1 /* Copyright (c) 2007-2010 Massachusetts Institute of Technology
3 * Permission is hereby granted, free of charge, to any person obtaining
4 * a copy of this software and associated documentation files (the
5 * "Software"), to deal in the Software without restriction, including
6 * without limitation the rights to use, copy, modify, merge, publish,
7 * distribute, sublicense, and/or sell copies of the Software, and to
8 * permit persons to whom the Software is furnished to do so, subject to
9 * the following conditions:
11 * The above copyright notice and this permission notice shall be
12 * included in all copies or substantial portions of the Software.
14 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
15 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
16 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
17 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
18 * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
19 * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
20 * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
27 #include "nlopt-internal.h"
29 /*********************************************************************/
32 static int my_isnan(double x) { return x != x; }
33 # define isnan my_isnan
36 /*********************************************************************/
48 # include "l-bfgs-b.h"
59 #include "neldermead.h"
64 /*********************************************************************/
66 static double f_bound(int n, const double *x, void *data_)
69 nlopt_opt data = (nlopt_opt) data_;
72 /* some methods do not support bound constraints, but support
73 discontinuous objectives so we can just return Inf for invalid x */
74 for (i = 0; i < n; ++i)
75 if (x[i] < data->lb[i] || x[i] > data->ub[i])
78 f = data->f((unsigned) n, x, NULL, data->f_data);
79 return (isnan(f) || nlopt_isinf(f) ? HUGE_VAL : f);
82 static double f_noderiv(int n, const double *x, void *data_)
84 nlopt_opt data = (nlopt_opt) data_;
85 return data->f((unsigned) n, x, NULL, data->f_data);
88 static double f_direct(int n, const double *x, int *undefined, void *data_)
90 nlopt_opt data = (nlopt_opt) data_;
93 f = data->f((unsigned) n, x, NULL, data->f_data);
94 *undefined = isnan(f) || nlopt_isinf(f);
95 for (i = 0; i < data->m && !*undefined; ++i)
96 if (data->fc[i].f((unsigned) n, x, NULL, data->fc[i].f_data) > 0)
101 /*********************************************************************/
103 /* get min(dx) for algorithms requiring a scalar initial step size */
104 static nlopt_result initial_step(nlopt_opt opt, const double *x, double *step)
106 unsigned freedx = 0, i;
110 if (nlopt_set_default_initial_step(opt, x) != NLOPT_SUCCESS)
111 return NLOPT_OUT_OF_MEMORY;
115 for (i = 0; i < opt->n; ++i)
116 if (*step > fabs(opt->dx[i]))
117 *step = fabs(opt->dx[i]);
119 if (freedx) { free(opt->dx); opt->dx = NULL; }
120 return NLOPT_SUCCESS;
123 /*********************************************************************/
125 /* return true if [lb,ub] is finite in every dimension (n dimensions) */
126 static int finite_domain(unsigned n, const double *lb, const double *ub)
129 for (i = 0; i < n; ++i)
130 if (nlopt_isinf(ub[i] - lb[i])) return 0;
134 /*********************************************************************/
136 #define POP(defaultpop) (opt->stochastic_population > 0 ? \
137 opt->stochastic_population : \
138 (nlopt_stochastic_population > 0 ? \
139 nlopt_stochastic_population : (defaultpop)))
141 /* unlike nlopt_optimize() below, only handles minimization case */
142 static nlopt_result nlopt_optimize_(nlopt_opt opt, double *x, double *minf)
144 const double *lb, *ub;
145 nlopt_algorithm algorithm;
146 nlopt_func f; void *f_data;
151 if (!opt || !x || !minf || !opt->f
152 || opt->maximize) return NLOPT_INVALID_ARGS;
154 /* reset stopping flag */
155 nlopt_set_force_stop(opt, 0);
156 opt->force_stop_child = NULL;
158 /* copy a few params to local vars for convenience */
160 ni = (int) n; /* most of the subroutines take "int" arg */
161 lb = opt->lb; ub = opt->ub;
162 algorithm = opt->algorithm;
163 f = opt->f; f_data = opt->f_data;
165 if (n == 0) { /* trivial case: no degrees of freedom */
166 *minf = opt->f(n, x, NULL, opt->f_data);
167 return NLOPT_SUCCESS;
172 /* make sure rand generator is inited */
173 nlopt_srand_time_default(); /* default is non-deterministic */
175 /* check bound constraints */
176 for (i = 0; i < n; ++i)
177 if (lb[i] > ub[i] || x[i] < lb[i] || x[i] > ub[i])
178 return NLOPT_INVALID_ARGS;
181 stop.minf_max = opt->stopval;
182 stop.ftol_rel = opt->ftol_rel;
183 stop.ftol_abs = opt->ftol_abs;
184 stop.xtol_rel = opt->xtol_rel;
185 stop.xtol_abs = opt->xtol_abs;
187 stop.maxeval = opt->maxeval;
188 stop.maxtime = opt->maxtime;
189 stop.start = nlopt_seconds();
190 stop.force_stop = &(opt->force_stop);
193 case NLOPT_GN_DIRECT:
194 case NLOPT_GN_DIRECT_L:
195 case NLOPT_GN_DIRECT_L_RAND:
196 if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
197 return cdirect(ni, f, f_data,
198 lb, ub, x, minf, &stop, 0.0,
199 (algorithm != NLOPT_GN_DIRECT)
200 + 3 * (algorithm == NLOPT_GN_DIRECT_L_RAND
201 ? 2 : (algorithm != NLOPT_GN_DIRECT))
202 + 9 * (algorithm == NLOPT_GN_DIRECT_L_RAND
203 ? 1 : (algorithm != NLOPT_GN_DIRECT)));
205 case NLOPT_GN_DIRECT_NOSCAL:
206 case NLOPT_GN_DIRECT_L_NOSCAL:
207 case NLOPT_GN_DIRECT_L_RAND_NOSCAL:
208 if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
209 return cdirect_unscaled(ni, f, f_data, lb, ub, x, minf,
211 (algorithm != NLOPT_GN_DIRECT)
212 + 3 * (algorithm == NLOPT_GN_DIRECT_L_RAND ? 2 : (algorithm != NLOPT_GN_DIRECT))
213 + 9 * (algorithm == NLOPT_GN_DIRECT_L_RAND ? 1 : (algorithm != NLOPT_GN_DIRECT)));
215 case NLOPT_GN_ORIG_DIRECT:
216 case NLOPT_GN_ORIG_DIRECT_L:
217 if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
218 switch (direct_optimize(f_direct, opt, ni, lb, ub, x, minf,
219 stop.maxeval, -1, 0.0, 0.0,
220 pow(stop.xtol_rel, (double) n), -1.0,
223 algorithm == NLOPT_GN_ORIG_DIRECT
225 : DIRECT_GABLONSKY)) {
226 case DIRECT_INVALID_BOUNDS:
227 case DIRECT_MAXFEVAL_TOOBIG:
228 case DIRECT_INVALID_ARGS:
229 return NLOPT_INVALID_ARGS;
230 case DIRECT_INIT_FAILED:
231 case DIRECT_SAMPLEPOINTS_FAILED:
232 case DIRECT_SAMPLE_FAILED:
233 return NLOPT_FAILURE;
234 case DIRECT_MAXFEVAL_EXCEEDED:
235 case DIRECT_MAXITER_EXCEEDED:
236 return NLOPT_MAXEVAL_REACHED;
237 case DIRECT_GLOBAL_FOUND:
238 return NLOPT_MINF_MAX_REACHED;
240 case DIRECT_SIGMATOL:
241 return NLOPT_XTOL_REACHED;
242 case DIRECT_OUT_OF_MEMORY:
243 return NLOPT_OUT_OF_MEMORY;
248 case NLOPT_GD_STOGO_RAND:
250 if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
251 if (!stogo_minimize(ni, f, f_data, x, minf, lb, ub, &stop,
252 algorithm == NLOPT_GD_STOGO
253 ? 0 : (int) POP(2*n)))
254 return NLOPT_FAILURE;
257 return NLOPT_FAILURE;
261 /* lacking a free/open-source license, we no longer use
262 Rowan's code, and instead use by "sbplx" re-implementation */
263 case NLOPT_LN_SUBPLEX: {
264 int iret, freedx = 0;
267 if (nlopt_set_default_initial_step(opt, x) != NLOPT_SUCCESS)
268 return NLOPT_OUT_OF_MEMORY;
270 iret = nlopt_subplex(f_bound, minf, x, n, opt, &stop, opt->dx);
271 if (freedx) { free(opt->dx); opt->dx = NULL; }
273 case -2: return NLOPT_INVALID_ARGS;
274 case -20: return NLOPT_FORCED_STOP;
275 case -10: return NLOPT_MAXTIME_REACHED;
276 case -1: return NLOPT_MAXEVAL_REACHED;
277 case 0: return NLOPT_XTOL_REACHED;
278 case 1: return NLOPT_SUCCESS;
279 case 2: return NLOPT_MINF_MAX_REACHED;
280 case 20: return NLOPT_FTOL_REACHED;
281 case -200: return NLOPT_OUT_OF_MEMORY;
282 default: return NLOPT_FAILURE; /* unknown return code */
288 case NLOPT_LN_PRAXIS: {
290 if (initial_step(opt, x, &step) != NLOPT_SUCCESS)
291 return NLOPT_OUT_OF_MEMORY;
292 return praxis_(0.0, DBL_EPSILON,
293 step, ni, x, f_bound, opt, &stop, minf);
297 case NLOPT_LD_LBFGS_NOCEDAL: {
298 int iret, *nbd = (int *) malloc(sizeof(int) * n);
299 if (!nbd) return NLOPT_OUT_OF_MEMORY;
300 for (i = 0; i < n; ++i) {
301 int linf = nlopt_isinf(lb[i]) && lb[i] < 0;
302 int uinf = nlopt_isinf(ub[i]) && ub[i] > 0;
303 nbd[i] = linf && uinf ? 0 : (uinf ? 1 : (linf ? 3 : 2));
305 iret = lbfgsb_minimize(ni, f, f_data, x, nbd, lb, ub,
306 ni < 5 ? ni : 5, 0.0, stop.ftol_rel,
307 stop.xtol_abs[0] > 0 ? stop.xtol_abs[0]
313 case -1: return NLOPT_INVALID_ARGS;
314 case -2: default: return NLOPT_FAILURE;
318 *minf = f(n, x, NULL, f_data);
320 case 5: return NLOPT_MAXEVAL_REACHED;
321 case 2: return NLOPT_XTOL_REACHED;
322 case 1: return NLOPT_FTOL_REACHED;
323 default: return NLOPT_SUCCESS;
331 return luksan_plis(ni, f, f_data, lb, ub, x, minf, &stop);
335 return luksan_plip(ni, f, f_data, lb, ub, x, minf, &stop,
336 algorithm == NLOPT_LD_VAR1 ? 1 : 2);
338 case NLOPT_LD_TNEWTON:
339 case NLOPT_LD_TNEWTON_RESTART:
340 case NLOPT_LD_TNEWTON_PRECOND:
341 case NLOPT_LD_TNEWTON_PRECOND_RESTART:
342 return luksan_pnet(ni, f, f_data, lb, ub, x, minf, &stop,
343 1 + (algorithm - NLOPT_LD_TNEWTON) % 2,
344 1 + (algorithm - NLOPT_LD_TNEWTON) / 2);
346 case NLOPT_GN_CRS2_LM:
347 if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
348 return crs_minimize(ni, f, f_data, lb, ub, x, minf, &stop,
353 case NLOPT_GN_MLSL_LDS:
354 case NLOPT_GD_MLSL_LDS: {
355 if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
356 nlopt_opt local_opt = opt->local_opt;
358 if (!local_opt) { /* default */
359 nlopt_algorithm local_alg = (algorithm == NLOPT_GN_MLSL ||
360 algorithm == NLOPT_GN_MLSL_LDS)
361 ? nlopt_local_search_alg_nonderiv
362 : nlopt_local_search_alg_deriv;
363 /* don't call MLSL recursively! */
364 if (local_alg >= NLOPT_GN_MLSL
365 && local_alg <= NLOPT_GD_MLSL_LDS)
366 local_alg = (algorithm == NLOPT_GN_MLSL ||
367 algorithm == NLOPT_GN_MLSL_LDS)
368 ? NLOPT_LN_COBYLA : NLOPT_LD_MMA;
369 local_opt = nlopt_create(local_alg, n);
370 if (!local_opt) return NLOPT_FAILURE;
371 nlopt_set_ftol_rel(local_opt, opt->ftol_rel);
372 nlopt_set_ftol_abs(local_opt, opt->ftol_abs);
373 nlopt_set_xtol_rel(local_opt, opt->xtol_rel);
374 nlopt_set_xtol_abs(local_opt, opt->xtol_abs);
375 nlopt_set_maxeval(local_opt, nlopt_local_search_maxeval);
376 nlopt_set_initial_step(local_opt, opt->dx);
378 for (i = 0; i < n && stop.xtol_abs[i] > 0; ++i) ;
379 if (local_opt->ftol_rel <= 0 && local_opt->ftol_abs <= 0 &&
380 local_opt->xtol_rel <= 0 && i < n) {
381 /* it is not sensible to call MLSL without *some*
382 nonzero tolerance for the local search */
383 nlopt_set_ftol_rel(local_opt, 1e-15);
384 nlopt_set_xtol_rel(local_opt, 1e-7);
386 opt->force_stop_child = local_opt;
387 ret = mlsl_minimize(ni, f, f_data, lb, ub, x, minf, &stop,
388 local_opt, (int) POP(0),
389 algorithm >= NLOPT_GN_MLSL_LDS);
390 opt->force_stop_child = NULL;
391 if (!opt->local_opt) nlopt_destroy(local_opt);
398 #define LO(param, def) (opt->local_opt ? opt->local_opt->param : (def))
399 dual_opt = nlopt_create(LO(algorithm,
400 nlopt_local_search_alg_deriv),
402 if (!dual_opt) return NLOPT_FAILURE;
403 nlopt_set_ftol_rel(dual_opt, LO(ftol_rel, 1e-12));
404 nlopt_set_ftol_abs(dual_opt, LO(ftol_abs, 0.0));
405 nlopt_set_maxeval(dual_opt, LO(maxeval, 100000));
408 ret = mma_minimize(ni, f, f_data, (int) (opt->m), opt->fc,
409 lb, ub, x, minf, &stop, dual_opt);
410 nlopt_destroy(dual_opt);
414 case NLOPT_LN_COBYLA: {
416 if (initial_step(opt, x, &step) != NLOPT_SUCCESS)
417 return NLOPT_OUT_OF_MEMORY;
418 return cobyla_minimize(ni, f, f_data,
420 lb, ub, x, minf, &stop,
424 case NLOPT_LN_NEWUOA: {
426 if (initial_step(opt, x, &step) != NLOPT_SUCCESS)
427 return NLOPT_OUT_OF_MEMORY;
428 return newuoa(ni, 2*n+1, x, 0, 0, step,
429 &stop, minf, f_noderiv, opt);
432 case NLOPT_LN_NEWUOA_BOUND: {
434 if (initial_step(opt, x, &step) != NLOPT_SUCCESS)
435 return NLOPT_OUT_OF_MEMORY;
436 return newuoa(ni, 2*n+1, x, lb, ub, step,
437 &stop, minf, f_noderiv, opt);
440 case NLOPT_LN_BOBYQA: {
442 if (initial_step(opt, x, &step) != NLOPT_SUCCESS)
443 return NLOPT_OUT_OF_MEMORY;
444 return bobyqa(ni, 2*n+1, x, lb, ub, step,
445 &stop, minf, f_noderiv, opt);
448 case NLOPT_LN_NELDERMEAD:
455 if (nlopt_set_default_initial_step(opt, x) != NLOPT_SUCCESS)
456 return NLOPT_OUT_OF_MEMORY;
458 if (algorithm == NLOPT_LN_NELDERMEAD)
459 ret= nldrmd_minimize(ni,f,f_data,lb,ub,x,minf,opt->dx,&stop);
461 ret= sbplx_minimize(ni,f,f_data,lb,ub,x,minf,opt->dx,&stop);
462 if (freedx) { free(opt->dx); opt->dx = NULL; }
467 case NLOPT_AUGLAG_EQ:
468 case NLOPT_LN_AUGLAG:
469 case NLOPT_LN_AUGLAG_EQ:
470 case NLOPT_LD_AUGLAG:
471 case NLOPT_LD_AUGLAG_EQ: {
472 nlopt_opt local_opt = opt->local_opt;
474 if ((algorithm == NLOPT_AUGLAG || algorithm == NLOPT_AUGLAG_EQ)
476 return NLOPT_INVALID_ARGS;
477 if (!local_opt) { /* default */
478 local_opt = nlopt_create(
479 algorithm == NLOPT_LN_AUGLAG ||
480 algorithm == NLOPT_LN_AUGLAG_EQ
481 ? nlopt_local_search_alg_nonderiv
482 : nlopt_local_search_alg_deriv, n);
483 if (!local_opt) return NLOPT_FAILURE;
484 nlopt_set_ftol_rel(local_opt, opt->ftol_rel);
485 nlopt_set_ftol_abs(local_opt, opt->ftol_abs);
486 nlopt_set_xtol_rel(local_opt, opt->xtol_rel);
487 nlopt_set_xtol_abs(local_opt, opt->xtol_abs);
488 nlopt_set_maxeval(local_opt, nlopt_local_search_maxeval);
489 nlopt_set_initial_step(local_opt, opt->dx);
491 opt->force_stop_child = local_opt;
492 ret = auglag_minimize(ni, f, f_data,
495 lb, ub, x, minf, &stop,
497 algorithm == NLOPT_AUGLAG_EQ
498 || algorithm == NLOPT_LN_AUGLAG_EQ
499 || algorithm == NLOPT_LD_AUGLAG_EQ);
500 opt->force_stop_child = NULL;
501 if (!opt->local_opt) nlopt_destroy(local_opt);
506 if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
507 return isres_minimize(ni, f, f_data,
508 (int) (opt->m), opt->fc,
509 (int) (opt->p), opt->h,
510 lb, ub, x, minf, &stop,
514 return NLOPT_INVALID_ARGS;
517 return NLOPT_SUCCESS; /* never reached */
520 /*********************************************************************/
527 /* wrapper for maximizing: just flip the sign of f and grad */
528 static double f_max(unsigned n, const double *x, double *grad, void *data)
530 f_max_data *d = (f_max_data *) data;
531 double val = d->f(n, x, grad, d->f_data);
534 for (i = 0; i < n; ++i)
540 nlopt_result nlopt_optimize(nlopt_opt opt, double *x, double *opt_f)
542 nlopt_func f; void *f_data;
547 if (!opt || !opt_f || !opt->f) return NLOPT_INVALID_ARGS;
548 f = opt->f; f_data = opt->f_data;
550 /* for maximizing, just minimize the f_max wrapper, which
551 flips the sign of everything */
552 if ((maximize = opt->maximize)) {
553 fmd.f = f; fmd.f_data = f_data;
554 opt->f = f_max; opt->f_data = &fmd;
555 opt->stopval = -opt->stopval;
559 ret = nlopt_optimize_(opt, x, opt_f);
561 if (maximize) { /* restore original signs */
562 opt->maximize = maximize;
563 opt->stopval = -opt->stopval;
564 opt->f = f; opt->f_data = f_data;
571 /*********************************************************************/
573 nlopt_result nlopt_optimize_limited(nlopt_opt opt, double *x, double *minf,
574 int maxeval, double maxtime)
580 if (!opt) return NLOPT_INVALID_ARGS;
582 save_maxeval = nlopt_get_maxeval(opt);
583 save_maxtime = nlopt_get_maxtime(opt);
585 /* override opt limits if maxeval and/or maxtime are more stringent */
586 if (save_maxeval <= 0 || (maxeval > 0 && maxeval < save_maxeval))
587 nlopt_set_maxeval(opt, maxeval);
588 if (save_maxtime <= 0 || (maxtime > 0 && maxtime < save_maxtime))
589 nlopt_set_maxtime(opt, maxtime);
591 ret = nlopt_optimize(opt, x, minf);
593 nlopt_set_maxeval(opt, save_maxeval);
594 nlopt_set_maxtime(opt, save_maxtime);
599 /*********************************************************************/