p>Modify the tolerance for termination. </p>
<p>Definition at line <a class="el" href="gradient__descent_8hpp_source.html#l00101">101</a> of file <a class="el" href="gradient__descent_8hpp_source.html">gradient_descent.hpp</a>.</p>
<p>References <a class="el" href="gradient__descent_8hpp_source.html#l00114">mlpack::optimization::GradientDescent&lt; FunctionType &gt;::tolerance</a>.</p>
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<h2 class="groupheader">Member Data Documentation</h2>
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<p>The instantiated function. </p>
<p>Definition at line <a class="el" href="gradient__descent_8hpp_source.html#l00105">105</a> of file <a class="el" href="gradient__descent_8hpp_source.html">gradient_descent.hpp</a>.</p>
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<p>The maximum number of allowed iterations. </p>
<p>Definition at line <a class="el" href="gradient__descent_8hpp_source.html#l00111">111</a> of file <a class="el" href="gradient__descent_8hpp_source.html">gradient_descent.hpp</a>.</p>
<p>Referenced by <a class="el" href="gradient__descent_8hpp_source.html#l00094">mlpack::optimization::GradientDescent&lt; FunctionType &gt;::MaxIterations()</a>.</p>
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<p>The step size for each example. </p>
<p>Definition at line <a class="el" href="gradient__descent_8hpp_source.html#l00108">108</a> of file <a class="el" href="gradient__descent_8hpp_source.html">gradient_descent.hpp</a>.</p>
<p>Referenced by <a class="el" href="gradient__descent_8hpp_source.html#l00089">mlpack::optimization::GradientDescent&lt; FunctionType &gt;::StepSize()</a>.</p>
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<p>The tolerance for termination. </p>
<p>Definition at line <a class="el" href="gradient__descent_8hpp_source.html#l00114">114</a> of file <a class="el" href="gradient__descent_8hpp_source.html">gradient_descent.hpp</a>.</p>
<p>Referenced by <a class="el" href="gradient__descent_8hpp_source.html#l00099">mlpack::optimization::GradientDescent&lt; FunctionType &gt;::Tolerance()</a>.</p>
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<hr/>The documentation for this class was generated from the following file:<ul>
<li>src/mlpack/core/optimizers/gradient_descent/<a class="el" href="gradient__descent_8hpp_source.html">gradient_descent.hpp</a></li>
</ul>
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