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
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
|
<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from qpipopt_mat.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="qpipopt_mat" xml:lang="en"
xmlns="http://docbook.org/ns/docbook"
xmlns:xlink="http://www.w3.org/1999/xlink"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns:ns3="http://www.w3.org/1999/xhtml"
xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:scilab="http://www.scilab.org"
xmlns:db="http://docbook.org/ns/docbook">
<refnamediv>
<refname>qpipopt_mat</refname>
<refpurpose>Solves a linear quadratic problem.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
xopt = qpipopt_mat(nbVar,nbCon,Q,p,LB,UB,conMatrix,conLB,conUB)
x = qpipopt_mat(H,f)
x = qpipopt_mat(H,f,A,b)
x = qpipopt_mat(H,f,A,b,Aeq,beq)
x = qpipopt_mat(H,f,A,b,Aeq,beq,lb,ub)
[xopt,fopt,exitflag,output,lamda] = qpipopt_mat( ... )
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>H :</term>
<listitem><para> a n x n matrix of doubles, where n is number of variables, represents coefficients of quadratic in the quadratic problem.</para></listitem></varlistentry>
<varlistentry><term>f :</term>
<listitem><para> a n x 1 matrix of doubles, where n is number of variables, represents coefficients of linear in the quadratic problem</para></listitem></varlistentry>
<varlistentry><term>A :</term>
<listitem><para> a m x n matrix of doubles, represents the linear coefficients in the inequality constraints</para></listitem></varlistentry>
<varlistentry><term>b :</term>
<listitem><para> a column vector of doubles, represents the linear coefficients in the inequality constraints</para></listitem></varlistentry>
<varlistentry><term>Aeq :</term>
<listitem><para> a meq x n matrix of doubles, represents the linear coefficients in the equality constraints</para></listitem></varlistentry>
<varlistentry><term>beq :</term>
<listitem><para> a vector of doubles, represents the linear coefficients in the equality constraints</para></listitem></varlistentry>
<varlistentry><term>LB :</term>
<listitem><para> a n x 1 matrix of doubles, where n is number of variables, contains lower bounds of the variables.</para></listitem></varlistentry>
<varlistentry><term>UB :</term>
<listitem><para> a n x 1 matrix of doubles, where n is number of variables, contains upper bounds of the variables.</para></listitem></varlistentry>
<varlistentry><term>xopt :</term>
<listitem><para> a nx1 matrix of doubles, the computed solution of the optimization problem.</para></listitem></varlistentry>
<varlistentry><term>fopt :</term>
<listitem><para> a 1x1 matrix of doubles, the function value at x.</para></listitem></varlistentry>
<varlistentry><term>exitflag :</term>
<listitem><para> Integer identifying the reason the algorithm terminated.</para></listitem></varlistentry>
<varlistentry><term>output :</term>
<listitem><para> Structure containing information about the optimization.</para></listitem></varlistentry>
<varlistentry><term>lambda :</term>
<listitem><para> Structure containing the Lagrange multipliers at the solution x (separated by constraint type).</para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
Search the minimum of a constrained linear quadratic optimization problem specified by :
find the minimum of f(x) such that
</para>
<para>
<latex>
\begin{eqnarray}
&\mbox{min}_{x}
& 1/2*x'*H*x + f'*x \\
& \text{subject to} & A.x \leq b \\
& & Aeq.x \leq beq \\
& & lb \leq x \leq ub \\
\end{eqnarray}
</latex>
</para>
<para>
We are calling IPOpt for solving the quadratic problem, IPOpt is a library written in C++. The code has been written by Andreas Wächter and Carl Laird.
</para>
<para>
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
//Find x in R^6 such that:
Aeq= [1,-1,1,0,3,1;
-1,0,-3,-4,5,6;
2,5,3,0,1,0];
beq=[1; 2; 3];
A= [0,1,0,1,2,-1;
-1,0,2,1,1,0];
b = [-1; 2.5];
lb=[-1000; -10000; 0; -1000; -1000; -1000];
ub=[10000; 100; 1.5; 100; 100; 1000];
//and minimize 0.5*x'*Q*x + p'*x with
f=[1; 2; 3; 4; 5; 6]; H=eye(6,6);
[xopt,fopt,exitflag,output,lambda]=qpipopt_mat(H,f,A,b,Aeq,beq,lb,ub)
clear H f A b Aeq beq lb ub;
]]></programlisting>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
//Find the value of x that minimize following function
// f(x) = 0.5*x1^2 + x2^2 - x1*x2 - 2*x1 - 6*x2
// Subject to:
// x1 + x2 ≤ 2
// –x1 + 2x2 ≤ 2
// 2x1 + x2 ≤ 3
// 0 ≤ x1, 0 ≤ x2.
H = [1 -1; -1 2];
f = [-2; -6];
A = [1 1; -1 2; 2 1];
b = [2; 2; 3];
lb = [0; 0];
ub = [%inf; %inf];
[xopt,fopt,exitflag,output,lambda] = qpipopt_mat(H,f,A,b,[],[],lb,ub)
]]></programlisting>
</refsection>
<refsection>
<title>Authors</title>
<simplelist type="vert">
<member>Keyur Joshi, Saikiran, Iswarya, Harpreet Singh</member>
</simplelist>
</refsection>
</refentry>
|
