1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
|
<html lang="en">
<head>
<title>Quadratic Programming - Untitled</title>
<meta http-equiv="Content-Type" content="text/html">
<meta name="description" content="Untitled">
<meta name="generator" content="makeinfo 4.11">
<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">
<p>
<a name="Quadratic-Programming"></a>
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">24.2 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>
<!-- ./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, q, A, b, lb, ub, A_lb, A_in, A_ub</var>)<var><a name="index-qp-1802"></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.
<p>The value <var>info</var> is a structure with the following fields:
<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, as follows:
<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>
</p></blockquote></div>
</body></html>
|
