/*
* Main solver routine.
*/
idxint ECOS_solve(pwork* w)
{
idxint i, initcode, KKT_FACTOR_RETURN_CODE;
pfloat dtau_denom, dtauaff, dkapaff, sigma, dtau, dkap, bkap, pres_prev;
idxint exitcode = ECOS_FATAL;
#if PROFILING > 0
timer tsolve;
#endif
#if PROFILING > 1
timer tfactor, tkktsolve;
#endif
#if PROFILING > 0
/* start timer */
tic(&tsolve);
#endif
/* Initialize solver */
initcode = init(w);
if( initcode == ECOS_FATAL ){
#if PRINTLEVEL > 0
if( w->stgs->verbose ) PRINTTEXT("\nFatal error during initialization, aborting.");
#endif
return ECOS_FATAL;
}
/* MAIN INTERIOR POINT LOOP ---------------------------------------------------------------------- */
for( w->info->iter = 0; w->info->iter <= w->stgs->maxit; w->info->iter++ ){
/* Compute residuals */
computeResiduals(w);
/* Update statistics */
updateStatistics(w);
#if PRINTLEVEL > 1
/* Print info */
if( w->stgs->verbose ) printProgress(w->info);
#endif
/* SAFEGUARD: Backtrack to old iterate if the update was bad such that the primal residual PRES has
* increased by a factor of SAFEGUARD.
* If the safeguard is activated, the solver quits with the flag ECOS_NUMERICS.
*/
if( w->info->iter > 0 && w->info->pres > SAFEGUARD*pres_prev ){
#if PRINTLEVEL > 1
if( w->stgs->verbose ) PRINTTEXT("\nNUMERICAL PROBLEMS, recovering iterate %d and stopping.\n", (int)w->info->iter-1);
#endif
/* Backtrack */
for( i=0; i < w->n; i++ ){ w->x[i] -= w->info->step * w->KKT->dx2[i]; }
for( i=0; i < w->p; i++ ){ w->y[i] -= w->info->step * w->KKT->dy2[i]; }
for( i=0; i < w->m; i++ ){ w->z[i] -= w->info->step * w->KKT->dz2[i]; }
for( i=0; i < w->m; i++ ){ w->s[i] -= w->info->step * w->dsaff[i]; }
w->kap -= w->info->step * dkap;
w->tau -= w->info->step * dtau;
exitcode = ECOS_NUMERICS;
computeResiduals(w);
updateStatistics(w);
break;
}
pres_prev = w->info->pres;
/* Check termination criteria and exit if necessary */
/* Optimal? */
if( ( ( -w->cx > 0 ) || ( -w->by - w->hz > 0) ) &&
w->info->pres < w->stgs->feastol && w->info->dres < w->stgs->feastol &&
( w->info->gap < w->stgs->abstol || w->info->relgap < w->stgs->reltol ) ){
#if PRINTLEVEL > 0
if( w->stgs->verbose ) PRINTTEXT("\nOPTIMAL (within feastol=%3.1e, reltol=%3.1e, abstol=%3.1e).", w->stgs->feastol, w->stgs->reltol, w->stgs->abstol);
#endif
exitcode = ECOS_OPTIMAL;
break;
}
/* Primal infeasible? */
else if( ((w->info->pinfres != NAN) && (w->info->pinfres < w->stgs->feastol)) ||
((w->tau < w->stgs->feastol) && (w->kap < w->stgs->feastol && w->info->pinfres < w->stgs->feastol)) ){
#if PRINTLEVEL > 0
if( w->stgs->verbose ) PRINTTEXT("\nPRIMAL INFEASIBLE (within feastol=%3.1e, reltol=%3.1e, abstol=%3.1e).", w->stgs->feastol, w->stgs->reltol, w->stgs->abstol);
#endif
w->info->pinf = 1;
w->info->dinf = 0;
exitcode = ECOS_PINF;
break;
}
/* Dual infeasible? */
else if( (w->info->dinfres != NAN) && (w->info->dinfres < w->stgs->feastol) ){
#if PRINTLEVEL > 0
if( w->stgs->verbose ) PRINTTEXT("\nUNBOUNDED (within feastol=%3.1e, reltol=%3.1e, abstol=%3.1e).", w->stgs->feastol, w->stgs->reltol, w->stgs->abstol);
#endif
w->info->pinf = 0;
w->info->dinf = 1;
exitcode = ECOS_DINF;
break;
}
/* Did the line search c**k up? (zero step length) */
else if( w->info->iter > 0 && w->info->step == STEPMIN*GAMMA ){
#if PRINTLEVEL > 0
if( w->stgs->verbose ) PRINTTEXT("\nNo further progress possible (- numerics?), exiting.");
#endif
exitcode = ECOS_NUMERICS;
break;
}
/* MAXIT reached? */
else if( w->info->iter == w->stgs->maxit ){
#if PRINTLEVEL > 0
if( w->stgs->verbose ) PRINTTEXT("\nMaximum number of iterations reached, exiting.");
#endif
exitcode = ECOS_MAXIT;
break;
}
/* Compute scalings */
if( updateScalings(w->C, w->s, w->z, w->lambda) == OUTSIDE_CONE ){
#if PRINTLEVEL > 0
if( w->stgs->verbose ) PRINTTEXT("\nSlacks or multipliers leaving the positive orthant (- numerics ?), exiting.\n");
#endif
return ECOS_OUTCONE;
}
/* Update KKT matrix with scalings */
kkt_update(w->KKT->PKPt, w->KKT->PK, w->C);
#if DEBUG > 0
dumpSparseMatrix(w->KKT->PKPt,"PKPt_updated.txt");
#endif
/* factor KKT matrix */
#if PROFILING > 1
tic(&tfactor);
KKT_FACTOR_RETURN_CODE = kkt_factor(w->KKT, w->stgs->eps, w->stgs->delta, &w->info->tfactor_t1, &w->info->tfactor_t2);
w->info->tfactor += toc(&tfactor);
#else
KKT_FACTOR_RETURN_CODE = kkt_factor(w->KKT, w->stgs->eps, w->stgs->delta);
#endif
/* Solve for RHS1, which is used later also in combined direction */
#if PROFILING > 1
tic(&tkktsolve);
#endif
w->info->nitref1 = kkt_solve(w->KKT, w->A, w->G, w->KKT->RHS1, w->KKT->dx1, w->KKT->dy1, w->KKT->dz1, w->n, w->p, w->m, w->C, 0, w->stgs->nitref);
#if PROFILING > 1
w->info->tkktsolve += toc(&tkktsolve);
#endif
/* AFFINE SEARCH DIRECTION (predictor, need dsaff and dzaff only) */
RHS_affine(w);
#if PROFILING > 1
tic(&tkktsolve);
#endif
w->info->nitref2 = kkt_solve(w->KKT, w->A, w->G, w->KKT->RHS2, w->KKT->dx2, w->KKT->dy2, w->KKT->dz2, w->n, w->p, w->m, w->C, 0, w->stgs->nitref);
#if PROFILING > 1
w->info->tkktsolve += toc(&tkktsolve);
#endif
/* dtau_denom = kap/tau - (c'*x1 + by1 + h'*z1); */
dtau_denom = w->kap/w->tau - ddot(w->n, w->c, w->KKT->dx1) - ddot(w->p, w->b, w->KKT->dy1) - ddot(w->m, w->h, w->KKT->dz1);
/* dtauaff = (dt + c'*x2 + by2 + h'*z2) / dtau_denom; */
dtauaff = (w->rt - w->kap + ddot(w->n, w->c, w->KKT->dx2) + ddot(w->p, w->b, w->KKT->dy2) + ddot(w->m, w->h, w->KKT->dz2)) / dtau_denom;
/* dzaff = dz2 + dtau_aff*dz1 */
for( i=0; i<w->m; i++ ){ w->W_times_dzaff[i] = w->KKT->dz2[i] + dtauaff*w->KKT->dz1[i]; }
scale(w->W_times_dzaff, w->C, w->W_times_dzaff);
/* W\dsaff = -W*dzaff -lambda; */
for( i=0; i<w->m; i++ ){ w->dsaff_by_W[i] = -w->W_times_dzaff[i] - w->lambda[i]; }
/* dkapaff = -(bkap + kap*dtauaff)/tau; bkap = kap*tau*/
dkapaff = -w->kap - w->kap/w->tau*dtauaff;
/* Line search on W\dsaff and W*dzaff */
w->info->step_aff = lineSearch(w->lambda, w->dsaff_by_W, w->W_times_dzaff, w->tau, dtauaff, w->kap, dkapaff, w->C, w->KKT);
/* Centering parameter */
sigma = 1.0 - w->info->step_aff;
sigma = sigma*sigma*sigma;
if( sigma > SIGMAMAX ) sigma = SIGMAMAX;
if( sigma < SIGMAMIN ) sigma = SIGMAMIN;
w->info->sigma = sigma;
/* COMBINED SEARCH DIRECTION */
RHS_combined(w);
#if PROFILING > 1
tic(&tkktsolve);
#endif
w->info->nitref3 = kkt_solve(w->KKT, w->A, w->G, w->KKT->RHS2, w->KKT->dx2, w->KKT->dy2, w->KKT->dz2, w->n, w->p, w->m, w->C, 0, w->stgs->nitref);
#if PROFILING > 1
w->info->tkktsolve += toc(&tkktsolve);
#endif
/* bkap = kap*tau + dkapaff*dtauaff - sigma*info.mu; */
bkap = w->kap*w->tau + dkapaff*dtauaff - sigma*w->info->mu;
/* dtau = ((1-sigma)*rt - bkap/tau + c'*x2 + by2 + h'*z2) / dtau_denom; */
dtau = ((1-sigma)*w->rt - bkap/w->tau + ddot(w->n, w->c, w->KKT->dx2) + ddot(w->p, w->b, w->KKT->dy2) + ddot(w->m, w->h, w->KKT->dz2)) / dtau_denom;
/* dx = x2 + dtau*x1; dy = y2 + dtau*y1; dz = z2 + dtau*z1; */
for( i=0; i < w->n; i++ ){ w->KKT->dx2[i] += dtau*w->KKT->dx1[i]; }
for( i=0; i < w->p; i++ ){ w->KKT->dy2[i] += dtau*w->KKT->dy1[i]; }
for( i=0; i < w->m; i++ ){ w->KKT->dz2[i] += dtau*w->KKT->dz1[i]; }
/* ds_by_W = -(lambda \ bs + conelp_timesW(scaling,dz,dims)); */
/* note that ath this point w->dsaff_by_W holds already (lambda \ ds) */
scale(w->KKT->dz2, w->C, w->W_times_dzaff);
for( i=0; i < w->m; i++ ){ w->dsaff_by_W[i] = -(w->dsaff_by_W[i] + w->W_times_dzaff[i]); }
/* dkap = -(bkap + kap*dtau)/tau; */
dkap = -(bkap + w->kap*dtau)/w->tau;
/* Line search on combined direction */
w->info->step = lineSearch(w->lambda, w->dsaff_by_W, w->W_times_dzaff, w->tau, dtau, w->kap, dkap, w->C, w->KKT) * w->stgs->gamma;
/* ds = W*ds_by_W */
scale(w->dsaff_by_W, w->C, w->dsaff);
/* Update variables */
for( i=0; i < w->n; i++ ){ w->x[i] += w->info->step * w->KKT->dx2[i]; }
for( i=0; i < w->p; i++ ){ w->y[i] += w->info->step * w->KKT->dy2[i]; }
for( i=0; i < w->m; i++ ){ w->z[i] += w->info->step * w->KKT->dz2[i]; }
for( i=0; i < w->m; i++ ){ w->s[i] += w->info->step * w->dsaff[i]; }
w->kap += w->info->step * dkap;
w->tau += w->info->step * dtau;
}
/* scale variables back */
backscale(w);
/* stop timer */
#if PROFILING > 0
w->info->tsolve = toc(&tsolve);
#endif
#if PRINTLEVEL > 0
#if PROFILING > 0
if( w->stgs->verbose ) PRINTTEXT("\nRuntime: %f seconds.", w->info->tsetup + w->info->tsolve);
#endif
if( w->stgs->verbose ) PRINTTEXT("\n\n");
#endif
return exitcode;
}
/*
* Main solver routine.
*/
idxint ECOS_solve(pwork* w)
{
idxint i, initcode, KKT_FACTOR_RETURN_CODE;
pfloat dtau_denom, dtauaff, dkapaff, sigma, dtau, dkap, bkap, pres_prev;
idxint exitcode = ECOS_FATAL, interrupted;
#if DEBUG
char fn[20];
#endif
#if (defined _WIN32 || defined _WIN64 )
/* sets width of exponent for floating point numbers to 2 instead of 3 */
unsigned int old_output_format = _set_output_format(_TWO_DIGIT_EXPONENT);
#endif
#if PROFILING > 0
timer tsolve;
#endif
#if PROFILING > 1
timer tfactor, tkktsolve;
#endif
#if PROFILING > 0
/* start timer */
tic(&tsolve);
#endif
/* initialize ctrl-c support */
init_ctrlc();
/* Initialize solver */
initcode = init(w);
if( initcode == ECOS_FATAL ){
#if PRINTLEVEL > 0
if( w->stgs->verbose ) PRINTTEXT("\nFatal error during initialization, aborting.");
#endif
return ECOS_FATAL;
}
/* MAIN INTERIOR POINT LOOP ---------------------------------------------------------------------- */
for( w->info->iter = 0; w->info->iter <= w->stgs->maxit ; w->info->iter++ ){
/* Compute residuals */
computeResiduals(w);
/* Update statistics */
updateStatistics(w);
#if PRINTLEVEL > 1
/* Print info */
if( w->stgs->verbose ) printProgress(w->info);
#endif
/* SAFEGUARD: Backtrack to best previously seen iterate if
*
* - the update was bad such that the primal residual PRES has increased by a factor of SAFEGUARD, or
* - the gap became negative
*
* If the safeguard is activated, the solver tests if reduced precision has been reached, and reports
* accordingly. If not even reduced precision is reached, ECOS returns the flag ECOS_NUMERICS.
*/
if( w->info->iter > 0 && (w->info->pres > SAFEGUARD*pres_prev || w->info->gap < 0) ){
#if PRINTLEVEL > 1
if( w->stgs->verbose ) deleteLastProgressLine( w->info );
if( w->stgs->verbose ) PRINTTEXT("Unreliable search direction detected, recovering best iterate (%d) and stopping.\n", (int)w->best_info->iter);
#endif
restoreBestIterate( w );
/* Determine whether we have reached at least reduced accuracy */
exitcode = checkExitConditions( w, ECOS_INACC_OFFSET );
/* if not, exit anyways */
if( exitcode == ECOS_NOT_CONVERGED_YET ){
exitcode = ECOS_NUMERICS;
#if PRINTLEVEL > 0
if( w->stgs->verbose ) PRINTTEXT("\nNUMERICAL PROBLEMS (reached feastol=%3.1e, reltol=%3.1e, abstol=%3.1e).", MAX(w->info->dres, w->info->pres), w->info->relgap, w->info->gap);
#endif
break;
} else {
break;
}
}
pres_prev = w->info->pres;
/* Check termination criteria to full precision and exit if necessary */
exitcode = checkExitConditions( w, 0 );
interrupted = check_ctrlc();
if( exitcode == ECOS_NOT_CONVERGED_YET ){
/*
* Full precision has not been reached yet. Check for two more cases of exit:
* (i) min step size, in which case we assume we won't make progress any more, and
* (ii) maximum number of iterations reached
* If these two are not fulfilled, another iteration will be made.
*/
/* Did the line search c**k up? (zero step length) */
if( w->info->iter > 0 && w->info->step == STEPMIN*GAMMA ){
#if PRINTLEVEL > 0
if( w->stgs->verbose ) deleteLastProgressLine( w->info );
if( w->stgs->verbose ) PRINTTEXT("No further progress possible, recovering best iterate (%d) and stopping.", (int)w->best_info->iter );
#endif
restoreBestIterate( w );
/* Determine whether we have reached reduced precision */
exitcode = checkExitConditions( w, ECOS_INACC_OFFSET );
if( exitcode == ECOS_NOT_CONVERGED_YET ){
exitcode = ECOS_NUMERICS;
#if PRINTLEVEL > 0
if( w->stgs->verbose ) PRINTTEXT("\nNUMERICAL PROBLEMS (reached feastol=%3.1e, reltol=%3.1e, abstol=%3.1e).", MAX(w->info->dres, w->info->pres), w->info->relgap, w->info->gap);
#endif
}
break;
}
/* MAXIT reached? */
else if( interrupted || w->info->iter == w->stgs->maxit ){
#if PRINTLEVEL > 0
const char *what = interrupted ? "SIGINT intercepted" : "Maximum number of iterations reached";
#endif
/* Determine whether current iterate is better than what we had so far */
if( compareStatistics( w->info, w->best_info) ){
#if PRINTLEVEL > 0
if( w->stgs->verbose )
PRINTTEXT("%s, stopping.\n",what);
#endif
} else
{
#if PRINTLEVEL > 0
if( w->stgs->verbose )
PRINTTEXT("%s, recovering best iterate (%d) and stopping.\n", what, (int)w->best_info->iter);
#endif
restoreBestIterate( w );
}
/* Determine whether we have reached reduced precision */
exitcode = checkExitConditions( w, ECOS_INACC_OFFSET );
if( exitcode == ECOS_NOT_CONVERGED_YET ){
exitcode = interrupted ? ECOS_SIGINT : ECOS_MAXIT;
#if PRINTLEVEL > 0
if( w->stgs->verbose ) {
const char* what = interrupted ? "INTERRUPTED" : "RAN OUT OF ITERATIONS";
PRINTTEXT("\n%s (reached feastol=%3.1e, reltol=%3.1e, abstol=%3.1e).", what, MAX(w->info->dres, w->info->pres), w->info->relgap, w->info->gap);
}
#endif
}
break;
}
} else {
/* Full precision has been reached, stop solver */
break;
}
/* SAFEGUARD:
* Check whether current iterate is worth keeping as the best solution so far,
* before doing another iteration
*/
if (w->info->iter == 0) {
/* we're at the first iterate, so there's nothing to compare yet */
saveIterateAsBest( w );
} else if( compareStatistics( w->info, w->best_info) ){
/* PRINTTEXT("Better solution found, saving as best so far \n"); */
saveIterateAsBest( w );
}
/* Compute scalings */
if( updateScalings(w->C, w->s, w->z, w->lambda) == OUTSIDE_CONE ){
/* SAFEGUARD: we have to recover here */
#if PRINTLEVEL > 0
if( w->stgs->verbose ) deleteLastProgressLine( w->info );
if( w->stgs->verbose ) PRINTTEXT("Slacks/multipliers leaving the cone, recovering best iterate (%d) and stopping.\n", (int)w->best_info->iter);
#endif
restoreBestIterate( w );
/* Determine whether we have reached at least reduced accuracy */
exitcode = checkExitConditions( w, ECOS_INACC_OFFSET );
if( exitcode == ECOS_NOT_CONVERGED_YET ){
#if PRINTLEVEL > 0
if( w->stgs->verbose ) PRINTTEXT("\nNUMERICAL PROBLEMS (reached feastol=%3.1e, reltol=%3.1e, abstol=%3.1e).", MAX(w->info->dres, w->info->pres), w->info->relgap, w->info->gap);
#endif
return ECOS_OUTCONE;
} else {
break;
}
}
/* Update KKT matrix with scalings */
kkt_update(w->KKT->PKPt, w->KKT->PK, w->C);
#if DEBUG > 0
/* DEBUG: Store matrix to be factored */
sprintf(fn, "PKPt_updated_%02i.txt", (int)w->info->iter);
dumpSparseMatrix(w->KKT->PKPt, fn);
#endif
/* factor KKT matrix */
#if PROFILING > 1
tic(&tfactor);
KKT_FACTOR_RETURN_CODE = kkt_factor(w->KKT, w->stgs->eps, w->stgs->delta, &w->info->tfactor_t1, &w->info->tfactor_t2);
w->info->tfactor += toc(&tfactor);
#else
KKT_FACTOR_RETURN_CODE = kkt_factor(w->KKT, w->stgs->eps, w->stgs->delta);
#endif
#if DEBUG > 0
/* DEBUG: store factor */
sprintf(fn, "PKPt_factor_%02i.txt", (int)w->info->iter);
dumpSparseMatrix(w->KKT->L, fn);
#endif
/* Solve for RHS1, which is used later also in combined direction */
#if PROFILING > 1
tic(&tkktsolve);
#endif
w->info->nitref1 = kkt_solve(w->KKT, w->A, w->G, w->KKT->RHS1, w->KKT->dx1, w->KKT->dy1, w->KKT->dz1, w->n, w->p, w->m, w->C, 0, w->stgs->nitref);
#if PROFILING > 1
w->info->tkktsolve += toc(&tkktsolve);
#endif
#if DEBUG > 0 && PRINTLEVEL > 2
/* Print result of linear system solve */
printDenseMatrix(w->KKT->dx1, 1, 5, "dx1(1:5)");
printDenseMatrix(w->KKT->dy1, 1, 5, "dy1(1:5)");
printDenseMatrix(w->KKT->dz1, 1, 5, "dz1(1:5)");
#endif
/* AFFINE SEARCH DIRECTION (predictor, need dsaff and dzaff only) */
RHS_affine(w);
#if PROFILING > 1
tic(&tkktsolve);
#endif
w->info->nitref2 = kkt_solve(w->KKT, w->A, w->G, w->KKT->RHS2, w->KKT->dx2, w->KKT->dy2, w->KKT->dz2, w->n, w->p, w->m, w->C, 0, w->stgs->nitref);
#if PROFILING > 1
w->info->tkktsolve += toc(&tkktsolve);
#endif
/* dtau_denom = kap/tau - (c'*x1 + by1 + h'*z1); */
dtau_denom = w->kap/w->tau - eddot(w->n, w->c, w->KKT->dx1) - eddot(w->p, w->b, w->KKT->dy1) - eddot(w->m, w->h, w->KKT->dz1);
/* dtauaff = (dt + c'*x2 + by2 + h'*z2) / dtau_denom; */
dtauaff = (w->rt - w->kap + eddot(w->n, w->c, w->KKT->dx2) + eddot(w->p, w->b, w->KKT->dy2) + eddot(w->m, w->h, w->KKT->dz2)) / dtau_denom;
/* dzaff = dz2 + dtau_aff*dz1 */
for( i=0; i<w->m; i++ ){ w->W_times_dzaff[i] = w->KKT->dz2[i] + dtauaff*w->KKT->dz1[i]; }
scale(w->W_times_dzaff, w->C, w->W_times_dzaff);
/* W\dsaff = -W*dzaff -lambda; */
for( i=0; i<w->m; i++ ){ w->dsaff_by_W[i] = -w->W_times_dzaff[i] - w->lambda[i]; }
/* dkapaff = -(bkap + kap*dtauaff)/tau; bkap = kap*tau*/
dkapaff = -w->kap - w->kap/w->tau*dtauaff;
/* Line search on W\dsaff and W*dzaff */
w->info->step_aff = lineSearch(w->lambda, w->dsaff_by_W, w->W_times_dzaff, w->tau, dtauaff, w->kap, dkapaff, w->C, w->KKT);
/* Centering parameter */
sigma = 1.0 - w->info->step_aff;
sigma = sigma*sigma*sigma;
if( sigma > SIGMAMAX ) sigma = SIGMAMAX;
if( sigma < SIGMAMIN ) sigma = SIGMAMIN;
w->info->sigma = sigma;
/* COMBINED SEARCH DIRECTION */
RHS_combined(w);
#if PROFILING > 1
tic(&tkktsolve);
#endif
w->info->nitref3 = kkt_solve(w->KKT, w->A, w->G, w->KKT->RHS2, w->KKT->dx2, w->KKT->dy2, w->KKT->dz2, w->n, w->p, w->m, w->C, 0, w->stgs->nitref);
#if PROFILING > 1
w->info->tkktsolve += toc(&tkktsolve);
#endif
/* bkap = kap*tau + dkapaff*dtauaff - sigma*info.mu; */
bkap = w->kap*w->tau + dkapaff*dtauaff - sigma*w->info->mu;
/* dtau = ((1-sigma)*rt - bkap/tau + c'*x2 + by2 + h'*z2) / dtau_denom; */
dtau = ((1-sigma)*w->rt - bkap/w->tau + eddot(w->n, w->c, w->KKT->dx2) + eddot(w->p, w->b, w->KKT->dy2) + eddot(w->m, w->h, w->KKT->dz2)) / dtau_denom;
/* dx = x2 + dtau*x1; dy = y2 + dtau*y1; dz = z2 + dtau*z1; */
for( i=0; i < w->n; i++ ){ w->KKT->dx2[i] += dtau*w->KKT->dx1[i]; }
for( i=0; i < w->p; i++ ){ w->KKT->dy2[i] += dtau*w->KKT->dy1[i]; }
for( i=0; i < w->m; i++ ){ w->KKT->dz2[i] += dtau*w->KKT->dz1[i]; }
/* ds_by_W = -(lambda \ bs + conelp_timesW(scaling,dz,dims)); */
/* note that ath this point w->dsaff_by_W holds already (lambda \ ds) */
scale(w->KKT->dz2, w->C, w->W_times_dzaff);
for( i=0; i < w->m; i++ ){ w->dsaff_by_W[i] = -(w->dsaff_by_W[i] + w->W_times_dzaff[i]); }
/* dkap = -(bkap + kap*dtau)/tau; */
dkap = -(bkap + w->kap*dtau)/w->tau;
/* Line search on combined direction */
w->info->step = lineSearch(w->lambda, w->dsaff_by_W, w->W_times_dzaff, w->tau, dtau, w->kap, dkap, w->C, w->KKT) * w->stgs->gamma;
/* ds = W*ds_by_W */
scale(w->dsaff_by_W, w->C, w->dsaff);
/* Update variables */
for( i=0; i < w->n; i++ ){ w->x[i] += w->info->step * w->KKT->dx2[i]; }
for( i=0; i < w->p; i++ ){ w->y[i] += w->info->step * w->KKT->dy2[i]; }
for( i=0; i < w->m; i++ ){ w->z[i] += w->info->step * w->KKT->dz2[i]; }
for( i=0; i < w->m; i++ ){ w->s[i] += w->info->step * w->dsaff[i]; }
w->kap += w->info->step * dkap;
w->tau += w->info->step * dtau;
}
/* scale variables back */
backscale(w);
/* stop timer */
#if PROFILING > 0
w->info->tsolve = toc(&tsolve);
#endif
#if PRINTLEVEL > 0
#if PROFILING > 0
if( w->stgs->verbose ) PRINTTEXT("\nRuntime: %f seconds.", w->info->tsetup + w->info->tsolve);
#endif
if( w->stgs->verbose ) PRINTTEXT("\n\n");
#endif
remove_ctrlc();
return exitcode;
}