forked from johannesgerer/jburkardt-cpp
-
Notifications
You must be signed in to change notification settings - Fork 0
/
test_opt_con.html
468 lines (425 loc) · 13.3 KB
/
test_opt_con.html
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
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
<html>
<head>
<title>
TEST_OPT_CON - Test Functions for Scalar Optimization, Constrained to a Hyper-Rectangle
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_OPT_CON <br>
Test Functions for Scalar Optimization <br>
Constrained to a Hyper-Rectangle
</h1>
<hr>
<p>
<b>TEST_OPT_CON</b>
is a C++ library which
defines a set of constrained global optimization problems.
</p>
<p>
A typical constrained global optimization problem presents an M-dimensional
hyper-rectangle bounded by A(1:M) <= X(1:M) <= B(1:M), and a scalar-valued
function F(X). The task is to find a point X within the hyper-rectangle
at which the function takes its minimum value.
</p>
<p>
This task is impossible, mathematically and in general. However, the problems
that can be solved mathematically are often not the ones encountered in
real life. Thus, it is useful to try to solve an impossible problem, since
an approximate answer to such a problem can be all we can hope for or need.
</p>
<p>
The functions defined include:
<ol>
<li>
NM1: Niederreiter-McCurley function #1, M = 4;
</li>
<li>
NM2: Niederreiter-McCurley function #2, M = 4;
</li>
<li>
NM3: Niederreiter-McCurley function #3, M = 4;
</li>
<li>
NM4: Niederreiter-McCurley function #4, M = 4;
</li>
<li>
NM5: Niederreiter-McCurley function #5, M = 4;
</li>
<li>
NM6: Niederreiter-McCurley function #6, M = 4;
</li>
<li>
L02: Langerman function, M = 2;
</li>
<li>
L10: Langerman function, M = 10;
</li>
</ol>
</p>
<p>
For each function, the library includes a routine to evaluate the function,
but also routines to return the limits of the hyper-rectangle, the
spatial dimension, the solution, if known, and a title for the problem.
These routines have a standard set of names based on the function index.
For instance, for function #3, we have the routines:
<ul>
<li>
<b>P03_AB</b> returns bounds for problem 3.
</li>
<li>
<b>P03_F</b> returns the objective function value for problem 3.
</li>
<li>
<b>P03_M</b> returns the spatial dimension for problem 3.
</li>
<li>
<b>P03_SOL</b> returns known solutions for problem 3.
</li>
<li>
<b>P03_TITLE</b> returns a title for problem 3.
</li>
</ul>
</p>
<p>
Since the same interface is used for each function,
if you wish to work with problem 6 instead, you simply change
the "03" to "06" in your routine calls.
</p>
<p>
If you wish to call <i>all</i> of the functions, you can write a concise
program to do so by using the generic interface, in which the function
names use the prefix <b>P00_</b>, and require the specific problem index
to be supplied as an extra input argument:
<ul>
<li>
<b>P00_AB</b> returns bounds for a problem specified by index.
</li>
<li>
<b>P00_F</b> returns the objective function value for a problem specified by index.
</li>
<li>
<b>P00_M</b> returns the spatial dimension for a problem specified by index.
</li>
<li>
<b>P00_SOL</b> returns known solutions for a problem specified by index.
</li>
<li>
<b>P00_TITLE</b> returns a title for a problem specified by index.
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this
web page are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TEST_OPT_CON</b> is available in
<a href = "../../c_src/test_opt_con/test_opt_con.html">a C version</a> and
<a href = "../../cpp_src/test_opt_con/test_opt_con.html">a C++ version</a> and
<a href = "../../f77_src/test_opt_con/test_opt_con.html">a FORTRAN77 version</a> and
<a href = "../../f_src/test_opt_con/test_opt_con.html">a FORTRAN90 version</a> and
<a href = "../../m_src/test_opt_con/test_opt_con.html">a MATLAB version</a>.
</p>
<h3 align="center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/asa047/asa047.html">
ASA047</a>,
a C++ library which
minimizes a scalar function of several variables using the Nelder-Mead algorithm.
</p>
<p>
<a href = "../../cpp_src/brent/brent.html">
BRENT</a>,
a C++ library which
contains Richard Brent's routines for finding the zero, local minimizer,
or global minimizer of a scalar function of a scalar argument, without
the use of derivative information.
</p>
<p>
<a href = "../../cpp_src/compass_search/compass_search.html">
COMPASS_SEARCH</a>,
a C++ program which
minimizes a scalar function of several variables using the compass search algorithm.
</p>
<p>
<a href = "../../f_src/dqed/dqed.html">
DQED</a>,
a FORTRAN90 library which
solves constrained least squares problems.
</p>
<p>
<a href = "../../m_src/entrust/entrust.html">
ENTRUST</a>,
a MATLAB program which
minimizes a scalar function of several variables using trust-region methods.
</p>
<p>
<a href = "../../m_src/fmincon/fmincon.html">
FMINCON</a>,
a MATLAB library which
demonstrates the use of the <b>fmincon()</b> function to seek the minimizer
of a function <b>f(x)</b> subject to a constraint.
</p>
<p>
<a href = "../../m_src/nelder_mead/nelder_mead.html">
NELDER_MEAD</a>,
a MATLAB program which
minimizes a scalar function of several variables using the Nelder-Mead algorithm,
by Jeff Borggaard.
</p>
<p>
<a href = "../../f_src/praxis/praxis.html">
PRAXIS</a>,
a FORTRAN90 library which
implements the principal axis method of Richard Brent for minimization of
a function without the use of derivatives.
</p>
<p>
<a href = "../../f_src/test_opt/test_opt.html">
TEST_OPT</a>,
a FORTRAN90 library which
defines test problems
requiring the minimization of a scalar function of several variables.
</p>
<p>
<a href = "../../f_src/test_optimization/test_optimization.html">
TEST_OPTIMIZATION</a>,
a FORTRAN90 library which
defines test problems for the minimization of a scalar function
of several variables, as described by Molga and Smutnicki.
</p>
<p>
<a href = "../../cpp_src/toms178/toms178.html">
TOMS178</a>,
a C++ library which
optimizes a scalar functional of multiple variables using the Hooke-Jeeves method.
</p>
<p>
<a href = "../../f_src/toms611/toms611.html">
TOMS611</a>,
a FORTRAN90 library which
can be used to seek the minimizer of a scalar functional
of multiple variables.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Harald Niederreiter, Kevin McCurley,<br>
Optimization of functions by quasi-random search methods,<br>
Computing,<br>
Volume 22, Number 2, 1979, pages 119-123.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "test_opt_con.cpp">test_opt_con.cpp</a>, the source code.
</li>
<li>
<a href = "test_opt_con.hpp">test_opt_con.hpp</a>, the include file.
</li>
<li>
<a href = "test_opt_con.sh">test_opt_con.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_opt_con_prb.cpp">test_opt_con_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "test_opt_con_prb.sh">test_opt_con_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "test_opt_con_prb_output.txt">test_opt_con_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>P00_AB</b> returns bounds for a problem specified by index.
</li>
<li>
<b>P00_F</b> returns the objective function value for a problem specified by index.
</li>
<li>
<b>P00_M</b> returns the spatial dimension for a problem specified by index.
</li>
<li>
<b>P00_PROBLEM_NUM</b> returns the number of problems.
</li>
<li>
<b>P00_SOL</b> returns known solutions for a problem specified by index.
</li>
<li>
<b>P00_TITLE</b> returns a title for a problem specified by index.
</li>
<li>
<b>P01_AB</b> returns bounds for problem 1.
</li>
<li>
<b>P01_F</b> returns the objective function value for problem 1.
</li>
<li>
<b>P01_M</b> returns the spatial dimension for problem 1.
</li>
<li>
<b>P01_SOL</b> returns known solutions for problem 1.
</li>
<li>
<b>P01_TITLE</b> returns a title for problem 1.
</li>
<li>
<b>P02_AB</b> returns bounds for problem 2.
</li>
<li>
<b>P02_F</b> returns the objective function value for problem 2.
</li>
<li>
<b>P02_M</b> returns the spatial dimension for problem 2.
</li>
<li>
<b>P02_SOL</b> returns known solutions for problem 2.
</li>
<li>
<b>P02_TITLE</b> returns a title for problem 2.
</li>
<li>
<b>P03_AB</b> returns bounds for problem 3.
</li>
<li>
<b>P03_F</b> returns the objective function value for problem 3.
</li>
<li>
<b>P03_M</b> returns the spatial dimension for problem 3.
</li>
<li>
<b>P03_SOL</b> returns known solutions for problem 3.
</li>
<li>
<b>P03_TITLE</b> returns a title for problem 3.
</li>
<li>
<b>P04_AB</b> returns bounds for problem 4.
</li>
<li>
<b>P04_F</b> returns the objective function value for problem 4.
</li>
<li>
<b>P04_M</b> returns the spatial dimension for problem 4.
</li>
<li>
<b>P04_SOL</b> returns known solutions for problem 4.
</li>
<li>
<b>P04_TITLE</b> returns a title for problem 4.
</li>
<li>
<b>P05_AB</b> returns bounds for problem 5.
</li>
<li>
<b>P05_F</b> returns the objective function value for problem 5.
</li>
<li>
<b>P05_M</b> returns the spatial dimension for problem 5.
</li>
<li>
<b>P05_SOL</b> returns known solutions for problem 5.
</li>
<li>
<b>P05_TITLE</b> returns a title for problem 5.
</li>
<li>
<b>P06_AB</b> returns bounds for problem 6.
</li>
<li>
<b>P06_F</b> returns the objective function value for problem 6.
</li>
<li>
<b>P06_M</b> returns the spatial dimension for problem 6.
</li>
<li>
<b>P06_SOL</b> returns known solutions for problem 6.
</li>
<li>
<b>P06_TITLE</b> returns a title for problem 6.
</li>
<li>
<b>P07_AB</b> returns bounds for problem 7.
</li>
<li>
<b>P07_F</b> returns the objective function value for problem 5.
</li>
<li>
<b>P07_M</b> returns the spatial dimension for problem 7.
</li>
<li>
<b>P07_SOL</b> returns known solutions for problem 7.
</li>
<li>
<b>P07_TITLE</b> returns a title for problem 7.
</li>
<li>
<b>P08_AB</b> returns bounds for problem 8.
</li>
<li>
<b>P08_F</b> returns the objective function value for problem 8.
</li>
<li>
<b>P08_M</b> returns the spatial dimension for problem 8.
</li>
<li>
<b>P08_SOL</b> returns known solutions for problem 8.
</li>
<li>
<b>P08_TITLE</b> returns a title for problem 8.
</li>
<li>
<b>R8COL_UNIFORM_NEW</b> fills an R8COL with scaled pseudorandom numbers.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 16 February 2012.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>