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Bayesian-Optimization / nlopt2 / api / optimize.c

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/* Copyright (c) 2007-2012 Massachusetts Institute of Technology
 *
 * Permission is hereby granted, free of charge, to any person obtaining
 * a copy of this software and associated documentation files (the
 * "Software"), to deal in the Software without restriction, including
 * without limitation the rights to use, copy, modify, merge, publish,
 * distribute, sublicense, and/or sell copies of the Software, and to
 * permit persons to whom the Software is furnished to do so, subject to
 * the following conditions:
 * 
 * The above copyright notice and this permission notice shall be
 * included in all copies or substantial portions of the Software.
 * 
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
 * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
 * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
 * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 
 */

#include <stdlib.h>
#include <math.h>
#include <float.h>

#include "nlopt-internal.h"

/*********************************************************************/

#ifndef HAVE_ISNAN
static int my_isnan(double x) { return x != x; }
#  define isnan my_isnan
#endif

/*********************************************************************/

#include "praxis.h"
#include "direct.h"

#ifdef WITH_CXX
#  include "stogo.h"
#endif

#include "cdirect.h"

#include "luksan.h"

#include "crs.h"

#include "mlsl.h"
#include "mma.h"
#include "cobyla.h"
#include "newuoa.h"
#include "neldermead.h"
#include "auglag.h"
#include "bobyqa.h"
#include "isres.h"
#include "esch.h"
#include "slsqp.h"

/*********************************************************************/

static double f_bound(int n, const double *x, void *data_)
{
     int i;
     nlopt_opt data = (nlopt_opt) data_;
     double f;

     /* some methods do not support bound constraints, but support
	discontinuous objectives so we can just return Inf for invalid x */
     for (i = 0; i < n; ++i)
	  if (x[i] < data->lb[i] || x[i] > data->ub[i])
	       return HUGE_VAL;

     f = data->f((unsigned) n, x, NULL, data->f_data);
     return (isnan(f) || nlopt_isinf(f) ? HUGE_VAL : f);
}

static double f_noderiv(int n, const double *x, void *data_)
{
     nlopt_opt data = (nlopt_opt) data_;
     return data->f((unsigned) n, x, NULL, data->f_data);
}

static double f_direct(int n, const double *x, int *undefined, void *data_)
{
     nlopt_opt data = (nlopt_opt) data_;
     double *work = (double*) data->work;
     double f;
     unsigned i, j;
     f = data->f((unsigned) n, x, NULL, data->f_data);
     *undefined = isnan(f) || nlopt_isinf(f);
     if (nlopt_get_force_stop(data)) return f;
     for (i = 0; i < data->m && !*undefined; ++i) {
	  nlopt_eval_constraint(work, NULL, data->fc+i, (unsigned) n, x);
	  if (nlopt_get_force_stop(data)) return f;
	  for (j = 0; j < data->fc[i].m; ++j)
	       if (work[j] > 0)
		    *undefined = 1;
     }
     return f;
}

/*********************************************************************/

/* get min(dx) for algorithms requiring a scalar initial step size */
static nlopt_result initial_step(nlopt_opt opt, const double *x, double *step)
{
     unsigned freedx = 0, i;

     if (!opt->dx) {
	  freedx = 1;
	  if (nlopt_set_default_initial_step(opt, x) != NLOPT_SUCCESS)
	       return NLOPT_OUT_OF_MEMORY;
     }

     *step = HUGE_VAL;
     for (i = 0; i < opt->n; ++i)
	  if (*step > fabs(opt->dx[i]))
	       *step = fabs(opt->dx[i]);

     if (freedx) { free(opt->dx); opt->dx = NULL; }
     return NLOPT_SUCCESS;
}

/*********************************************************************/

/* return true if [lb,ub] is finite in every dimension (n dimensions) */
static int finite_domain(unsigned n, const double *lb, const double *ub)
{
     unsigned i;
     for (i = 0; i < n; ++i)
	  if (nlopt_isinf(ub[i] - lb[i])) return 0;
     return 1;
}

/*********************************************************************/
/* wrapper functions, only for derivative-free methods, that
   eliminate dimensions with lb == ub.   (The gradient-based methods
   should handle this case directly, since they operate on much
   larger vectors where I am loathe to make copies unnecessarily.) */

typedef struct {
     nlopt_func f;
     nlopt_mfunc mf;
     void *f_data;
     unsigned n; /* true dimension */
     double *x; /* scratch vector of length n */
     double *grad; /* optional scratch vector of length n */
     const double *lb, *ub; /* bounds, of length n */
} elimdim_data;

static void *elimdim_makedata(nlopt_func f, nlopt_mfunc mf, void *f_data,
			      unsigned n, double *x, const double *lb,
			      const double *ub, double *grad)
{
     elimdim_data *d = (elimdim_data *) malloc(sizeof(elimdim_data));
     if (!d) return NULL;
     d->f = f; d->mf = mf; d->f_data = f_data; d->n = n; d->x = x;
     d->lb = lb; d->ub = ub;
     d->grad = grad;
     return d;
}

static double elimdim_func(unsigned n0, const double *x0, double *grad, void *d_)
{
     elimdim_data *d = (elimdim_data *) d_;
     double *x = d->x;
     const double *lb = d->lb, *ub = d->ub;
     double val;
     unsigned n = d->n, i, j;

     (void) n0; /* unused */
     for (i = j = 0; i < n; ++i) {
	  if (lb[i] == ub[i])
	       x[i] = lb[i];
	  else /* assert: j < n0 */
	       x[i] = x0[j++];
     }
     val = d->f(n, x, grad ? d->grad : NULL, d->f_data);
     if (grad) {
	  /* assert: d->grad != NULL */
	  for (i = j = 0; i < n; ++i)
	       if (lb[i] != ub[i])
		    grad[j++] = d->grad[i];
     }
     return val;
}


static void elimdim_mfunc(unsigned m, double *result,
			  unsigned n0, const double *x0, double *grad, void *d_)
{
     elimdim_data *d = (elimdim_data *) d_;
     double *x = d->x;
     const double *lb = d->lb, *ub = d->ub;
     unsigned n = d->n, i, j;

     (void) n0; /* unused */
     (void) grad; /* assert: grad == NULL */
     for (i = j = 0; i < n; ++i) {
	  if (lb[i] == ub[i])
	       x[i] = lb[i];
	  else /* assert: j < n0 */
	       x[i] = x0[j++];
     }
     d->mf(m, result, n, x, NULL, d->f_data);
}

/* compute the eliminated dimension: number of dims with lb[i] != ub[i] */
static unsigned elimdim_dimension(unsigned n, const double *lb, const double *ub)
{
     unsigned n0 = 0, i;
     for (i = 0; i < n; ++i) n0 += lb[i] != ub[i] ? 1U : 0;
     return n0;
}

/* modify v to "shrunk" version, with dimensions for lb[i] == ub[i] elim'ed */
static void elimdim_shrink(unsigned n, double *v,
			   const double *lb, const double *ub)
{
     unsigned i, j;
     if (v)
	  for (i = j = 0; i < n; ++i)
	       if (lb[i] != ub[i])
		    v[j++] = v[i];
}

/* inverse of elimdim_shrink */
static void elimdim_expand(unsigned n, double *v,
			   const double *lb, const double *ub)
{
     unsigned i, j;
     if (v && n > 0) {
	  j = elimdim_dimension(n, lb, ub) - 1;
	  for (i = n - 1; i > 0; --i) {
	       if (lb[i] != ub[i])
		    v[i] = v[j--];
	       else
		    v[i] = lb[i];
	  }
	  if (lb[0] == ub[0])
	       v[0] = lb[0];
     }
}

/* given opt, create a new opt with equal-constraint dimensions eliminated */
static nlopt_opt elimdim_create(nlopt_opt opt)
{
     nlopt_opt opt0 = nlopt_copy(opt);
     double *x, *grad = NULL;
     unsigned i;
     
     if (!opt0) return NULL;
     x = (double *) malloc(sizeof(double) * opt->n);
     if (opt->n && !x) { nlopt_destroy(opt0); return NULL; }

     if (opt->algorithm == NLOPT_GD_STOGO
         || opt->algorithm == NLOPT_GD_STOGO_RAND) {
	  grad = (double *) malloc(sizeof(double) * opt->n);
	  if (opt->n && !grad) goto bad;
     }

     opt0->n = elimdim_dimension(opt->n, opt->lb, opt->ub);
     elimdim_shrink(opt->n, opt0->lb, opt->lb, opt->ub);
     elimdim_shrink(opt->n, opt0->ub, opt->lb, opt->ub);
     elimdim_shrink(opt->n, opt0->xtol_abs, opt->lb, opt->ub);
     elimdim_shrink(opt->n, opt0->dx, opt->lb, opt->ub);

     opt0->munge_on_destroy = opt0->munge_on_copy = NULL;

     opt0->f = elimdim_func;
     opt0->f_data = elimdim_makedata(opt->f, NULL, opt->f_data,
				     opt->n, x, opt->lb, opt->ub, grad);
     if (!opt0->f_data) goto bad;

     for (i = 0; i < opt->m; ++i) {
	  opt0->fc[i].f = elimdim_func;
	  opt0->fc[i].mf = elimdim_mfunc;
	  opt0->fc[i].f_data = elimdim_makedata(opt->fc[i].f, opt->fc[i].mf,
						opt->fc[i].f_data,
						opt->n, x, opt->lb, opt->ub,
						NULL);
	  if (!opt0->fc[i].f_data) goto bad;
     }

     for (i = 0; i < opt->p; ++i) {
	  opt0->h[i].f = elimdim_func;
	  opt0->h[i].mf = elimdim_mfunc;
	  opt0->h[i].f_data = elimdim_makedata(opt->h[i].f, opt->h[i].mf,
					       opt->h[i].f_data,
					       opt->n, x, opt->lb, opt->ub,
					       NULL);
	  if (!opt0->h[i].f_data) goto bad;
     }

     return opt0;
bad:
     free(grad);
     free(x);
     nlopt_destroy(opt0);
     return NULL;
}

/* like nlopt_destroy, but also frees elimdim_data */
static void elimdim_destroy(nlopt_opt opt)
{
     unsigned i;
     if (!opt) return;

     free(((elimdim_data*) opt->f_data)->x);
     free(((elimdim_data*) opt->f_data)->grad);
     free(opt->f_data); opt->f_data = NULL;

     for (i = 0; i < opt->m; ++i) {
	  free(opt->fc[i].f_data);
	  opt->fc[i].f_data = NULL;
     }
     for (i = 0; i < opt->p; ++i) {
	  free(opt->h[i].f_data);
	  opt->h[i].f_data = NULL;
     }

     nlopt_destroy(opt);
}

/* return whether to use elimdim wrapping. */
static int elimdim_wrapcheck(nlopt_opt opt)
{
     if (!opt) return 0;
     if (elimdim_dimension(opt->n, opt->lb, opt->ub) == opt->n) return 0;
     switch (opt->algorithm) {
	 case NLOPT_GN_DIRECT:
	 case NLOPT_GN_DIRECT_L: 
	 case NLOPT_GN_DIRECT_L_RAND: 
	 case NLOPT_GN_DIRECT_NOSCAL:
	 case NLOPT_GN_DIRECT_L_NOSCAL: 
	 case NLOPT_GN_DIRECT_L_RAND_NOSCAL: 
	 case NLOPT_GN_ORIG_DIRECT:
	 case NLOPT_GN_ORIG_DIRECT_L:
	 case NLOPT_LN_PRAXIS:
	 case NLOPT_LN_COBYLA:
	 case NLOPT_LN_NEWUOA:
	 case NLOPT_LN_NEWUOA_BOUND:
	 case NLOPT_LN_BOBYQA:
	 case NLOPT_LN_NELDERMEAD:
	 case NLOPT_LN_SBPLX:
	 case NLOPT_GN_ISRES:
	 case NLOPT_GN_ESCH:
	 case NLOPT_GD_STOGO:
         case NLOPT_GD_STOGO_RAND:
	      return 1;

	 default: return 0;
     }
}

/*********************************************************************/

#define POP(defaultpop) (opt->stochastic_population > 0 ?		\
                         opt->stochastic_population :			\
                         (nlopt_stochastic_population > 0 ?		\
			  nlopt_stochastic_population : (defaultpop)))

/* unlike nlopt_optimize() below, only handles minimization case */
static nlopt_result nlopt_optimize_(nlopt_opt opt, double *x, double *minf)
{
     const double *lb, *ub;
     nlopt_algorithm algorithm;
     nlopt_func f; void *f_data;
     unsigned n, i;
     int ni;
     nlopt_stopping stop;

     if (!opt || !x || !minf || !opt->f
	 || opt->maximize) return NLOPT_INVALID_ARGS;

     /* reset stopping flag */
     nlopt_set_force_stop(opt, 0);
     opt->force_stop_child = NULL;
     
     /* copy a few params to local vars for convenience */
     n = opt->n;
     ni = (int) n; /* most of the subroutines take "int" arg */
     lb = opt->lb; ub = opt->ub;
     algorithm = opt->algorithm;
     f = opt->f; f_data = opt->f_data;

     if (n == 0) { /* trivial case: no degrees of freedom */
	  *minf = opt->f(n, x, NULL, opt->f_data);
	  return NLOPT_SUCCESS;
     }

     *minf = HUGE_VAL;
     
     /* make sure rand generator is inited */
     nlopt_srand_time_default(); /* default is non-deterministic */

     /* check bound constraints */
     for (i = 0; i < n; ++i)
	  if (lb[i] > ub[i] || x[i] < lb[i] || x[i] > ub[i])
	       return NLOPT_INVALID_ARGS;

     stop.n = n;
     stop.minf_max = opt->stopval;
     stop.ftol_rel = opt->ftol_rel;
     stop.ftol_abs = opt->ftol_abs;
     stop.xtol_rel = opt->xtol_rel;
     stop.xtol_abs = opt->xtol_abs;
     stop.nevals = 0;
     stop.maxeval = opt->maxeval;
     stop.maxtime = opt->maxtime;
     stop.start = nlopt_seconds();
     stop.force_stop = &(opt->force_stop);

     switch (algorithm) {
	 case NLOPT_GN_DIRECT:
	 case NLOPT_GN_DIRECT_L: 
	 case NLOPT_GN_DIRECT_L_RAND: 
	      if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
	      return cdirect(ni, f, f_data, 
			     lb, ub, x, minf, &stop, 0.0, 
			     (algorithm != NLOPT_GN_DIRECT)
			     + 3 * (algorithm == NLOPT_GN_DIRECT_L_RAND 
				    ? 2 : (algorithm != NLOPT_GN_DIRECT))
			     + 9 * (algorithm == NLOPT_GN_DIRECT_L_RAND 
				    ? 1 : (algorithm != NLOPT_GN_DIRECT)));
	      
	 case NLOPT_GN_DIRECT_NOSCAL:
	 case NLOPT_GN_DIRECT_L_NOSCAL: 
	 case NLOPT_GN_DIRECT_L_RAND_NOSCAL: 
	      if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
	      return cdirect_unscaled(ni, f, f_data, lb, ub, x, minf, 
				      &stop, 0.0, 
				      (algorithm != NLOPT_GN_DIRECT)
				      + 3 * (algorithm == NLOPT_GN_DIRECT_L_RAND ? 2 : (algorithm != NLOPT_GN_DIRECT))
				      + 9 * (algorithm == NLOPT_GN_DIRECT_L_RAND ? 1 : (algorithm != NLOPT_GN_DIRECT)));
	      
	 case NLOPT_GN_ORIG_DIRECT:
	 case NLOPT_GN_ORIG_DIRECT_L: {
	      direct_return_code dret;
	      if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
	      opt->work = malloc(sizeof(double) *
				 nlopt_max_constraint_dim(opt->m,
							  opt->fc));
	      if (!opt->work) return NLOPT_OUT_OF_MEMORY;
	      dret = direct_optimize(f_direct, opt, ni, lb, ub, x, minf,
				     stop.maxeval, -1,
				     stop.start, stop.maxtime,
				     0.0, 0.0,
				     pow(stop.xtol_rel, (double) n), -1.0,
				     stop.force_stop,
				     stop.minf_max, 0.0,
				     NULL, 
				     algorithm == NLOPT_GN_ORIG_DIRECT
				     ? DIRECT_ORIGINAL
				     : DIRECT_GABLONSKY);
	      free(opt->work); opt->work = NULL;
	      switch (dret) {
		  case DIRECT_INVALID_BOUNDS:
		  case DIRECT_MAXFEVAL_TOOBIG:
		  case DIRECT_INVALID_ARGS:
		       return NLOPT_INVALID_ARGS;
		  case DIRECT_INIT_FAILED:
		  case DIRECT_SAMPLEPOINTS_FAILED:
		  case DIRECT_SAMPLE_FAILED:
		       return NLOPT_FAILURE;
		  case DIRECT_MAXFEVAL_EXCEEDED:
		  case DIRECT_MAXITER_EXCEEDED:
		       return NLOPT_MAXEVAL_REACHED;
		  case DIRECT_MAXTIME_EXCEEDED:
		       return NLOPT_MAXTIME_REACHED;
		  case DIRECT_GLOBAL_FOUND:
		       return NLOPT_MINF_MAX_REACHED;
		  case DIRECT_VOLTOL:
		  case DIRECT_SIGMATOL:
		       return NLOPT_XTOL_REACHED;
		  case DIRECT_OUT_OF_MEMORY:
		       return NLOPT_OUT_OF_MEMORY;
		  case DIRECT_FORCED_STOP:
		       return NLOPT_FORCED_STOP;
	      }
	      break;
	 }

	 case NLOPT_GD_STOGO:
	 case NLOPT_GD_STOGO_RAND:
#ifdef WITH_CXX
	      if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
	      if (!stogo_minimize(ni, f, f_data, x, minf, lb, ub, &stop,
				  algorithm == NLOPT_GD_STOGO
				  ? 0 : (int) POP(2*n)))
		   return NLOPT_FAILURE;
	      break;
#else
	      return NLOPT_INVALID_ARGS;
#endif

#if 0
	      /* lacking a free/open-source license, we no longer use
		 Rowan's code, and instead use by "sbplx" re-implementation */
	 case NLOPT_LN_SUBPLEX: {
	      int iret, freedx = 0;
	      if (!opt->dx) {
		   freedx = 1;
		   if (nlopt_set_default_initial_step(opt, x) != NLOPT_SUCCESS)
			return NLOPT_OUT_OF_MEMORY;
	      }		       
	      iret = nlopt_subplex(f_bound, minf, x, n, opt, &stop, opt->dx);
	      if (freedx) { free(opt->dx); opt->dx = NULL; }
	      switch (iret) {
		  case -2: return NLOPT_INVALID_ARGS;
		  case -20: return NLOPT_FORCED_STOP;
		  case -10: return NLOPT_MAXTIME_REACHED;
		  case -1: return NLOPT_MAXEVAL_REACHED;
		  case 0: return NLOPT_XTOL_REACHED;
		  case 1: return NLOPT_SUCCESS;
		  case 2: return NLOPT_MINF_MAX_REACHED;
		  case 20: return NLOPT_FTOL_REACHED;
		  case -200: return NLOPT_OUT_OF_MEMORY;
		  default: return NLOPT_FAILURE; /* unknown return code */
	      }
	      break;
	 }
#endif

	 case NLOPT_LN_PRAXIS: {
	      double step;
	      if (initial_step(opt, x, &step) != NLOPT_SUCCESS)
		   return NLOPT_OUT_OF_MEMORY;
	      return praxis_(0.0, DBL_EPSILON, 
			     step, ni, x, f_bound, opt, &stop, minf);
	 }

	 case NLOPT_LD_LBFGS: 
	      return luksan_plis(ni, f, f_data, lb, ub, x, minf, 
				 &stop, opt->vector_storage);

	 case NLOPT_LD_VAR1: 
	 case NLOPT_LD_VAR2: 
	      return luksan_plip(ni, f, f_data, lb, ub, x, minf, 
				 &stop, opt->vector_storage,
				 algorithm == NLOPT_LD_VAR1 ? 1 : 2);

	 case NLOPT_LD_TNEWTON: 
	 case NLOPT_LD_TNEWTON_RESTART: 
	 case NLOPT_LD_TNEWTON_PRECOND: 
	 case NLOPT_LD_TNEWTON_PRECOND_RESTART: 
	      return luksan_pnet(ni, f, f_data, lb, ub, x, minf,
				 &stop, opt->vector_storage,
				 1 + (algorithm - NLOPT_LD_TNEWTON) % 2,
				 1 + (algorithm - NLOPT_LD_TNEWTON) / 2);

	 case NLOPT_GN_CRS2_LM:
	      if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
	      return crs_minimize(ni, f, f_data, lb, ub, x, minf, &stop, 
				  (int) POP(0), 0);

	 case NLOPT_G_MLSL:
	 case NLOPT_G_MLSL_LDS:
	 case NLOPT_GN_MLSL:
	 case NLOPT_GD_MLSL:
	 case NLOPT_GN_MLSL_LDS:
	 case NLOPT_GD_MLSL_LDS: {
	      nlopt_opt local_opt = opt->local_opt;
	      nlopt_result ret;
	      if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
	      if (!local_opt && (algorithm == NLOPT_G_MLSL 
				 || algorithm == NLOPT_G_MLSL_LDS))
		   return NLOPT_INVALID_ARGS;
	      if (!local_opt) { /* default */
		   nlopt_algorithm local_alg = (algorithm == NLOPT_GN_MLSL ||
						algorithm == NLOPT_GN_MLSL_LDS)
			? nlopt_local_search_alg_nonderiv
			: nlopt_local_search_alg_deriv;
		   /* don't call MLSL recursively! */
		   if (local_alg >= NLOPT_GN_MLSL
		       && local_alg <= NLOPT_GD_MLSL_LDS)
			local_alg = (algorithm == NLOPT_GN_MLSL ||
				     algorithm == NLOPT_GN_MLSL_LDS)
			     ? NLOPT_LN_COBYLA : NLOPT_LD_MMA;
		   local_opt = nlopt_create(local_alg, n);
		   if (!local_opt) return NLOPT_FAILURE;
		   nlopt_set_ftol_rel(local_opt, opt->ftol_rel);
		   nlopt_set_ftol_abs(local_opt, opt->ftol_abs);
		   nlopt_set_xtol_rel(local_opt, opt->xtol_rel);
		   nlopt_set_xtol_abs(local_opt, opt->xtol_abs);
		   nlopt_set_maxeval(local_opt, nlopt_local_search_maxeval);
	      }
	      if (opt->dx) nlopt_set_initial_step(local_opt, opt->dx);
	      for (i = 0; i < n && stop.xtol_abs[i] > 0; ++i) ;
	      if (local_opt->ftol_rel <= 0 && local_opt->ftol_abs <= 0 &&
		  local_opt->xtol_rel <= 0 && i < n) {
		   /* it is not sensible to call MLSL without *some*
		      nonzero tolerance for the local search */
		   nlopt_set_ftol_rel(local_opt, 1e-15);
		   nlopt_set_xtol_rel(local_opt, 1e-7);
	      }
	      opt->force_stop_child = local_opt;
	      ret = mlsl_minimize(ni, f, f_data, lb, ub, x, minf, &stop,
				  local_opt, (int) POP(0),
				  algorithm >= NLOPT_GN_MLSL_LDS &&
				  algorithm != NLOPT_G_MLSL);
	      opt->force_stop_child = NULL;
	      if (!opt->local_opt) nlopt_destroy(local_opt);
	      return ret;
	 }

	 case NLOPT_LD_MMA: case NLOPT_LD_CCSAQ: {
	      nlopt_opt dual_opt;
	      nlopt_result ret;
#define LO(param, def) (opt->local_opt ? opt->local_opt->param : (def))
	      dual_opt = nlopt_create(LO(algorithm,
					 nlopt_local_search_alg_deriv),
				      nlopt_count_constraints(opt->m,
							      opt->fc));
	      if (!dual_opt) return NLOPT_FAILURE;
	      nlopt_set_ftol_rel(dual_opt, LO(ftol_rel, 1e-14));
	      nlopt_set_ftol_abs(dual_opt, LO(ftol_abs, 0.0));
	      nlopt_set_maxeval(dual_opt, LO(maxeval, 100000));
#undef LO

	      if (algorithm == NLOPT_LD_MMA)
		   ret = mma_minimize(n, f, f_data, opt->m, opt->fc,
				      lb, ub, x, minf, &stop, dual_opt);
	      else
		   ret = ccsa_quadratic_minimize(
			n, f, f_data, opt->m, opt->fc, opt->pre,
			lb, ub, x, minf, &stop, dual_opt);
	      nlopt_destroy(dual_opt);
	      return ret;
	 }

	 case NLOPT_LN_COBYLA: {
	      nlopt_result ret;
	      int freedx = 0;
	      if (!opt->dx) {
		   freedx = 1;
		   if (nlopt_set_default_initial_step(opt, x) != NLOPT_SUCCESS)
			return NLOPT_OUT_OF_MEMORY;
	      }
	      return cobyla_minimize(n, f, f_data, 
				     opt->m, opt->fc,
				     opt->p, opt->h,
				     lb, ub, x, minf, &stop,
				     opt->dx);
	      if (freedx) { free(opt->dx); opt->dx = NULL; }
	      return ret;
	 }
				     
	 case NLOPT_LN_NEWUOA: {
	      double step;
	      if (initial_step(opt, x, &step) != NLOPT_SUCCESS)
		   return NLOPT_OUT_OF_MEMORY;
	      return newuoa(ni, 2*n+1, x, 0, 0, step,
			    &stop, minf, f_noderiv, opt);
	 }
				     
	 case NLOPT_LN_NEWUOA_BOUND: {
	      double step;
	      if (initial_step(opt, x, &step) != NLOPT_SUCCESS)
		   return NLOPT_OUT_OF_MEMORY;
	      return newuoa(ni, 2*n+1, x, lb, ub, step,
			    &stop, minf, f_noderiv, opt);
	 }

	 case NLOPT_LN_BOBYQA: {
	      nlopt_result ret;
	      int freedx = 0;
	      if (!opt->dx) {
		   freedx = 1;
		   if (nlopt_set_default_initial_step(opt, x) != NLOPT_SUCCESS)
			return NLOPT_OUT_OF_MEMORY;
	      }
	      ret = bobyqa(ni, 2*n+1, x, lb, ub, opt->dx,
			   &stop, minf, opt->f, opt->f_data);
	      if (freedx) { free(opt->dx); opt->dx = NULL; }
	      return ret;
	 }

	 case NLOPT_LN_NELDERMEAD: 
	 case NLOPT_LN_SBPLX: 
	 {
	      nlopt_result ret;
	      int freedx = 0;
	      if (!opt->dx) {
		   freedx = 1;
		   if (nlopt_set_default_initial_step(opt, x) != NLOPT_SUCCESS)
			return NLOPT_OUT_OF_MEMORY;
	      }
	      if (algorithm == NLOPT_LN_NELDERMEAD)
		   ret= nldrmd_minimize(ni,f,f_data,lb,ub,x,minf,opt->dx,&stop);
	      else
		   ret= sbplx_minimize(ni,f,f_data,lb,ub,x,minf,opt->dx,&stop);
	      if (freedx) { free(opt->dx); opt->dx = NULL; }
	      return ret;
	 }

	 case NLOPT_AUGLAG:
	 case NLOPT_AUGLAG_EQ:
	 case NLOPT_LN_AUGLAG:
	 case NLOPT_LN_AUGLAG_EQ:
	 case NLOPT_LD_AUGLAG:
	 case NLOPT_LD_AUGLAG_EQ: {
	      nlopt_opt local_opt = opt->local_opt;
	      nlopt_result ret;
	      if ((algorithm == NLOPT_AUGLAG || algorithm == NLOPT_AUGLAG_EQ)
		  && !local_opt)
		   return NLOPT_INVALID_ARGS;
	      if (!local_opt) { /* default */
		   local_opt = nlopt_create(
			algorithm == NLOPT_LN_AUGLAG || 
			algorithm == NLOPT_LN_AUGLAG_EQ
			? nlopt_local_search_alg_nonderiv
			: nlopt_local_search_alg_deriv, n);
		   if (!local_opt) return NLOPT_FAILURE;
		   nlopt_set_ftol_rel(local_opt, opt->ftol_rel);
		   nlopt_set_ftol_abs(local_opt, opt->ftol_abs);
		   nlopt_set_xtol_rel(local_opt, opt->xtol_rel);
		   nlopt_set_xtol_abs(local_opt, opt->xtol_abs);
		   nlopt_set_maxeval(local_opt, nlopt_local_search_maxeval);
	      }
	      if (opt->dx) nlopt_set_initial_step(local_opt, opt->dx);
	      opt->force_stop_child = local_opt;
	      ret = auglag_minimize(ni, f, f_data, 
				    opt->m, opt->fc, 
				    opt->p, opt->h,
				    lb, ub, x, minf, &stop,
				    local_opt,
				    algorithm == NLOPT_AUGLAG_EQ
				    || algorithm == NLOPT_LN_AUGLAG_EQ
				    || algorithm == NLOPT_LD_AUGLAG_EQ);
	      opt->force_stop_child = NULL;
	      if (!opt->local_opt) nlopt_destroy(local_opt);
	      return ret;
	 }

	 case NLOPT_GN_ISRES:
	      if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
	      return isres_minimize(ni, f, f_data, 
				    (int) (opt->m), opt->fc,
				    (int) (opt->p), opt->h,
				    lb, ub, x, minf, &stop,
				    (int) POP(0));

	case NLOPT_GN_ESCH:
	      if (!finite_domain(n, lb, ub)) return NLOPT_INVALID_ARGS;
	      return chevolutionarystrategy(n, f, f_data, 
					    lb, ub, x, minf, &stop,
					    (unsigned) POP(0),
					    (unsigned) (POP(0)*1.5));

	 case NLOPT_LD_SLSQP:
	      return nlopt_slsqp(n, f, f_data,
				 opt->m, opt->fc,
				 opt->p, opt->h,
				 lb, ub, x, minf, &stop);
				     
	 default:
	      return NLOPT_INVALID_ARGS;
     }

     return NLOPT_SUCCESS; /* never reached */
}

/*********************************************************************/

typedef struct {
     nlopt_func f;
     nlopt_precond pre;
     void *f_data;
} f_max_data;

/* wrapper for maximizing: just flip the sign of f and grad */
static double f_max(unsigned n, const double *x, double *grad, void *data)
{
     f_max_data *d = (f_max_data *) data;
     double val = d->f(n, x, grad, d->f_data);
     if (grad) {
	  unsigned i;
	  for (i = 0; i < n; ++i)
	       grad[i] = -grad[i];
     }
     return -val;
}

static void pre_max(unsigned n, const double *x, const double *v,
		    double *vpre, void *data)
{
     f_max_data *d = (f_max_data *) data;
     unsigned i;
     d->pre(n, x, v, vpre, d->f_data);
     for (i = 0; i < n; ++i) vpre[i] = -vpre[i];
}

nlopt_result 
NLOPT_STDCALL nlopt_optimize(nlopt_opt opt, double *x, double *opt_f)
{
     nlopt_func f; void *f_data; nlopt_precond pre;
     f_max_data fmd;
     int maximize;
     nlopt_result ret;

     if (!opt || !opt_f || !opt->f) return NLOPT_INVALID_ARGS;
     f = opt->f; f_data = opt->f_data; pre = opt->pre;

     /* for maximizing, just minimize the f_max wrapper, which 
	flips the sign of everything */
     if ((maximize = opt->maximize)) {
	  fmd.f = f; fmd.f_data = f_data; fmd.pre = pre;
	  opt->f = f_max; opt->f_data = &fmd; 
	  if (opt->pre) opt->pre = pre_max;
	  opt->stopval = -opt->stopval;
	  opt->maximize = 0;
     }

     { /* possibly eliminate lb == ub dimensions for some algorithms */
	  nlopt_opt elim_opt = opt;
	  if (elimdim_wrapcheck(opt)) {
	       elim_opt = elimdim_create(opt);
	       if (!elim_opt) { ret = NLOPT_OUT_OF_MEMORY; goto done; }
	       elimdim_shrink(opt->n, x, opt->lb, opt->ub);
	  }

	  ret = nlopt_optimize_(elim_opt, x, opt_f);

	  if (elim_opt != opt) {
	       elimdim_destroy(elim_opt);
	       elimdim_expand(opt->n, x, opt->lb, opt->ub);
	  }
     }

done:
     if (maximize) { /* restore original signs */
	  opt->maximize = maximize;
	  opt->stopval = -opt->stopval;
	  opt->f = f; opt->f_data = f_data; opt->pre = pre;
     	  *opt_f = -*opt_f;
     }

     return ret;
}

/*********************************************************************/

nlopt_result nlopt_optimize_limited(nlopt_opt opt, double *x, double *minf,
				    int maxeval, double maxtime)
{
     int save_maxeval;
     double save_maxtime;
     nlopt_result ret;

     if (!opt) return NLOPT_INVALID_ARGS;

     save_maxeval = nlopt_get_maxeval(opt);
     save_maxtime = nlopt_get_maxtime(opt);
     
     /* override opt limits if maxeval and/or maxtime are more stringent */
     if (save_maxeval <= 0 || (maxeval > 0 && maxeval < save_maxeval))
	  nlopt_set_maxeval(opt, maxeval);
     if (save_maxtime <= 0 || (maxtime > 0 && maxtime < save_maxtime))
	  nlopt_set_maxtime(opt, maxtime);

     ret = nlopt_optimize(opt, x, minf);

     nlopt_set_maxeval(opt, save_maxeval);
     nlopt_set_maxtime(opt, save_maxtime);

     return ret;
}

/*********************************************************************/