nlopt_result auglag_minimize(int n, nlopt_func f, void *f_data,
int m, nlopt_constraint *fc,
int p, nlopt_constraint *h,
const double *lb, const double *ub, /* bounds */
double *x, /* in: initial guess, out: minimizer */
double *minf,
nlopt_stopping *stop,
nlopt_opt sub_opt, int sub_has_fc)
{
auglag_data d;
nlopt_result ret = NLOPT_SUCCESS;
double ICM = HUGE_VAL, minf_penalty = HUGE_VAL, penalty;
double *xcur = NULL, fcur;
int i, ii, feasible, minf_feasible = 0;
unsigned int k;
int auglag_iters = 0;
int max_constraint_dim;
/* magic parameters from Birgin & Martinez */
const double tau = 0.5, gam = 10;
const double lam_min = -1e20, lam_max = 1e20, mu_max = 1e20;
d.f = f; d.f_data = f_data;
d.m = m; d.fc = fc;
d.p = p; d.h = h;
d.stop = stop;
/* whether we handle inequality constraints via the augmented
Lagrangian penalty function, or directly in the sub-algorithm */
if (sub_has_fc)
d.m = 0;
else
m = 0;
max_constraint_dim = MAX(nlopt_max_constraint_dim(d.m, fc),
nlopt_max_constraint_dim(d.p, h));
d.mm = nlopt_count_constraints(d.m, fc);
d.pp = nlopt_count_constraints(d.p, h);
ret = nlopt_set_min_objective(sub_opt, auglag, &d); if (ret<0) return ret;
ret = nlopt_set_lower_bounds(sub_opt, lb); if (ret<0) return ret;
ret = nlopt_set_upper_bounds(sub_opt, ub); if (ret<0) return ret;
ret = nlopt_set_stopval(sub_opt,
d.m==0 && d.p==0 ? stop->minf_max : -HUGE_VAL);
if (ret<0) return ret;
ret = nlopt_remove_inequality_constraints(sub_opt); if (ret<0) return ret;
ret = nlopt_remove_equality_constraints(sub_opt); if (ret<0) return ret;
for (i = 0; i < m; ++i) {
if (fc[i].f)
ret = nlopt_add_inequality_constraint(sub_opt,
fc[i].f, fc[i].f_data,
fc[i].tol[0]);
else
ret = nlopt_add_inequality_mconstraint(sub_opt, fc[i].m,
fc[i].mf, fc[i].f_data,
fc[i].tol);
if (ret < 0) return ret;
}
xcur = (double *) malloc(sizeof(double) * (n
+ max_constraint_dim * (1 + n)
+ d.pp + d.mm));
if (!xcur) return NLOPT_OUT_OF_MEMORY;
memcpy(xcur, x, sizeof(double) * n);
d.restmp = xcur + n;
d.gradtmp = d.restmp + max_constraint_dim;
memset(d.gradtmp, 0, sizeof(double) * (n*max_constraint_dim + d.pp+d.mm));
d.lambda = d.gradtmp + n * max_constraint_dim;
d.mu = d.lambda + d.pp;
*minf = HUGE_VAL;
/* starting rho suggested by B & M */
if (d.p > 0 || d.m > 0) {
double con2 = 0;
++ *(d.stop->nevals_p);
fcur = f(n, xcur, NULL, f_data);
if (nlopt_stop_forced(stop)) {
ret = NLOPT_FORCED_STOP; goto done; }
penalty = 0;
feasible = 1;
for (i = 0; i < d.p; ++i) {
nlopt_eval_constraint(d.restmp, NULL, d.h + i, n, xcur);
if (nlopt_stop_forced(stop)) {
ret = NLOPT_FORCED_STOP; goto done; }
for (k = 0; k < d.h[i].m; ++k) {
double hi = d.restmp[k];
penalty += fabs(hi);
feasible = feasible && fabs(hi) <= h[i].tol[k];
con2 += hi * hi;
}
}
for (i = 0; i < d.m; ++i) {
nlopt_eval_constraint(d.restmp, NULL, d.fc + i, n, xcur);
if (nlopt_stop_forced(stop)) {
ret = NLOPT_FORCED_STOP; goto done; }
for (k = 0; k < d.fc[i].m; ++k) {
double fci = d.restmp[k];
penalty += fci > 0 ? fci : 0;
feasible = feasible && fci <= fc[i].tol[k];
if (fci > 0) con2 += fci * fci;
}
}
*minf = fcur;
minf_penalty = penalty;
minf_feasible = feasible;
d.rho = MAX(1e-6, MIN(10, 2 * fabs(*minf) / con2));
}
else
d.rho = 1; /* whatever, doesn't matter */
if (auglag_verbose) {
printf("auglag: initial rho=%g\nauglag initial lambda=", d.rho);
for (i = 0; i < d.pp; ++i) printf(" %g", d.lambda[i]);
printf("\nauglag initial mu = ");
for (i = 0; i < d.mm; ++i) printf(" %g", d.mu[i]);
printf("\n");
}
do {
double prev_ICM = ICM;
ret = nlopt_optimize_limited(sub_opt, xcur, &fcur,
stop->maxeval - *(stop->nevals_p),
stop->maxtime - (nlopt_seconds()
- stop->start));
if (auglag_verbose)
printf("auglag: subopt return code %d\n", ret);
if (ret < 0) break;
++ *(d.stop->nevals_p);
fcur = f(n, xcur, NULL, f_data);
if (nlopt_stop_forced(stop)) {
ret = NLOPT_FORCED_STOP; goto done; }
if (auglag_verbose)
printf("auglag: fcur = %g\n", fcur);
ICM = 0;
penalty = 0;
feasible = 1;
for (i = ii = 0; i < d.p; ++i) {
nlopt_eval_constraint(d.restmp, NULL, d.h + i, n, xcur);
if (nlopt_stop_forced(stop)) {
ret = NLOPT_FORCED_STOP; goto done; }
for (k = 0; k < d.h[i].m; ++k) {
double hi = d.restmp[k];
double newlam = d.lambda[ii] + d.rho * hi;
penalty += fabs(hi);
feasible = feasible && fabs(hi) <= h[i].tol[k];
ICM = MAX(ICM, fabs(hi));
d.lambda[ii++] = MIN(MAX(lam_min, newlam), lam_max);
}
}
for (i = ii = 0; i < d.m; ++i) {
nlopt_eval_constraint(d.restmp, NULL, d.fc + i, n, xcur);
if (nlopt_stop_forced(stop)) {
ret = NLOPT_FORCED_STOP; goto done; }
for (k = 0; k < d.fc[i].m; ++k) {
double fci = d.restmp[k];
double newmu = d.mu[ii] + d.rho * fci;
penalty += fci > 0 ? fci : 0;
feasible = feasible && fci <= fc[i].tol[k];
ICM = MAX(ICM, fabs(MAX(fci, -d.mu[ii] / d.rho)));
d.mu[ii++] = MIN(MAX(0.0, newmu), mu_max);
}
}
if (ICM > tau * prev_ICM) {
d.rho *= gam;
}
auglag_iters++;
if (auglag_verbose) {
printf("auglag %d: ICM=%g (%sfeasible), rho=%g\nauglag lambda=",
auglag_iters, ICM, feasible ? "" : "not ", d.rho);
for (i = 0; i < d.pp; ++i) printf(" %g", d.lambda[i]);
printf("\nauglag %d: mu = ", auglag_iters);
for (i = 0; i < d.mm; ++i) printf(" %g", d.mu[i]);
printf("\n");
}
if ((feasible && (!minf_feasible || penalty < minf_penalty
|| fcur < *minf)) ||
(!minf_feasible && penalty < minf_penalty)) {
ret = NLOPT_SUCCESS;
if (feasible) {
if (fcur < stop->minf_max)
ret = NLOPT_MINF_MAX_REACHED;
else if (nlopt_stop_ftol(stop, fcur, *minf))
ret = NLOPT_FTOL_REACHED;
else if (nlopt_stop_x(stop, xcur, x))
ret = NLOPT_XTOL_REACHED;
}
*minf = fcur;
minf_penalty = penalty;
minf_feasible = feasible;
memcpy(x, xcur, sizeof(double) * n);
if (ret != NLOPT_SUCCESS) break;
}
if (nlopt_stop_forced(stop)) {ret = NLOPT_FORCED_STOP; break;}
if (nlopt_stop_evals(stop)) {ret = NLOPT_MAXEVAL_REACHED; break;}
if (nlopt_stop_time(stop)) {ret = NLOPT_MAXTIME_REACHED; break;}
/* TODO: use some other stopping criterion on ICM? */
/* The paper uses ICM <= epsilon and DFM <= epsilon, where
DFM is a measure of the size of the Lagrangian gradient.
Besides the fact that these kinds of absolute tolerances
(non-scale-invariant) are unsatisfying and it is not
clear how the user should specify it, the ICM <= epsilon
condition seems not too different from requiring feasibility,
especially now that the user can provide constraint-specific
tolerances analogous to epsilon. */
if (ICM == 0) {ret = NLOPT_FTOL_REACHED; break;}
} while (1);
done:
free(xcur);
return ret;
}
nlopt_result mma_minimize(unsigned n, nlopt_func f, void *f_data,
unsigned m, nlopt_constraint *fc,
const double *lb, const double *ub, /* bounds */
double *x, /* in: initial guess, out: minimizer */
double *minf,
nlopt_stopping *stop,
nlopt_opt dual_opt)
{
nlopt_result ret = NLOPT_SUCCESS;
double *xcur, rho, *sigma, *dfdx, *dfdx_cur, *xprev, *xprevprev, fcur;
double *dfcdx, *dfcdx_cur;
double *fcval, *fcval_cur, *rhoc, *gcval, *y, *dual_lb, *dual_ub;
unsigned i, ifc, j, k = 0;
dual_data dd;
int feasible;
double infeasibility;
unsigned mfc;
m = nlopt_count_constraints(mfc = m, fc);
if (nlopt_get_dimension(dual_opt) != m) return NLOPT_INVALID_ARGS;
sigma = (double *) malloc(sizeof(double) * (6*n + 2*m*n + m*7));
if (!sigma) return NLOPT_OUT_OF_MEMORY;
dfdx = sigma + n;
dfdx_cur = dfdx + n;
xcur = dfdx_cur + n;
xprev = xcur + n;
xprevprev = xprev + n;
fcval = xprevprev + n;
fcval_cur = fcval + m;
rhoc = fcval_cur + m;
gcval = rhoc + m;
dual_lb = gcval + m;
dual_ub = dual_lb + m;
y = dual_ub + m;
dfcdx = y + m;
dfcdx_cur = dfcdx + m*n;
dd.n = n;
dd.x = x;
dd.lb = lb;
dd.ub = ub;
dd.sigma = sigma;
dd.dfdx = dfdx;
dd.dfcdx = dfcdx;
dd.fcval = fcval;
dd.rhoc = rhoc;
dd.xcur = xcur;
dd.gcval = gcval;
for (j = 0; j < n; ++j) {
if (nlopt_isinf(ub[j]) || nlopt_isinf(lb[j]))
sigma[j] = 1.0; /* arbitrary default */
else
sigma[j] = 0.5 * (ub[j] - lb[j]);
}
rho = 1.0;
for (i = 0; i < m; ++i) {
rhoc[i] = 1.0;
dual_lb[i] = y[i] = 0.0;
dual_ub[i] = HUGE_VAL;
}
dd.fval = fcur = *minf = f(n, x, dfdx, f_data);
stop->nevals++;
memcpy(xcur, x, sizeof(double) * n);
if (nlopt_stop_forced(stop)) { ret = NLOPT_FORCED_STOP; goto done; }
feasible = 1; infeasibility = 0;
for (i = ifc = 0; ifc < mfc; ++ifc) {
nlopt_eval_constraint(fcval + i, dfcdx + i*n,
fc + ifc, n, x);
i += fc[ifc].m;
if (nlopt_stop_forced(stop)) { ret = NLOPT_FORCED_STOP; goto done; }
}
for (i = 0; i < m; ++i) {
feasible = feasible && (fcval[i] <= 0 || isnan(fcval[i]));
if (fcval[i] > infeasibility) infeasibility = fcval[i];
}
/* For non-feasible initial points, set a finite (large)
upper-bound on the dual variables. What this means is that,
if no feasible solution is found from the dual problem, it
will minimize the dual objective with the unfeasible
constraint weighted by 1e40 -- basically, minimizing the
unfeasible constraint until it becomes feasible or until we at
least obtain a step towards a feasible point.
Svanberg suggested a different approach in his 1987 paper, basically
introducing additional penalty variables for unfeasible constraints,
but this is easier to implement and at least as efficient. */
if (!feasible)
for (i = 0; i < m; ++i) dual_ub[i] = 1e40;
nlopt_set_min_objective(dual_opt, dual_func, &dd);
nlopt_set_lower_bounds(dual_opt, dual_lb);
nlopt_set_upper_bounds(dual_opt, dual_ub);
nlopt_set_stopval(dual_opt, -HUGE_VAL);
nlopt_remove_inequality_constraints(dual_opt);
nlopt_remove_equality_constraints(dual_opt);
while (1) { /* outer iterations */
double fprev = fcur;
if (nlopt_stop_forced(stop)) ret = NLOPT_FORCED_STOP;
else if (nlopt_stop_evals(stop)) ret = NLOPT_MAXEVAL_REACHED;
else if (nlopt_stop_time(stop)) ret = NLOPT_MAXTIME_REACHED;
else if (feasible && *minf < stop->minf_max)
ret = NLOPT_MINF_MAX_REACHED;
if (ret != NLOPT_SUCCESS) goto done;
if (++k > 1) memcpy(xprevprev, xprev, sizeof(double) * n);
memcpy(xprev, xcur, sizeof(double) * n);
while (1) { /* inner iterations */
double min_dual, infeasibility_cur;
int feasible_cur, inner_done;
unsigned save_verbose;
int new_infeasible_constraint;
nlopt_result reti;
/* solve dual problem */
dd.rho = rho; dd.count = 0;
save_verbose = mma_verbose;
mma_verbose = 0; /* no recursive verbosity */
reti = nlopt_optimize_limited(dual_opt, y, &min_dual,
0,
stop->maxtime - (nlopt_seconds()
- stop->start));
mma_verbose = save_verbose;
if (reti < 0 || reti == NLOPT_MAXTIME_REACHED) {
ret = reti;
goto done;
}
dual_func(m, y, NULL, &dd); /* evaluate final xcur etc. */
if (mma_verbose) {
printf("MMA dual converged in %d iterations to g=%g:\n",
dd.count, dd.gval);
for (i = 0; i < MIN(mma_verbose, m); ++i)
printf(" MMA y[%d]=%g, gc[%d]=%g\n",
i, y[i], i, dd.gcval[i]);
}
fcur = f(n, xcur, dfdx_cur, f_data);
stop->nevals++;
if (nlopt_stop_forced(stop)) {
ret = NLOPT_FORCED_STOP; goto done; }
feasible_cur = 1; infeasibility_cur = 0;
new_infeasible_constraint = 0;
inner_done = dd.gval >= fcur;
for (i = ifc = 0; ifc < mfc; ++ifc) {
nlopt_eval_constraint(fcval_cur + i, dfcdx_cur + i*n,
fc + ifc, n, xcur);
i += fc[ifc].m;
if (nlopt_stop_forced(stop)) {
ret = NLOPT_FORCED_STOP; goto done; }
}
for (i = ifc = 0; ifc < mfc; ++ifc) {
unsigned i0 = i, inext = i + fc[ifc].m;
for (; i < inext; ++i)
if (!isnan(fcval_cur[i])) {
feasible_cur = feasible_cur
&& (fcval_cur[i] <= fc[ifc].tol[i-i0]);
if (!isnan(fcval[i]))
inner_done = inner_done &&
(dd.gcval[i] >= fcval_cur[i]);
else if (fcval_cur[i] > 0)
new_infeasible_constraint = 1;
if (fcval_cur[i] > infeasibility_cur)
infeasibility_cur = fcval_cur[i];
}
}
if ((fcur < *minf && (inner_done || feasible_cur || !feasible))
|| (!feasible && infeasibility_cur < infeasibility)) {
if (mma_verbose && !feasible_cur)
printf("MMA - using infeasible point?\n");
dd.fval = *minf = fcur;
infeasibility = infeasibility_cur;
memcpy(fcval, fcval_cur, sizeof(double)*m);
memcpy(x, xcur, sizeof(double)*n);
memcpy(dfdx, dfdx_cur, sizeof(double)*n);
memcpy(dfcdx, dfcdx_cur, sizeof(double)*n*m);
/* once we have reached a feasible solution, the
algorithm should never make the solution infeasible
again (if inner_done), although the constraints may
be violated slightly by rounding errors etc. so we
must be a little careful about checking feasibility */
if (infeasibility_cur == 0) {
if (!feasible) { /* reset upper bounds to infin. */
for (i = 0; i < m; ++i) dual_ub[i] = HUGE_VAL;
nlopt_set_upper_bounds(dual_opt, dual_ub);
}
feasible = 1;
}
else if (new_infeasible_constraint) feasible = 0;
}
if (nlopt_stop_forced(stop)) ret = NLOPT_FORCED_STOP;
else if (nlopt_stop_evals(stop)) ret = NLOPT_MAXEVAL_REACHED;
else if (nlopt_stop_time(stop)) ret = NLOPT_MAXTIME_REACHED;
else if (feasible && *minf < stop->minf_max)
ret = NLOPT_MINF_MAX_REACHED;
if (ret != NLOPT_SUCCESS) goto done;
if (inner_done) break;
if (fcur > dd.gval)
rho = MIN(10*rho, 1.1 * (rho + (fcur-dd.gval) / dd.wval));
for (i = 0; i < m; ++i)
if (!isnan(fcval_cur[i]) && fcval_cur[i] > dd.gcval[i])
rhoc[i] =
MIN(10*rhoc[i],
1.1 * (rhoc[i] + (fcval_cur[i]-dd.gcval[i])
/ dd.wval));
if (mma_verbose)
printf("MMA inner iteration: rho -> %g\n", rho);
for (i = 0; i < MIN(mma_verbose, m); ++i)
printf(" MMA rhoc[%d] -> %g\n", i,rhoc[i]);
}
if (nlopt_stop_ftol(stop, fcur, fprev))
ret = NLOPT_FTOL_REACHED;
if (nlopt_stop_x(stop, xcur, xprev))
ret = NLOPT_XTOL_REACHED;
if (ret != NLOPT_SUCCESS) goto done;
/* update rho and sigma for iteration k+1 */
rho = MAX(0.1 * rho, MMA_RHOMIN);
if (mma_verbose)
printf("MMA outer iteration: rho -> %g\n", rho);
for (i = 0; i < m; ++i)
rhoc[i] = MAX(0.1 * rhoc[i], MMA_RHOMIN);
for (i = 0; i < MIN(mma_verbose, m); ++i)
printf(" MMA rhoc[%d] -> %g\n", i, rhoc[i]);
if (k > 1) {
for (j = 0; j < n; ++j) {
double dx2 = (xcur[j]-xprev[j]) * (xprev[j]-xprevprev[j]);
double gam = dx2 < 0 ? 0.7 : (dx2 > 0 ? 1.2 : 1);
sigma[j] *= gam;
if (!nlopt_isinf(ub[j]) && !nlopt_isinf(lb[j])) {
sigma[j] = MIN(sigma[j], 10*(ub[j]-lb[j]));
sigma[j] = MAX(sigma[j], 0.01*(ub[j]-lb[j]));
}
}
for (j = 0; j < MIN(mma_verbose, n); ++j)
printf(" MMA sigma[%d] -> %g\n",
j, sigma[j]);
}
}
done:
free(sigma);
return ret;
}
nlopt_result mlsl_minimize(int n, nlopt_func f, void *f_data,
const double *lb, const double *ub, /* bounds */
double *x, /* in: initial guess, out: minimizer */
double *minf,
nlopt_stopping *stop,
nlopt_opt local_opt,
int Nsamples, /* #samples/iteration (0=default) */
int lds) /* random or low-discrepancy seq. (lds) */
{
nlopt_result ret = NLOPT_SUCCESS;
mlsl_data d;
int i;
pt *p;
if (!Nsamples)
d.N = 4; /* FIXME: what is good number of samples per iteration? */
else
d.N = Nsamples;
if (d.N < 1) return NLOPT_INVALID_ARGS;
d.n = n;
d.lb = lb; d.ub = ub;
d.stop = stop;
d.f = f; d.f_data = f_data;
rb_tree_init(&d.pts, pt_compare);
rb_tree_init(&d.lms, lm_compare);
d.s = lds ? nlopt_sobol_create((unsigned) n) : NULL;
nlopt_set_min_objective(local_opt, fcount, &d);
nlopt_set_lower_bounds(local_opt, lb);
nlopt_set_upper_bounds(local_opt, ub);
nlopt_set_stopval(local_opt, stop->minf_max);
d.gamma = MLSL_GAMMA;
d.R_prefactor = sqrt(2./K2PI) * pow(gam(n) * MLSL_SIGMA, 1.0/n);
for (i = 0; i < n; ++i)
d.R_prefactor *= pow(ub[i] - lb[i], 1.0/n);
/* MLSL also suggests setting some minimum distance from points
to previous local minimiza and to the boundaries; I don't know
how to choose this as a fixed number, so I set it proportional
to R; see also the comments at top. dlm and dbound are the
proportionality constants. */
d.dlm = 1.0; /* min distance/R to local minima (FIXME: good value?) */
d.dbound = 1e-6; /* min distance/R to ub/lb boundaries (good value?) */
p = alloc_pt(n);
if (!p) { ret = NLOPT_OUT_OF_MEMORY; goto done; }
/* FIXME: how many sobol points to skip, if any? */
nlopt_sobol_skip(d.s, (unsigned) (10*n+d.N), p->x);
memcpy(p->x, x, n * sizeof(double));
p->f = f(n, x, NULL, f_data);
stop->nevals++;
if (!rb_tree_insert(&d.pts, (rb_key) p)) {
free(p); ret = NLOPT_OUT_OF_MEMORY;
}
if (nlopt_stop_forced(stop)) ret = NLOPT_FORCED_STOP;
else if (nlopt_stop_evals(stop)) ret = NLOPT_MAXEVAL_REACHED;
else if (nlopt_stop_time(stop)) ret = NLOPT_MAXTIME_REACHED;
else if (p->f < stop->minf_max) ret = NLOPT_MINF_MAX_REACHED;
while (ret == NLOPT_SUCCESS) {
rb_node *node;
double R;
get_minf(&d, minf, x);
/* sampling phase: add random/quasi-random points */
for (i = 0; i < d.N && ret == NLOPT_SUCCESS; ++i) {
p = alloc_pt(n);
if (!p) { ret = NLOPT_OUT_OF_MEMORY; goto done; }
if (d.s) nlopt_sobol_next(d.s, p->x, lb, ub);
else { /* use random points instead of LDS */
int j;
for (j = 0; j < n; ++j) p->x[j] = nlopt_urand(lb[j],ub[j]);
}
p->f = f(n, p->x, NULL, f_data);
stop->nevals++;
if (!rb_tree_insert(&d.pts, (rb_key) p)) {
free(p); ret = NLOPT_OUT_OF_MEMORY;
}
if (nlopt_stop_forced(stop)) ret = NLOPT_FORCED_STOP;
else if (nlopt_stop_evals(stop)) ret = NLOPT_MAXEVAL_REACHED;
else if (nlopt_stop_time(stop)) ret = NLOPT_MAXTIME_REACHED;
else if (p->f < stop->minf_max) ret = NLOPT_MINF_MAX_REACHED;
else {
find_closest_pt(n, &d.pts, p);
find_closest_lm(n, &d.lms, p);
pts_update_newpt(n, &d.pts, p);
}
}
/* distance threshhold parameter R in MLSL */
R = d.R_prefactor
* pow(log((double) d.pts.N) / d.pts.N, 1.0 / n);
/* local search phase: do local opt. for promising points */
node = rb_tree_min(&d.pts);
for (i = (int) (ceil(d.gamma * d.pts.N) + 0.5);
node && i > 0 && ret == NLOPT_SUCCESS; --i) {
p = (pt *) node->k;
if (is_potential_minimizer(&d, p,
R, d.dlm*R, d.dbound*R)) {
nlopt_result lret;
double *lm;
double t = nlopt_seconds();
if (nlopt_stop_forced(stop)) {
ret = NLOPT_FORCED_STOP; break;
}
if (nlopt_stop_evals(stop)) {
ret = NLOPT_MAXEVAL_REACHED; break;
}
if (stop->maxtime > 0 &&
t - stop->start >= stop->maxtime) {
ret = NLOPT_MAXTIME_REACHED; break;
}
lm = (double *) malloc(sizeof(double) * (n+1));
if (!lm) { ret = NLOPT_OUT_OF_MEMORY; goto done; }
memcpy(lm+1, p->x, sizeof(double) * n);
lret = nlopt_optimize_limited(local_opt, lm+1, lm,
stop->maxeval - stop->nevals,
stop->maxtime -
(t - stop->start));
p->minimized = 1;
if (lret < 0) { free(lm); ret = lret; goto done; }
if (!rb_tree_insert(&d.lms, lm)) {
free(lm); ret = NLOPT_OUT_OF_MEMORY;
}
else if (nlopt_stop_forced(stop)) ret = NLOPT_FORCED_STOP;
else if (*lm < stop->minf_max)
ret = NLOPT_MINF_MAX_REACHED;
else if (nlopt_stop_evals(stop))
ret = NLOPT_MAXEVAL_REACHED;
else if (nlopt_stop_time(stop))
ret = NLOPT_MAXTIME_REACHED;
else
pts_update_newlm(n, &d.pts, lm);
}
/* TODO: additional stopping criteria based
e.g. on improvement in function values, etc? */
node = rb_tree_succ(node);
}
}
get_minf(&d, minf, x);
done:
nlopt_sobol_destroy(d.s);
rb_tree_destroy_with_keys(&d.lms);
rb_tree_destroy_with_keys(&d.pts);
return ret;
}
