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
143
144
145
146
147
148
149
|
<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from qpipoptmat.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="qpipoptmat" 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>qpipoptmat</refname>
<refpurpose>Solves a linear quadratic problem.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
x = qpipoptmat(H,f)
x = qpipoptmat(H,f,A,b)
x = qpipoptmat(H,f,A,b,Aeq,beq)
x = qpipoptmat(H,f,A,b,Aeq,beq,lb,ub)
x = qpipoptmat(H,f,A,b,Aeq,beq,lb,ub,x0)
x = qpipoptmat(H,f,A,b,Aeq,beq,lb,ub,x0,param)
[xopt,fopt,exitflag,output,lamda] = qpipoptmat( ... )
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>H :</term>
<listitem><para> a symmetric matrix of doubles, represents coefficients of quadratic in the quadratic problem.</para></listitem></varlistentry>
<varlistentry><term>f :</term>
<listitem><para> a vector of doubles, represents coefficients of linear in the quadratic problem</para></listitem></varlistentry>
<varlistentry><term>A :</term>
<listitem><para> a vector of doubles, represents the linear coefficients in the inequality constraints</para></listitem></varlistentry>
<varlistentry><term>b :</term>
<listitem><para> a vector of doubles, represents the linear coefficients in the inequality constraints</para></listitem></varlistentry>
<varlistentry><term>Aeq :</term>
<listitem><para> a 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 vector of doubles, contains lower bounds of the variables.</para></listitem></varlistentry>
<varlistentry><term>UB :</term>
<listitem><para> a vector of doubles, contains upper bounds of the variables.</para></listitem></varlistentry>
<varlistentry><term>x0 :</term>
<listitem><para> a vector of doubles, contains initial guess of variables.</para></listitem></varlistentry>
<varlistentry><term>param :</term>
<listitem><para> a list containing the the parameters to be set.</para></listitem></varlistentry>
<varlistentry><term>xopt :</term>
<listitem><para> a vector of doubles, the computed solution of the optimization problem.</para></listitem></varlistentry>
<varlistentry><term>fopt :</term>
<listitem><para> a double, 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];
x0 = repmat(0,6,1);
param = list("MaxIter", 300, "CpuTime", 100);
//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]=qpipoptmat(H,f,A,b,Aeq,beq,lb,ub,[],param)
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] = qpipoptmat(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>
|
