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
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
|
<html><head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>linprog</title>
<style type="text/css" media="all">
@import url("scilab_code.css");
@import url("xml_code.css");
@import url("c_code.css");
@import url("style.css");
</style>
</head>
<body>
<div class="manualnavbar">
<table width="100%"><tr>
<td width="30%">
<span class="previous"><a href="intqpipopt.html"><< intqpipopt</a></span>
</td>
<td width="40%" class="center">
<span class="top"><a href="section_44e1f57c5225357b5fe53cb5fad967e9.html">FOSSEE Optimization Toolbox</a></span>
</td>
<td width="30%" class="next">
<span class="next"><a href="lsqlin.html">lsqlin >></a></span>
</td>
</tr></table>
<hr />
</div>
<span class="path"><a href="index.html">FOSSEE Optimization Toolbox</a> >> <a href="section_44e1f57c5225357b5fe53cb5fad967e9.html">FOSSEE Optimization Toolbox</a> > linprog</span>
<br /><br />
<div class="refnamediv"><h1 class="refname">linprog</h1>
<p class="refpurpose">Solves a linear programming 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">linprog</span><span class="default">(</span><span class="default">c</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">linprog</span><span class="default">(</span><span class="default">c</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">linprog</span><span class="default">(</span><span class="default">c</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">linprog</span><span class="default">(</span><span class="default">c</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">param</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">linprog</span><span class="default">(</span><span class="default">file</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">linprog</span><span class="default">(</span><span class="default">file</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">fopt</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">linprog</span><span class="default">( ... )</span></pre></div></div>
<div class="refsection"><h3 class="title">Input Parameters</h3>
<dl><dt><span class="term">c :</span>
<dd><p class="para">A vector of doubles, containing the coefficients of the variables in the objective function.</p></dd></dt>
<dt><span class="term">A :</span>
<dd><p class="para">A matrix of doubles, containing the coefficients of linear inequality constraints of size (m X n) where 'm' is the number of linear inequality constraints.</p></dd></dt>
<dt><span class="term">b :</span>
<dd><p class="para">A vector of doubles, related to 'A' and containing the the Right hand side equation of the linear inequality constraints of size (m X 1).</p></dd></dt>
<dt><span class="term">Aeq :</span>
<dd><p class="para">A matrix of doubles, containing the coefficients of linear equality constraints of size (m1 X n) where 'm1' is the number of linear equality constraints.</p></dd></dt>
<dt><span class="term">beq :</span>
<dd><p class="para">A vector of doubles, related to 'Aeq' and containing the the Right hand side equation of the linear equality constraints of size (m1 X 1).</p></dd></dt>
<dt><span class="term">lb :</span>
<dd><p class="para">A vector of doubles, containing the lower bounds of the variables of size (1 X n) or (n X 1) where 'n' is the number of variables.</p></dd></dt>
<dt><span class="term">ub :</span>
<dd><p class="para">A vector of doubles, containing the upper bounds of the variables of size (1 X n) or (n X 1) where 'n' is the number of variables.</p></dd></dt>
<dt><span class="term">options :</span>
<dd><p class="para">A list, containing the option for user to specify. See below for details.</p></dd></dt>
<dt><span class="term">file :</span>
<dd><p class="para">A string describing the path to the mps file.</p></dd></dt></dl></div>
<div class="refsection"><h3 class="title">Outputs</h3>
<dl><dt><span class="term">xopt :</span>
<dd><p class="para">A vector of doubles, containing the computed solution of the optimization problem.</p></dd></dt>
<dt><span class="term">fopt :</span>
<dd><p class="para">A double, containing the the function value at x.</p></dd></dt>
<dt><span class="term">exitflaf :</span>
<dd><p class="para">An integer, containing the flag which denotes the reason for termination of algorithm. See below for details.</p></dd></dt>
<dt><span class="term">output :</span>
<dd><p class="para">A structure, containing the information about the optimization. See below for details.</p></dd></dt>
<dt><span class="term">lambda :</span>
<dd><p class="para">A structure, containing the Lagrange multipliers of lower bound, upper bound and constraints at the optimized point. See below for details.</p></dd></dt></dl></div>
<div class="refsection"><h3 class="title">Description</h3>
<p class="para">Search the minimum of a constrained linear programming problem specified by :</p>
<p class="para"><span><img src='./_LaTeX_linprog.xml_1.png' style='position:relative;top:18px;width:241px;height:94px'/></span></p>
<p class="para">OSI-CLP, an optimization library written in C++, is used for solving the linear programming problems.</p>
<p class="para"><h3 class="title">Options</h3>
The options allow the user to set various parameters of the Optimization problem. The syntax for the options is given by:</p>
<p class="para">options= list("MaxIter", [---], "CpuTime", [---], "GradObj", ---, "Hessian", ---, "GradCon", ---);</p>
<p class="para">The options should be defined as type "list" and consist of the following fields:
<ul class="itemizedlist"><li>MaxIter : A Scalar, specifying the Maximum Number of iterations that the solver should take.</li></ul></p>
<p class="para">The default values for the various items are given as:</p>
<p class="para">options = list("MaxIter", [3000], "CpuTime", [600]);</p>
<p class="para">The exitflag allows the user to know the status of the optimization which is returned by Ipopt. The values it can take and what they indicate is described below:
<ul class="itemizedlist"><li>0 : Optimal Solution Found</li>
<li>1 : Primal Infeasible</li>
<li>2 : Dual Infeasible</li>
<li>3 : Maximum Number of Iterations Exceeded. Output may not be optimal.</li>
<li>4 : Solution Abandoned</li>
<li>5 : Primal objective limit reached.</li>
<li>6 : Dual objective limit reached.</li></ul></p>
<p class="para">The output data structure contains detailed information about the optimization process.
It is of type "struct" and contains the following fields.
<ul class="itemizedlist"><li>output.Iterations: The number of iterations performed.</li>
<li>output.constrviolation: The max-norm of the constraint violation.</li></ul></p>
<p class="para">The lambda data structure contains the Lagrange multipliers at the end of optimization. In the current version the values are returned only when the the solution is optimal.
It has type "struct" and contains the following fields.
<ul class="itemizedlist"><li>lambda.lower: The Lagrange multipliers for variable lower bounds.</li>
<li>lambda.eqlin: The Lagrange multipliers for the linear equality constraints.</li>
<li>lambda.ineqlin: The Lagrange multipliers for the linear inequality constraints.</li></ul></p>
<p class="para"></p></div>
<p class="para">A few examples displaying the various functionalities of linprog have been provided below. You will find a series of problems and the appropriate code snippets to solve them.</p>
<div class="refsection"><h3 class="title">Example</h3>
<p class="para">Here we solve a simple objective function, subjected to six linear inequality constraints.</p>
<p class="para">Find x in R^2 such that it minimizes:</p>
<p class="para"><span><img src='./_LaTeX_linprog.xml_2.png' style='position:relative;top:73px;width:272px;height:195px'/></span></p>
<p class="para"></p>
<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Example 1: Linear program, linear inequality constraints</span>
<span class="scilabid">c</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">3</span><span class="scilabopenclose">]</span><span class="scilaboperator">'</span>
<span class="scilabid">A</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span>
<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span>
<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</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">linprog</span><span class="scilabopenclose">(</span><span class="scilabid">c</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">Example</h3>
<p class="para">Here we build up on the previous example by adding linear equality constraints.
We add the following constraints to the problem specified above:</p>
<p class="para"><span><img src='./_LaTeX_linprog.xml_3.png' style='position:relative;top:16px;width:147px;height:40px'/></span></p>
<p class="para"></p>
<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Example 2: Linear program with Linear Inequalities and Equalities`</span>
<span class="scilabid">c</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">3</span><span class="scilabopenclose">]</span><span class="scilaboperator">'</span>
<span class="scilabid">A</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span>
<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span>
<span class="scilabid">Aeq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabopenclose">]</span>
<span class="scilabid">beq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span>
<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</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">linprog</span><span class="scilabopenclose">(</span><span class="scilabid">c</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="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">Example</h3>
<p class="para">In this example, we proceed to add the upper and lower bounds to the objective function.</p>
<p class="para"><span><img src='./_LaTeX_linprog.xml_4.png' style='position:relative;top:17px;width:162px;height:42px'/></span></p>
<p class="para"></p>
<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Example 3: Linear program with all constraint types</span>
<span class="scilabid">c</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">3</span><span class="scilabopenclose">]</span><span class="scilaboperator">'</span>
<span class="scilabid">A</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span>
<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span>
<span class="scilabid">Aeq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">4</span><span class="scilabopenclose">]</span>
<span class="scilabid">beq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilaboperator">/</span><span class="scilabnumber">2</span><span class="scilabopenclose">]</span>
<span class="scilabid">lb</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">0.5</span><span class="scilabopenclose">]</span>
<span class="scilabid">ub</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1.5</span><span class="scilabdefault">,</span><span class="scilabnumber">1.25</span><span class="scilabopenclose">]</span>
<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</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">linprog</span><span class="scilabopenclose">(</span><span class="scilabid">c</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>
<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">Example</h3>
<p class="para">Primal Infeasible Problems: Find x in R^3 such that it minimizes:</p>
<p class="para"><span><img src='./_LaTeX_linprog.xml_5.png' style='position:relative;top:27px;width:265px;height:176px'/></span></p>
<p class="para"></p> <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Example 4: Primal Infeasible Problem</span>
<span class="scilabid">c</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span><span class="scilaboperator">'</span>
<span class="scilabid">A</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span>
<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">4</span><span class="scilabopenclose">]</span>
<span class="scilabid">Aeq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">5</span><span class="scilabdefault">,</span><span class="scilabnumber">3</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span>
<span class="scilabid">beq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">10</span><span class="scilabdefault">,</span><span class="scilabnumber">100</span><span class="scilabopenclose">]</span>
<span class="scilabid">lb</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">0</span><span class="scilabopenclose">]</span>
<span class="scilabid">ub</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabconstants">%inf</span><span class="scilabdefault">,</span><span class="scilabconstants">%inf</span><span class="scilabdefault">,</span><span class="scilabconstants">%inf</span><span class="scilabopenclose">]</span>
<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</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">linprog</span><span class="scilabopenclose">(</span><span class="scilabid">c</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>
<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">Example</h3>
<p class="para">Unbounded Problems: Find x in R^3 such that it minimizes:</p>
<p class="para"><span><img src='./_LaTeX_linprog.xml_6.png' style='position:relative;top:27px;width:266px;height:156px'/></span></p>
<p class="para"></p>
<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">//Example 5: Unbounded Problem</span>
<span class="scilabid">c</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">3</span><span class="scilabdefault">,</span><span class="scilabnumber">5</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">7</span><span class="scilabopenclose">]</span><span class="scilaboperator">'</span>
<span class="scilabid">A</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">4</span><span class="scilabdefault">;</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">4</span><span class="scilabopenclose">]</span>
<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabnumber">8</span><span class="scilabdefault">,</span><span class="scilabnumber">5</span><span class="scilabopenclose">]</span>
<span class="scilabid">Aeq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span>
<span class="scilabid">beq</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span>
<span class="scilabid">lb</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilaboperator">-</span><span class="scilabconstants">%inf</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabconstants">%inf</span><span class="scilabdefault">,</span><span class="scilaboperator">-</span><span class="scilabconstants">%inf</span><span class="scilabopenclose">]</span>
<span class="scilabid">ub</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabconstants">%inf</span><span class="scilabdefault">,</span><span class="scilabconstants">%inf</span><span class="scilabdefault">,</span><span class="scilabconstants">%inf</span><span class="scilabopenclose">]</span>
<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</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">linprog</span><span class="scilabopenclose">(</span><span class="scilabid">c</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>
<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">Example</h3>
<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabid">filepath</span> <span class="scilaboperator">=</span> <a class="scilabcommand" href="scilab://get_absolute_file_path">get_absolute_file_path</a><span class="scilabopenclose">(</span><span class="scilabstring">'</span><span class="scilabstring">linprog.dem.sce</span><span class="scilabstring">'</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span>
<span class="scilabid">filepath</span> <span class="scilaboperator">=</span> <span class="scilabid">filepath</span> <span class="scilaboperator">+</span> <span class="scilabstring">"</span><span class="scilabstring">exmip1.mps</span><span class="scilabstring">"</span>
<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</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">linprog</span><span class="scilabopenclose">(</span><span class="scilabid">filepath</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">Bhanu Priya Sayal, Guru Pradeep Reddy</li></ul></div>
<br />
<div class="manualnavbar">
<table width="100%">
<tr><td colspan="3" class="next"><a href="http://bugzilla.scilab.org/enter_bug.cgi?product=Scilab%20software&component=Documentation%20pages" class="ulink">Report an issue</a></td></tr>
<tr>
<td width="30%">
<span class="previous"><a href="intqpipopt.html"><< intqpipopt</a></span>
</td>
<td width="40%" class="center">
<span class="top"><a href="section_44e1f57c5225357b5fe53cb5fad967e9.html">FOSSEE Optimization Toolbox</a></span>
</td>
<td width="30%" class="next">
<span class="next"><a href="lsqlin.html">lsqlin >></a></span>
</td>
</tr></table>
<hr />
</div>
</body>
</html>
|
