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<p>Implements the dual-scaling algorithm.
<a href="#details">More...</a></p>
<p><a href="dualalg_8c_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="func-members"></a>
Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="dualalg_8c.html#aff5c9ba243804682fe3b317dc98e2552">DSDPChooseBarrierParameter</a> (<a class="el" href="structDSDP__C.html">DSDP</a>, double, double *, double *)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">DSDP barrier heuristic choses the smalles value of mu such that X>0. <a href="#aff5c9ba243804682fe3b317dc98e2552"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="group__DSDPSolver.html#ga751ef8af8faeff2f298088cc875a35ac">DSDPComputeAndFactorS</a> (<a class="el" href="structDSDP__C.html">DSDP</a> dsdp, <a class="el" href="dsdpbasictypes_8h.html#ae667f2bff3ab5ab0bc109fa76dc4ed65">DSDPTruth</a> *psdefinite)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Compute and factor the dual matrix variables. <a href="group__DSDPSolver.html#ga751ef8af8faeff2f298088cc875a35ac"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="dualalg_8c.html#a6dbdc2c2d1fd767b6076fc2f20f6ee09">DSDPComputeDualStepDirections</a> (<a class="el" href="structDSDP__C.html">DSDP</a> dsdp)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Compute the step direction by computing a linear system and solving it. <a href="#a6dbdc2c2d1fd767b6076fc2f20f6ee09"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="dualalg_8c.html#a4a04f9882a4b6604ecffceac4264b391">DSDPInitializeVariables</a> (<a class="el" href="structDSDP__C.html">DSDP</a> dsdp)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Initialize variables and factor S. <a href="#a4a04f9882a4b6604ecffceac4264b391"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="dualalg_8c.html#af262352046fddd0988f0f5a59b008c6f">DSDPResetY0</a> (<a class="el" href="structDSDP__C.html">DSDP</a>)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">After 1 iteration, consider increasing the variable r. <a href="#af262352046fddd0988f0f5a59b008c6f"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="dualalg_8c.html#afb23fdbc50bdf8a8121c2ed619a1a313">DSDPSolveDynamicRho</a> (<a class="el" href="structDSDP__C.html">DSDP</a> dsdp)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Apply dual-scaling algorithm. <a href="#afb23fdbc50bdf8a8121c2ed619a1a313"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="dualalg_8c.html#a9ebf24d9826d192879688033b391d22a">DSDPYStepLineSearch</a> (<a class="el" href="structDSDP__C.html">DSDP</a>, double, double, <a class="el" href="dsdpvec_8h.html#a421243d35437ad44ded3c1e34198e8e9">DSDPVec</a>)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Used for Newton step, the merit function of this line search is the dual potential function. <a href="#a9ebf24d9826d192879688033b391d22a"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="dualalg_8c.html#aa1ba256ca46d2edbab2553f8317da613">DSDPYStepLineSearch2</a> (<a class="el" href="structDSDP__C.html">DSDP</a>, double, double, <a class="el" href="dsdpvec_8h.html#a421243d35437ad44ded3c1e34198e8e9">DSDPVec</a>)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Used for centering steps, the merit function of this line search is the objective function plus the barrier term. <a href="#aa1ba256ca46d2edbab2553f8317da613"></a><br/></td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Implements the dual-scaling algorithm. </p>
<p>Definition in file <a class="el" href="dualalg_8c_source.html">dualalg.c</a>.</p>
</div><hr/><h2>Function Documentation</h2>
<a class="anchor" id="aff5c9ba243804682fe3b317dc98e2552"></a><!-- doxytag: member="dualalg.c::DSDPChooseBarrierParameter" ref="aff5c9ba243804682fe3b317dc98e2552" args="(DSDP, double, double *, double *)" -->
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<td class="memname">int DSDPChooseBarrierParameter </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structDSDP__C.html">DSDP</a> </td>
<td class="paramname"><em>dsdp</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">double </td>
<td class="paramname"><em>mutarget</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">double * </td>
<td class="paramname"><em>ppstep</em>, </td>
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<td class="paramtype">double * </td>
<td class="paramname"><em>nextmutarget</em> </td>
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<p>DSDP barrier heuristic choses the smalles value of mu such that X>0. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">dsdp</td><td>solver </td></tr>
<tr><td class="paramname">mutarget</td><td>current barrier parameter </td></tr>
<tr><td class="paramname">ppstep</td><td>set to primal step length </td></tr>
<tr><td class="paramname">nextmutarget</td><td>set to new target barrier parameter This routine implements a dynamic strategy for reducing the barrier parameter. Basically, it looks for the smallest barrier parameter for which the primal matrix X is psd. Lower and upper bounds to this parameter also apply. </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="dualalg_8c_source.html#l00240">240</a> of file <a class="el" href="dualalg_8c_source.html">dualalg.c</a>.</p>
<p>Referenced by <a class="el" href="dualalg_8c_source.html#l00121">DSDPSolveDynamicRho()</a>.</p>
</div>
</div>
<a class="anchor" id="a6dbdc2c2d1fd767b6076fc2f20f6ee09"></a><!-- doxytag: member="dualalg.c::DSDPComputeDualStepDirections" ref="a6dbdc2c2d1fd767b6076fc2f20f6ee09" args="(DSDP dsdp)" -->
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<td class="memname">int DSDPComputeDualStepDirections </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structDSDP__C.html">DSDP</a> </td>
<td class="paramname"><em>dsdp</em></td><td>)</td>
<td></td>
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<p>Compute the step direction by computing a linear system and solving it. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">dsdp</td><td>the solver</td></tr>
</table>
</dd>
</dl>
<p>DSDP first attempts unpreconditioned CG to the matrix. Once the number of iterations becomes too large, it swithes a CG preconditioned by the Cholesky factorization. Usually only one iteration of the preconditioned CG is necessary, but solutions with large norms and very precise solutions may require additional iterations. </p>
<p>Definition at line <a class="el" href="dualalg_8c_source.html#l00370">370</a> of file <a class="el" href="dualalg_8c_source.html">dualalg.c</a>.</p>
<p>Referenced by <a class="el" href="dualalg_8c_source.html#l00121">DSDPSolveDynamicRho()</a>.</p>
</div>
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<a class="anchor" id="a4a04f9882a4b6604ecffceac4264b391"></a><!-- doxytag: member="dualalg.c::DSDPInitializeVariables" ref="a4a04f9882a4b6604ecffceac4264b391" args="(DSDP dsdp)" -->
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<td class="memname">int DSDPInitializeVariables </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structDSDP__C.html">DSDP</a> </td>
<td class="paramname"><em>dsdp</em></td><td>)</td>
<td></td>
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<p>Initialize variables and factor S. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">dsdp</td><td>the solver </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="dualalg_8c_source.html#l00475">475</a> of file <a class="el" href="dualalg_8c_source.html">dualalg.c</a>.</p>
<p>Referenced by <a class="el" href="dsdpsetup_8c_source.html#l00343">DSDPSolve()</a>.</p>
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<a class="anchor" id="af262352046fddd0988f0f5a59b008c6f"></a><!-- doxytag: member="dualalg.c::DSDPResetY0" ref="af262352046fddd0988f0f5a59b008c6f" args="(DSDP)" -->
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<td class="memname">int DSDPResetY0 </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structDSDP__C.html">DSDP</a> </td>
<td class="paramname"><em>dsdp</em></td><td>)</td>
<td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>After 1 iteration, consider increasing the variable r. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">dsdp</td><td>solver </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="dualalg_8c_source.html#l00328">328</a> of file <a class="el" href="dualalg_8c_source.html">dualalg.c</a>.</p>
<p>Referenced by <a class="el" href="dualalg_8c_source.html#l00121">DSDPSolveDynamicRho()</a>.</p>
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<a class="anchor" id="afb23fdbc50bdf8a8121c2ed619a1a313"></a><!-- doxytag: member="dualalg.c::DSDPSolveDynamicRho" ref="afb23fdbc50bdf8a8121c2ed619a1a313" args="(DSDP dsdp)" -->
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<td class="memname">int DSDPSolveDynamicRho </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structDSDP__C.html">DSDP</a> </td>
<td class="paramname"><em>dsdp</em></td><td>)</td>
<td></td>
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</table>
</div>
<div class="memdoc">
<p>Apply dual-scaling algorithm. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">dsdp</td><td>the solver </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="dualalg_8c_source.html#l00121">121</a> of file <a class="el" href="dualalg_8c_source.html">dualalg.c</a>.</p>
<p>Referenced by <a class="el" href="dsdpsetup_8c_source.html#l00343">DSDPSolve()</a>.</p>
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</div>
<a class="anchor" id="a9ebf24d9826d192879688033b391d22a"></a><!-- doxytag: member="dualalg.c::DSDPYStepLineSearch" ref="a9ebf24d9826d192879688033b391d22a" args="(DSDP, double, double, DSDPVec)" -->
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<td class="memname">int DSDPYStepLineSearch </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structDSDP__C.html">DSDP</a> </td>
<td class="paramname"><em>dsdp</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double </td>
<td class="paramname"><em>mutarget</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double </td>
<td class="paramname"><em>dstep0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="dsdpvec_8h.html#a421243d35437ad44ded3c1e34198e8e9">DSDPVec</a> </td>
<td class="paramname"><em>dy</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
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<div class="memdoc">
<p>Used for Newton step, the merit function of this line search is the dual potential function. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">dsdp</td><td>the solver </td></tr>
<tr><td class="paramname">mutarget</td><td>barrier parameter </td></tr>
<tr><td class="paramname">dstep0</td><td>initial step length </td></tr>
<tr><td class="paramname">dy</td><td>step direction </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="dualalg_8c_source.html#l00024">24</a> of file <a class="el" href="dualalg_8c_source.html">dualalg.c</a>.</p>
<p>Referenced by <a class="el" href="dualalg_8c_source.html#l00121">DSDPSolveDynamicRho()</a>.</p>
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</div>
<a class="anchor" id="aa1ba256ca46d2edbab2553f8317da613"></a><!-- doxytag: member="dualalg.c::DSDPYStepLineSearch2" ref="aa1ba256ca46d2edbab2553f8317da613" args="(DSDP, double, double, DSDPVec)" -->
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<td class="memname">int DSDPYStepLineSearch2 </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structDSDP__C.html">DSDP</a> </td>
<td class="paramname"><em>dsdp</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double </td>
<td class="paramname"><em>mutarget</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double </td>
<td class="paramname"><em>dstep0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="dsdpvec_8h.html#a421243d35437ad44ded3c1e34198e8e9">DSDPVec</a> </td>
<td class="paramname"><em>dy</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>Used for centering steps, the merit function of this line search is the objective function plus the barrier term. </p>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">dsdp</td><td>the solver </td></tr>
<tr><td class="paramname">mutarget</td><td>barrier parameter </td></tr>
<tr><td class="paramname">dstep0</td><td>initial step length </td></tr>
<tr><td class="paramname">dy</td><td>step direction </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="dualalg_8c_source.html#l00073">73</a> of file <a class="el" href="dualalg_8c_source.html">dualalg.c</a>.</p>
<p>Referenced by <a class="el" href="dualalg_8c_source.html#l00121">DSDPSolveDynamicRho()</a>.</p>
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