<html lang="en"> <head> <title>Quadratic Programming - GNU Octave</title> <meta http-equiv="Content-Type" content="text/html"> <meta name="description" content="GNU Octave"> <meta name="generator" content="makeinfo 4.13"> <link title="Top" rel="start" href="index.html#Top"> <link rel="up" href="Optimization.html#Optimization" title="Optimization"> <link rel="prev" href="Linear-Programming.html#Linear-Programming" title="Linear Programming"> <link rel="next" href="Nonlinear-Programming.html#Nonlinear-Programming" title="Nonlinear Programming"> <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage"> <meta http-equiv="Content-Style-Type" content="text/css"> <style type="text/css"><!-- pre.display { font-family:inherit } pre.format { font-family:inherit } pre.smalldisplay { font-family:inherit; font-size:smaller } pre.smallformat { font-family:inherit; font-size:smaller } pre.smallexample { font-size:smaller } pre.smalllisp { font-size:smaller } span.sc { font-variant:small-caps } span.roman { font-family:serif; font-weight:normal; } span.sansserif { font-family:sans-serif; font-weight:normal; } --></style> </head> <body> <div class="node"> <a name="Quadratic-Programming"></a> <p> Next: <a rel="next" accesskey="n" href="Nonlinear-Programming.html#Nonlinear-Programming">Nonlinear Programming</a>, Previous: <a rel="previous" accesskey="p" href="Linear-Programming.html#Linear-Programming">Linear Programming</a>, Up: <a rel="up" accesskey="u" href="Optimization.html#Optimization">Optimization</a> <hr> </div> <h3 class="section">25.2 Quadratic Programming</h3> <p>Octave can also solve Quadratic Programming problems, this is <pre class="example"> min 0.5 x'*H*x + x'*q </pre> <p>subject to <pre class="example"> A*x = b lb <= x <= ub A_lb <= A_in*x <= A_ub </pre> <!-- qp scripts/optimization/qp.m --> <p><a name="doc_002dqp"></a> <div class="defun"> — Function File: [<var>x</var>, <var>obj</var>, <var>info</var>, <var>lambda</var>] = <b>qp</b> (<var>x0, H</var>)<var><a name="index-qp-2374"></a></var><br> — Function File: [<var>x</var>, <var>obj</var>, <var>info</var>, <var>lambda</var>] = <b>qp</b> (<var>x0, H, q</var>)<var><a name="index-qp-2375"></a></var><br> — Function File: [<var>x</var>, <var>obj</var>, <var>info</var>, <var>lambda</var>] = <b>qp</b> (<var>x0, H, q, A, b</var>)<var><a name="index-qp-2376"></a></var><br> — Function File: [<var>x</var>, <var>obj</var>, <var>info</var>, <var>lambda</var>] = <b>qp</b> (<var>x0, H, q, A, b, lb, ub</var>)<var><a name="index-qp-2377"></a></var><br> — Function File: [<var>x</var>, <var>obj</var>, <var>info</var>, <var>lambda</var>] = <b>qp</b> (<var>x0, H, q, A, b, lb, ub, A_lb, A_in, A_ub</var>)<var><a name="index-qp-2378"></a></var><br> — Function File: [<var>x</var>, <var>obj</var>, <var>info</var>, <var>lambda</var>] = <b>qp</b> (<var><small class="dots">...</small>, options</var>)<var><a name="index-qp-2379"></a></var><br> <blockquote><p>Solve the quadratic program <pre class="example"> min 0.5 x'*H*x + x'*q x </pre> <p>subject to <pre class="example"> A*x = b lb <= x <= ub A_lb <= A_in*x <= A_ub </pre> <p class="noindent">using a null-space active-set method. <p>Any bound (<var>A</var>, <var>b</var>, <var>lb</var>, <var>ub</var>, <var>A_lb</var>, <var>A_ub</var>) may be set to the empty matrix (<code>[]</code>) if not present. If the initial guess is feasible the algorithm is faster. <dl> <dt><var>options</var><dd>An optional structure containing the following parameter(s) used to define the behavior of the solver. Missing elements in the structure take on default values, so you only need to set the elements that you wish to change from the default. <dl> <dt><code>MaxIter (default: 200)</code><dd>Maximum number of iterations. </dl> </dl> <dl> <dt><var>info</var><dd>Structure containing run-time information about the algorithm. The following fields are defined: <dl> <dt><code>solveiter</code><dd>The number of iterations required to find the solution. <br><dt><code>info</code><dd>An integer indicating the status of the solution. <dl> <dt>0<dd>The problem is feasible and convex. Global solution found. <br><dt>1<dd>The problem is not convex. Local solution found. <br><dt>2<dd>The problem is not convex and unbounded. <br><dt>3<dd>Maximum number of iterations reached. <br><dt>6<dd>The problem is infeasible. </dl> </dl> </dl> </p></blockquote></div> <!-- pqpnonneg scripts/optimization/pqpnonneg.m --> <p><a name="doc_002dpqpnonneg"></a> <div class="defun"> — Function File: <var>x</var> = <b>pqpnonneg</b> (<var>c, d</var>)<var><a name="index-pqpnonneg-2380"></a></var><br> — Function File: <var>x</var> = <b>pqpnonneg</b> (<var>c, d, x0</var>)<var><a name="index-pqpnonneg-2381"></a></var><br> — Function File: [<var>x</var>, <var>minval</var>] = <b>pqpnonneg</b> (<var><small class="dots">...</small></var>)<var><a name="index-pqpnonneg-2382"></a></var><br> — Function File: [<var>x</var>, <var>minval</var>, <var>exitflag</var>] = <b>pqpnonneg</b> (<var><small class="dots">...</small></var>)<var><a name="index-pqpnonneg-2383"></a></var><br> — Function File: [<var>x</var>, <var>minval</var>, <var>exitflag</var>, <var>output</var>] = <b>pqpnonneg</b> (<var><small class="dots">...</small></var>)<var><a name="index-pqpnonneg-2384"></a></var><br> — Function File: [<var>x</var>, <var>minval</var>, <var>exitflag</var>, <var>output</var>, <var>lambda</var>] = <b>pqpnonneg</b> (<var><small class="dots">...</small></var>)<var><a name="index-pqpnonneg-2385"></a></var><br> <blockquote><p>Minimize <code>1/2*x'*c*x + d'*x</code> subject to <var>x</var><code> >= 0</code>. <var>c</var> and <var>d</var> must be real, and <var>c</var> must be symmetric and positive definite. <var>x0</var> is an optional initial guess for <var>x</var>. <p>Outputs: <ul> <li>minval <p>The minimum attained model value, 1/2*xmin'*c*xmin + d'*xmin <li>exitflag <p>An indicator of convergence. 0 indicates that the iteration count was exceeded, and therefore convergence was not reached; >0 indicates that the algorithm converged. (The algorithm is stable and will converge given enough iterations.) <li>output <p>A structure with two fields: <ul> <li>"algorithm": The algorithm used ("nnls") <li>"iterations": The number of iterations taken. </ul> <li>lambda <p>Not implemented. </ul> <!-- Texinfo @sp should work but in practice produces ugly results for HTML. --> <!-- A simple blank line produces the correct behavior. --> <!-- @sp 1 --> <p class="noindent"><strong>See also:</strong> <a href="doc_002doptimset.html#doc_002doptimset">optimset</a>, <a href="doc_002dlsqnonneg.html#doc_002dlsqnonneg">lsqnonneg</a>, <a href="doc_002dqp.html#doc_002dqp">qp</a>. </p></blockquote></div> </body></html>