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<span class="path"><a href="index.html">Symphony Toolbox</a> >> <a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a> > lsqlin</span>
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<div class="refnamediv"><h1 class="refname">lsqlin</h1>
<p class="refpurpose">Solves a linear quadratic problem.</p></div>
<div class="refsynopsisdiv"><h3 class="title">Calling Sequence</h3>
<div class="synopsis"><pre><span class="default">xopt</span><span class="default"> = </span><span class="functionid">lsqlin</span><span class="default">(</span><span class="default">C</span><span class="default">,</span><span class="default">d</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">lsqlin</span><span class="default">(</span><span class="default">C</span><span class="default">,</span><span class="default">d</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">lsqlin</span><span class="default">(</span><span class="default">C</span><span class="default">,</span><span class="default">d</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">lsqlin</span><span class="default">(</span><span class="default">C</span><span class="default">,</span><span class="default">d</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">x0</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">lsqlin</span><span class="default">(</span><span class="default">C</span><span class="default">,</span><span class="default">d</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">param</span><span class="default">)</span>
<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">resnorm</span><span class="default">,</span><span class="default">residual</span><span class="default">,</span><span class="default">exitflag</span><span class="default">,</span><span class="default">output</span><span class="default">,</span><span class="default">lambda</span><span class="default">] = </span><span class="functionid">lsqlin</span><span class="default">( ... )</span></pre></div></div>
<div class="refsection"><h3 class="title">Parameters</h3>
<dl><dt><span class="term">C :</span>
<dd><p class="para">a matrix of double, represents the multiplier of the solution x in the expression C*x - d. Number of columns in C is equal to the number of elements in x.</p></dd></dt>
<dt><span class="term">d :</span>
<dd><p class="para">a vector of double, represents the additive constant term in the expression C*x - d. Number of elements in d is equal to the number of rows in C matrix.</p></dd></dt>
<dt><span class="term">A :</span>
<dd><p class="para">a vector of double, represents the linear coefficients in the inequality constraints</p></dd></dt>
<dt><span class="term">b :</span>
<dd><p class="para">a vector of double, represents the linear coefficients in the inequality constraints</p></dd></dt>
<dt><span class="term">Aeq :</span>
<dd><p class="para">a matrix of double, represents the linear coefficients in the equality constraints</p></dd></dt>
<dt><span class="term">beq :</span>
<dd><p class="para">a vector of double, represents the linear coefficients in the equality constraints</p></dd></dt>
<dt><span class="term">lb :</span>
<dd><p class="para">a vector of double, contains lower bounds of the variables.</p></dd></dt>
<dt><span class="term">ub :</span>
<dd><p class="para">a vector of double, contains upper bounds of the variables.</p></dd></dt>
<dt><span class="term">x0 :</span>
<dd><p class="para">a vector of double, contains initial guess of variables.</p></dd></dt>
<dt><span class="term">param :</span>
<dd><p class="para">a list containing the the parameters to be set.</p></dd></dt>
<dt><span class="term">xopt :</span>
<dd><p class="para">a vector of double, the computed solution of the optimization problem.</p></dd></dt>
<dt><span class="term">resnorm :</span>
<dd><p class="para">a double, objective value returned as the scalar value norm(C*x-d)^2.</p></dd></dt>
<dt><span class="term">residual :</span>
<dd><p class="para">a vector of double, solution residuals returned as the vector C*x-d.</p></dd></dt>
<dt><span class="term">exitflag :</span>
<dd><p class="para">Integer identifying the reason the algorithm terminated. It could be 0, 1 or 2 etc. i.e. Optimal, Maximum Number of Iterations Exceeded, CPU time exceeded. Other flags one can see in the lsqlin macro.</p></dd></dt>
<dt><span class="term">output :</span>
<dd><p class="para">Structure containing information about the optimization. This version only contains number of iterations.</p></dd></dt>
<dt><span class="term">lambda :</span>
<dd><p class="para">Structure containing the Lagrange multipliers at the solution x (separated by constraint type).It contains lower, upper bound multiplier and linear equality, inequality constraints.</p></dd></dt></dl></div>
<div class="refsection"><h3 class="title">Description</h3>
<p class="para">Search the minimum of a constrained linear least square problem specified by :</p>
<p class="para"><span><img src='./_LaTeX_lsqlin.xml_1.png' style='position:relative;top:41px;width:230px;height:90px'/></span></p>
<p class="para">The routine calls Ipopt for solving the linear least square problem, Ipopt is a library written in C++.</p>
<p class="para"></p></div>
<div class="refsection"><h3 class="title">Examples</h3>
<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//A simple linear least square example</span>
<span class="scilabid">C</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">0.9501</span> <span class="scilabnumber">0.7620</span> <span class="scilabnumber">0.6153</span> <span class="scilabnumber">0.4057</span>
<span class="scilabnumber">0.2311</span> <span class="scilabnumber">0.4564</span> <span class="scilabnumber">0.7919</span> <span class="scilabnumber">0.9354</span>
<span class="scilabnumber">0.6068</span> <span class="scilabnumber">0.0185</span> <span class="scilabnumber">0.9218</span> <span class="scilabnumber">0.9169</span>
<span class="scilabnumber">0.4859</span> <span class="scilabnumber">0.8214</span> <span class="scilabnumber">0.7382</span> <span class="scilabnumber">0.4102</span>
<span class="scilabnumber">0.8912</span> <span class="scilabnumber">0.4447</span> <span class="scilabnumber">0.1762</span> <span class="scilabnumber">0.8936</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">d</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">0.0578</span>
<span class="scilabnumber">0.3528</span>
<span class="scilabnumber">0.8131</span>
<span class="scilabnumber">0.0098</span>
<span class="scilabnumber">0.1388</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">A</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">0.2027</span> <span class="scilabnumber">0.2721</span> <span class="scilabnumber">0.7467</span> <span class="scilabnumber">0.4659</span>
<span class="scilabnumber">0.1987</span> <span class="scilabnumber">0.1988</span> <span class="scilabnumber">0.4450</span> <span class="scilabnumber">0.4186</span>
<span class="scilabnumber">0.6037</span> <span class="scilabnumber">0.0152</span> <span class="scilabnumber">0.9318</span> <span class="scilabnumber">0.8462</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">b</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">0.5251</span>
<span class="scilabnumber">0.2026</span>
<span class="scilabnumber">0.6721</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">resnorm</span><span class="scilabdefault">,</span><span class="scilabid">residual</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span> <span class="scilabid">lsqlin</span><span class="scilabopenclose">(</span><span class="scilabid">C</span><span class="scilabdefault">,</span><span class="scilabid">d</span><span class="scilabdefault">,</span><span class="scilabid">A</span><span class="scilabdefault">,</span><span class="scilabid">b</span><span class="scilabopenclose">)</span>
<span class="scilabcomment">// Press ENTER to continue</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div>
<div class="refsection"><h3 class="title">Examples</h3>
<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//A basic example for equality, inequality constraints and variable bounds</span>
<span class="scilabid">C</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">0.9501</span> <span class="scilabnumber">0.7620</span> <span class="scilabnumber">0.6153</span> <span class="scilabnumber">0.4057</span>
<span class="scilabnumber">0.2311</span> <span class="scilabnumber">0.4564</span> <span class="scilabnumber">0.7919</span> <span class="scilabnumber">0.9354</span>
<span class="scilabnumber">0.6068</span> <span class="scilabnumber">0.0185</span> <span class="scilabnumber">0.9218</span> <span class="scilabnumber">0.9169</span>
<span class="scilabnumber">0.4859</span> <span class="scilabnumber">0.8214</span> <span class="scilabnumber">0.7382</span> <span class="scilabnumber">0.4102</span>
<span class="scilabnumber">0.8912</span> <span class="scilabnumber">0.4447</span> <span class="scilabnumber">0.1762</span> <span class="scilabnumber">0.8936</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">d</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">0.0578</span>
<span class="scilabnumber">0.3528</span>
<span class="scilabnumber">0.8131</span>
<span class="scilabnumber">0.0098</span>
<span class="scilabnumber">0.1388</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">A</span> <span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">0.2027</span> <span class="scilabnumber">0.2721</span> <span class="scilabnumber">0.7467</span> <span class="scilabnumber">0.4659</span>
<span class="scilabnumber">0.1987</span> <span class="scilabnumber">0.1988</span> <span class="scilabnumber">0.4450</span> <span class="scilabnumber">0.4186</span>
<span class="scilabnumber">0.6037</span> <span class="scilabnumber">0.0152</span> <span class="scilabnumber">0.9318</span> <span class="scilabnumber">0.8462</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">b</span> <span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">0.5251</span>
<span class="scilabnumber">0.2026</span>
<span class="scilabnumber">0.6721</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">Aeq</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">3</span> <span class="scilabnumber">5</span> <span class="scilabnumber">7</span> <span class="scilabnumber">9</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">beq</span> <span class="scilaboperator">=</span> <span class="scilabnumber">4</span><span class="scilabdefault">;</span>
<span class="scilabid">lb</span> <span class="scilaboperator">=</span> <span class="scilaboperator">-</span><span class="scilabnumber">0.1</span><span class="scilaboperator">*</span><a class="scilabcommand" href="scilab://ones">ones</a><span class="scilabopenclose">(</span><span class="scilabnumber">4</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span>
<span class="scilabid">ub</span> <span class="scilaboperator">=</span> <span class="scilabnumber">2</span><span class="scilaboperator">*</span><a class="scilabcommand" href="scilab://ones">ones</a><span class="scilabopenclose">(</span><span class="scilabnumber">4</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span>
<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">resnorm</span><span class="scilabdefault">,</span><span class="scilabid">residual</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span> <span class="scilabid">lsqlin</span><span class="scilabopenclose">(</span><span class="scilabid">C</span><span class="scilabdefault">,</span><span class="scilabid">d</span><span class="scilabdefault">,</span><span class="scilabid">A</span><span class="scilabdefault">,</span><span class="scilabid">b</span><span class="scilabdefault">,</span><span class="scilabid">Aeq</span><span class="scilabdefault">,</span><span class="scilabid">beq</span><span class="scilabdefault">,</span><span class="scilabid">lb</span><span class="scilabdefault">,</span><span class="scilabid">ub</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div>
<div class="refsection"><h3 class="title">Authors</h3>
<ul class="itemizedlist"><li class="member">Harpreet Singh</li></ul></div>
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