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
|
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Created by GNU Texinfo 5.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>Maxima Manual: Introduction to simplex</title>
<meta name="description" content="Maxima Manual: Introduction to simplex">
<meta name="keywords" content="Maxima Manual: Introduction to simplex">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<link href="maxima_toc.html#Top" rel="start" title="Top">
<link href="maxima_264.html#g_t_0423_043a_0430_0437_0430_0442_0435_043b_044c-_0444_0443_043d_043a_0446_0438_0439-_0438-_043f_0435_0440_0435_043c_0435_043d_043d_044b_0445" rel="index" title="Указатель функций и переменных">
<link href="maxima_toc.html#SEC_Contents" rel="contents" title="Table of Contents">
<link href="maxima_231.html#simplex_002dpkg" rel="up" title="simplex-pkg">
<link href="maxima_233.html#Functions-and-Variables-for-simplex" rel="next" title="Functions and Variables for simplex">
<link href="maxima_231.html#simplex_002dpkg" rel="previous" title="simplex-pkg">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.indentedblock {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
div.smalllisp {margin-left: 3.2em}
kbd {font-style:oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nocodebreak {white-space:nowrap}
span.nolinebreak {white-space:nowrap}
span.roman {font-family:serif; font-weight:normal}
span.sansserif {font-family:sans-serif; font-weight:normal}
ul.no-bullet {list-style: none}
body {color: black; background: white; margin-left: 8%; margin-right: 13%;
font-family: "FreeSans", sans-serif}
h1 {font-size: 150%; font-family: "FreeSans", sans-serif}
h2 {font-size: 125%; font-family: "FreeSans", sans-serif}
h3 {font-size: 100%; font-family: "FreeSans", sans-serif}
a[href] {color: rgb(0,0,255); text-decoration: none;}
a[href]:hover {background: rgb(220,220,220);}
div.textbox {border: solid; border-width: thin; padding-top: 1em;
padding-bottom: 1em; padding-left: 2em; padding-right: 2em}
div.titlebox {border: none; padding-top: 1em; padding-bottom: 1em;
padding-left: 2em; padding-right: 2em; background: rgb(200,255,255);
font-family: sans-serif}
div.synopsisbox {
border: none; padding-top: 1em; padding-bottom: 1em; padding-left: 2em;
padding-right: 2em; background: rgb(255,220,255);}
pre.example {border: 1px solid rgb(180,180,180); padding-top: 1em;
padding-bottom: 1em; padding-left: 1em; padding-right: 1em;
background-color: rgb(238,238,255)}
div.spacerbox {border: none; padding-top: 2em; padding-bottom: 2em}
div.image {margin: 0; padding: 1em; text-align: center}
div.categorybox {border: 1px solid gray; padding-top: 1em; padding-bottom: 1em;
padding-left: 1em; padding-right: 1em; background: rgb(247,242,220)}
img {max-width:80%; max-height: 80%; display: block; margin-left: auto; margin-right: auto}
-->
</style>
<link rel="icon" href="figures/favicon.ico">
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6>"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
</head>
<body lang="ru" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
<a name="Introduction-to-simplex"></a>
<div class="header">
<p>
Next: <a href="maxima_233.html#Functions-and-Variables-for-simplex" accesskey="n" rel="next">Functions and Variables for simplex</a>, Previous: <a href="maxima_231.html#simplex_002dpkg" accesskey="p" rel="previous">simplex-pkg</a>, Up: <a href="maxima_231.html#simplex_002dpkg" accesskey="u" rel="up">simplex-pkg</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_264.html#g_t_0423_043a_0430_0437_0430_0442_0435_043b_044c-_0444_0443_043d_043a_0446_0438_0439-_0438-_043f_0435_0440_0435_043c_0435_043d_043d_044b_0445" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Introduction-to-simplex-1"></a>
<h3 class="section">66.1 Introduction to simplex</h3>
<p><code>simplex</code> is a package for linear optimization using the simplex algorithm.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) load("simplex")$
(%i2) minimize_lp(x+y, [3*x+2*y>2, x+4*y>3]);
9 7 1
(%o2) [--, [y = --, x = -]]
10 10 5
</pre></div>
<a name="Tests-for-simplex"></a>
<h4 class="subsection">66.1.1 Tests for simplex</h4>
<p>There are some tests in the directory <code>share/simplex/Tests</code>.
</p>
<a name="klee_005fminty"></a>
<h4 class="subsubsection">66.1.1.1 klee_minty</h4>
<p>The function <code>klee_minty</code> produces input for <code>linear_program</code>, for which
exponential time for solving is required without scaling.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">load("klee_minty")$
apply(linear_program, klee_minty(6));
</pre></div>
<p>A better approach:
</p>
<div class="example">
<pre class="example">epsilon_sx : 0$
scale_sx : true$
apply(linear_program, klee_minty(10));
</pre></div>
<a name="NETLIB"></a>
<h4 class="subsubsection">66.1.1.2 NETLIB</h4>
<p>Some smaller problems from netlib (<a href="https://www.netlib.org/lp/data/">https://www.netlib.org/lp/data/</a>)
test suite are converted to a format, readable by Maxima. Problems are
<code>adlittle</code>, <code>afiro</code>, <code>kb2</code>, <code>sc50a</code> and
<code>share2b</code>. Each problem has three input files in CSV format for
matrix <var>A</var> and vectors <var>b</var> and <var>c</var>.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">A : read_matrix("adlittle_A.csv", 'csv)$
b : read_list("adlittle_b.csv", 'csv)$
c : read_list("adlittle_c.csv", 'csv)$
linear_program(A, b, c)$
%[2];
=> 225494.9631623802
</pre></div>
<p>Results:
</p>
<div class="example">
<pre class="example">PROBLEM MINIMUM SCALING
adlittle +2.2549496316E+05 false
afiro -4.6475314286E+02 false
kb2 -1.7499001299E+03 true
sc50a -6.4575077059E+01 false
share2b -4.1573518187E+02 false
</pre></div>
<p>The Netlib website <a href="https://www.netlib.org/lp/data/readme">https://www.netlib.org/lp/data/readme</a> lists the values as
</p>
<div class="example">
<pre class="example">PROBLEM MINIMUM
adlittle +2.2549496316E+05
afiro -4.6475314286E+02
kb2 -1.7499001299E+03
sc50a -6.4575077059E+01
share2b -4.1573224074E+02
</pre></div>
<a name="Item_003a-simplex_002fnode_002fFunctions-and-Variables-for-simplex"></a><hr>
<div class="header">
<p>
Next: <a href="maxima_233.html#Functions-and-Variables-for-simplex" accesskey="n" rel="next">Functions and Variables for simplex</a>, Previous: <a href="maxima_231.html#simplex_002dpkg" accesskey="p" rel="previous">simplex-pkg</a>, Up: <a href="maxima_231.html#simplex_002dpkg" accesskey="u" rel="up">simplex-pkg</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_264.html#g_t_0423_043a_0430_0437_0430_0442_0435_043b_044c-_0444_0443_043d_043a_0446_0438_0439-_0438-_043f_0435_0440_0435_043c_0435_043d_043d_044b_0445" title="Index" rel="index">Index</a>]</p>
</div>
</body>
</html>
|
