static PetscErrorCode TaoSolve_SSILS(Tao tao)
{
TAO_SSLS *ssls = (TAO_SSLS *)tao->data;
PetscReal psi, ndpsi, normd, innerd, t=0;
PetscReal delta, rho;
PetscInt iter=0,kspits;
TaoConvergedReason reason;
TaoLineSearchConvergedReason ls_reason;
PetscErrorCode ierr;
PetscFunctionBegin;
/* Assume that Setup has been called!
Set the structure for the Jacobian and create a linear solver. */
delta = ssls->delta;
rho = ssls->rho;
ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
ierr = VecMedian(tao->XL,tao->solution,tao->XU,tao->solution);CHKERRQ(ierr);
ierr = TaoLineSearchSetObjectiveAndGradientRoutine(tao->linesearch,Tao_SSLS_FunctionGradient,tao);CHKERRQ(ierr);
ierr = TaoLineSearchSetObjectiveRoutine(tao->linesearch,Tao_SSLS_Function,tao);CHKERRQ(ierr);
/* Calculate the function value and fischer function value at the
current iterate */
ierr = TaoLineSearchComputeObjectiveAndGradient(tao->linesearch,tao->solution,&psi,ssls->dpsi);CHKERRQ(ierr);
ierr = VecNorm(ssls->dpsi,NORM_2,&ndpsi);CHKERRQ(ierr);
while (1) {
ierr=PetscInfo3(tao, "iter: %D, merit: %g, ndpsi: %g\n",iter, (double)ssls->merit, (double)ndpsi);CHKERRQ(ierr);
/* Check the termination criteria */
ierr = TaoMonitor(tao,iter++,ssls->merit,ndpsi,0.0,t,&reason);CHKERRQ(ierr);
if (reason!=TAO_CONTINUE_ITERATING) break;
/* Calculate direction. (Really negative of newton direction. Therefore,
rest of the code uses -d.) */
ierr = KSPSetOperators(tao->ksp,tao->jacobian,tao->jacobian_pre);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp,ssls->ff,tao->stepdirection);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(tao->ksp,&kspits);CHKERRQ(ierr);
tao->ksp_its+=kspits;
ierr = VecNorm(tao->stepdirection,NORM_2,&normd);CHKERRQ(ierr);
ierr = VecDot(tao->stepdirection,ssls->dpsi,&innerd);CHKERRQ(ierr);
/* Make sure that we have a descent direction */
if (innerd <= delta*pow(normd, rho)) {
ierr = PetscInfo(tao, "newton direction not descent\n");CHKERRQ(ierr);
ierr = VecCopy(ssls->dpsi,tao->stepdirection);CHKERRQ(ierr);
ierr = VecDot(tao->stepdirection,ssls->dpsi,&innerd);CHKERRQ(ierr);
}
ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
innerd = -innerd;
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);
ierr = TaoLineSearchApply(tao->linesearch,tao->solution,&psi,ssls->dpsi,tao->stepdirection,&t,&ls_reason);CHKERRQ(ierr);
ierr = VecNorm(ssls->dpsi,NORM_2,&ndpsi);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
static PetscErrorCode TronGradientProjections(Tao tao,TAO_TRON *tron)
{
PetscErrorCode ierr;
PetscInt i;
TaoLineSearchConvergedReason ls_reason;
PetscReal actred=-1.0,actred_max=0.0;
PetscReal f_new;
/*
The gradient and function value passed into and out of this
routine should be current and correct.
The free, active, and binding variables should be already identified
*/
PetscFunctionBegin;
if (tron->Free_Local) {
ierr = ISDestroy(&tron->Free_Local);CHKERRQ(ierr);
}
ierr = VecWhichBetween(tao->XL,tao->solution,tao->XU,&tron->Free_Local);CHKERRQ(ierr);
for (i=0;i<tron->maxgpits;i++){
if ( -actred <= (tron->pg_ftol)*actred_max) break;
tron->gp_iterates++; tron->total_gp_its++;
f_new=tron->f;
ierr = VecCopy(tao->gradient, tao->stepdirection);CHKERRQ(ierr);
ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,tron->pgstepsize);CHKERRQ(ierr);
ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f_new, tao->gradient, tao->stepdirection,
&tron->pgstepsize, &ls_reason);CHKERRQ(ierr);
ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
/* Update the iterate */
actred = f_new - tron->f;
actred_max = PetscMax(actred_max,-(f_new - tron->f));
tron->f = f_new;
if (tron->Free_Local) {
ierr = ISDestroy(&tron->Free_Local);CHKERRQ(ierr);
}
ierr = VecWhichBetween(tao->XL,tao->solution,tao->XU,&tron->Free_Local);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
static PetscErrorCode GPCGGradProjections(Tao tao)
{
PetscErrorCode ierr;
TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;
PetscInt i;
PetscReal actred=-1.0,actred_max=0.0, gAg,gtg=gpcg->gnorm,alpha;
PetscReal f_new,gdx,stepsize;
Vec DX=tao->stepdirection,XL=tao->XL,XU=tao->XU,Work=gpcg->Work;
Vec X=tao->solution,G=tao->gradient;
TaoLineSearchConvergedReason lsflag=TAOLINESEARCH_CONTINUE_ITERATING;
/*
The free, active, and binding variables should be already identified
*/
PetscFunctionBegin;
for (i=0;i<gpcg->maxgpits;i++){
if ( -actred <= (gpcg->pg_ftol)*actred_max) break;
ierr = VecBoundGradientProjection(G,X,XL,XU,DX);CHKERRQ(ierr);
ierr = VecScale(DX,-1.0);CHKERRQ(ierr);
ierr = VecDot(DX,G,&gdx);CHKERRQ(ierr);
ierr = MatMult(tao->hessian,DX,Work);CHKERRQ(ierr);
ierr = VecDot(DX,Work,&gAg);CHKERRQ(ierr);
gpcg->gp_iterates++;
gpcg->total_gp_its++;
gtg=-gdx;
alpha = PetscAbsReal(gtg/gAg);
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,alpha);CHKERRQ(ierr);
f_new=gpcg->f;
ierr = TaoLineSearchApply(tao->linesearch,X,&f_new,G,DX,&stepsize,&lsflag);CHKERRQ(ierr);
/* Update the iterate */
actred = f_new - gpcg->f;
actred_max = PetscMax(actred_max,-(f_new - gpcg->f));
gpcg->f = f_new;
ierr = ISDestroy(&gpcg->Free_Local);CHKERRQ(ierr);
ierr = VecWhichBetween(XL,X,XU,&gpcg->Free_Local);CHKERRQ(ierr);
}
gpcg->gnorm=gtg;
PetscFunctionReturn(0);
} /* End gradient projections */
static PetscErrorCode TaoSolve_TRON(Tao tao)
{
TAO_TRON *tron = (TAO_TRON *)tao->data;
PetscErrorCode ierr;
PetscInt its;
TaoConvergedReason reason = TAO_CONTINUE_ITERATING;
TaoLineSearchConvergedReason ls_reason = TAOLINESEARCH_CONTINUE_ITERATING;
PetscReal prered,actred,delta,f,f_new,rhok,gdx,xdiff,stepsize;
PetscFunctionBegin;
tron->pgstepsize=1.0;
tao->trust = tao->trust0;
/* Project the current point onto the feasible set */
ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
ierr = VecMedian(tao->XL,tao->solution,tao->XU,tao->solution);CHKERRQ(ierr);
ierr = TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);CHKERRQ(ierr);
ierr = TaoComputeObjectiveAndGradient(tao,tao->solution,&tron->f,tao->gradient);CHKERRQ(ierr);
ierr = ISDestroy(&tron->Free_Local);CHKERRQ(ierr);
ierr = VecWhichBetween(tao->XL,tao->solution,tao->XU,&tron->Free_Local);CHKERRQ(ierr);
/* Project the gradient and calculate the norm */
ierr = VecBoundGradientProjection(tao->gradient,tao->solution, tao->XL, tao->XU, tao->gradient);CHKERRQ(ierr);
ierr = VecNorm(tao->gradient,NORM_2,&tron->gnorm);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(tron->f) || PetscIsInfOrNanReal(tron->gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf pr NaN");
if (tao->trust <= 0) {
tao->trust=PetscMax(tron->gnorm*tron->gnorm,1.0);
}
tron->stepsize=tao->trust;
ierr = TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, tron->stepsize, &reason);CHKERRQ(ierr);
while (reason==TAO_CONTINUE_ITERATING){
tao->ksp_its=0;
ierr = TronGradientProjections(tao,tron);CHKERRQ(ierr);
f=tron->f; delta=tao->trust;
tron->n_free_last = tron->n_free;
ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
ierr = ISGetSize(tron->Free_Local, &tron->n_free);CHKERRQ(ierr);
/* If no free variables */
if (tron->n_free == 0) {
actred=0;
ierr = PetscInfo(tao,"No free variables in tron iteration.\n");CHKERRQ(ierr);
ierr = VecNorm(tao->gradient,NORM_2,&tron->gnorm);CHKERRQ(ierr);
ierr = TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, delta, &reason);CHKERRQ(ierr);
if (!reason) {
reason = TAO_CONVERGED_STEPTOL;
ierr = TaoSetConvergedReason(tao,reason);CHKERRQ(ierr);
}
break;
}
/* use free_local to mask/submat gradient, hessian, stepdirection */
ierr = TaoVecGetSubVec(tao->gradient,tron->Free_Local,tao->subset_type,0.0,&tron->R);CHKERRQ(ierr);
ierr = TaoVecGetSubVec(tao->gradient,tron->Free_Local,tao->subset_type,0.0,&tron->DXFree);CHKERRQ(ierr);
ierr = VecSet(tron->DXFree,0.0);CHKERRQ(ierr);
ierr = VecScale(tron->R, -1.0);CHKERRQ(ierr);
ierr = TaoMatGetSubMat(tao->hessian, tron->Free_Local, tron->diag, tao->subset_type, &tron->H_sub);CHKERRQ(ierr);
if (tao->hessian == tao->hessian_pre) {
ierr = MatDestroy(&tron->Hpre_sub);CHKERRQ(ierr);
ierr = PetscObjectReference((PetscObject)(tron->H_sub));CHKERRQ(ierr);
tron->Hpre_sub = tron->H_sub;
} else {
ierr = TaoMatGetSubMat(tao->hessian_pre, tron->Free_Local, tron->diag, tao->subset_type,&tron->Hpre_sub);CHKERRQ(ierr);
}
ierr = KSPReset(tao->ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(tao->ksp, tron->H_sub, tron->Hpre_sub);CHKERRQ(ierr);
while (1) {
/* Approximately solve the reduced linear system */
ierr = KSPSTCGSetRadius(tao->ksp,delta);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp, tron->R, tron->DXFree);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
tao->ksp_its+=its;
tao->ksp_tot_its+=its;
ierr = VecSet(tao->stepdirection,0.0);CHKERRQ(ierr);
/* Add dxfree matrix to compute step direction vector */
ierr = VecISAXPY(tao->stepdirection,tron->Free_Local,1.0,tron->DXFree);CHKERRQ(ierr);
if (0) {
PetscReal rhs,stepnorm;
ierr = VecNorm(tron->R,NORM_2,&rhs);CHKERRQ(ierr);
ierr = VecNorm(tron->DXFree,NORM_2,&stepnorm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"|rhs|=%g\t|s|=%g\n",(double)rhs,(double)stepnorm);CHKERRQ(ierr);
}
ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr);
ierr = PetscInfo1(tao,"Expected decrease in function value: %14.12e\n",(double)gdx);CHKERRQ(ierr);
ierr = VecCopy(tao->solution, tron->X_New);CHKERRQ(ierr);
ierr = VecCopy(tao->gradient, tron->G_New);CHKERRQ(ierr);
stepsize=1.0;f_new=f;
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);CHKERRQ(ierr);
ierr = TaoLineSearchApply(tao->linesearch, tron->X_New, &f_new, tron->G_New, tao->stepdirection,&stepsize,&ls_reason);CHKERRQ(ierr);CHKERRQ(ierr);
ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
ierr = MatMult(tao->hessian, tao->stepdirection, tron->Work);CHKERRQ(ierr);
ierr = VecAYPX(tron->Work, 0.5, tao->gradient);CHKERRQ(ierr);
ierr = VecDot(tao->stepdirection, tron->Work, &prered);CHKERRQ(ierr);
actred = f_new - f;
if (actred<0) {
rhok=PetscAbs(-actred/prered);
} else {
rhok=0.0;
}
/* Compare actual improvement to the quadratic model */
if (rhok > tron->eta1) { /* Accept the point */
/* d = x_new - x */
ierr = VecCopy(tron->X_New, tao->stepdirection);CHKERRQ(ierr);
ierr = VecAXPY(tao->stepdirection, -1.0, tao->solution);CHKERRQ(ierr);
ierr = VecNorm(tao->stepdirection, NORM_2, &xdiff);CHKERRQ(ierr);
xdiff *= stepsize;
/* Adjust trust region size */
if (rhok < tron->eta2 ){
delta = PetscMin(xdiff,delta)*tron->sigma1;
} else if (rhok > tron->eta4 ){
delta= PetscMin(xdiff,delta)*tron->sigma3;
} else if (rhok > tron->eta3 ){
delta=PetscMin(xdiff,delta)*tron->sigma2;
}
ierr = VecBoundGradientProjection(tron->G_New,tron->X_New, tao->XL, tao->XU, tao->gradient);CHKERRQ(ierr);
if (tron->Free_Local) {
ierr = ISDestroy(&tron->Free_Local);CHKERRQ(ierr);
}
ierr = VecWhichBetween(tao->XL, tron->X_New, tao->XU, &tron->Free_Local);CHKERRQ(ierr);
f=f_new;
ierr = VecNorm(tao->gradient,NORM_2,&tron->gnorm);CHKERRQ(ierr);
ierr = VecCopy(tron->X_New, tao->solution);CHKERRQ(ierr);
ierr = VecCopy(tron->G_New, tao->gradient);CHKERRQ(ierr);
break;
}
else if (delta <= 1e-30) {
break;
}
else {
delta /= 4.0;
}
} /* end linear solve loop */
tron->f=f; tron->actred=actred; tao->trust=delta;
tao->niter++;
ierr = TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, delta, &reason);CHKERRQ(ierr);
} /* END MAIN LOOP */
PetscFunctionReturn(0);
}
static PetscErrorCode TaoSolve_SQPCON(Tao tao)
{
TAO_SQPCON *sqpconP = (TAO_SQPCON*)tao->data;
PetscInt iter=0;
TaoConvergedReason reason = TAO_CONTINUE_ITERATING;
TaoLineSearchConvergedReason ls_reason = TAOLINESEARCH_CONTINUE_ITERATING;
PetscReal step=1.0,f,fm, fold;
PetscReal cnorm, mnorm;
PetscBool use_update=PETSC_TRUE; /* don't update Q if line search failed */
PetscErrorCode ierr;
PetscFunctionBegin;
/* Scatter to U,V */
ierr = VecScatterBegin(sqpconP->state_scatter, tao->solution, sqpconP->U, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(sqpconP->state_scatter, tao->solution, sqpconP->U, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterBegin(sqpconP->design_scatter, tao->solution, sqpconP->V, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(sqpconP->design_scatter, tao->solution, sqpconP->V, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
/* Evaluate Function, Gradient, Constraints, and Jacobian */
ierr = TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);CHKERRQ(ierr);
ierr = TaoComputeConstraints(tao,tao->solution, tao->constraints);CHKERRQ(ierr);
ierr = TaoComputeJacobianState(tao,tao->solution, &tao->jacobian_state, &tao->jacobian_state_pre, &tao->jacobian_state_inv, &sqpconP->statematflag);CHKERRQ(ierr);
ierr = TaoComputeJacobianDesign(tao,tao->solution, &tao->jacobian_design, &tao->jacobian_design_pre, &sqpconP->statematflag);CHKERRQ(ierr);
/* Scatter gradient to GU,GV */
ierr = VecScatterBegin(sqpconP->state_scatter, tao->gradient, sqpconP->GU, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(sqpconP->state_scatter, tao->gradient, sqpconP->GU, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterBegin(sqpconP->design_scatter, tao->gradient, sqpconP->GV, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(sqpconP->design_scatter, tao->gradient, sqpconP->GV, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecNorm(tao->gradient, NORM_2, &mnorm);CHKERRQ(ierr);
/* Evaluate constraint norm */
ierr = VecNorm(tao->constraints, NORM_2, &cnorm);CHKERRQ(ierr);
/* Monitor convergence */
ierr = TaoMonitor(tao, iter,f,mnorm,cnorm,step,&reason);CHKERRQ(ierr);
while (reason == TAO_CONTINUE_ITERATING) {
/* Solve tbar = -A\t (t is constraints vector) */
ierr = MatMult(tao->jacobian_state_inv, tao->constraints, sqpconP->Tbar);CHKERRQ(ierr);
ierr = VecScale(sqpconP->Tbar, -1.0);CHKERRQ(ierr);
/* aqwac = A'\(Q*Tbar + c) */
if (iter > 0) {
ierr = MatMult(sqpconP->Q,sqpconP->Tbar,sqpconP->WV);CHKERRQ(ierr);
} else {
ierr = VecCopy(sqpconP->Tbar, sqpconP->WV);CHKERRQ(ierr);
}
ierr = VecAXPY(sqpconP->WV,1.0,sqpconP->GU);CHKERRQ(ierr);
ierr = MatMultTranspose(tao->jacobian_state_inv, sqpconP->WV, sqpconP->aqwac);CHKERRQ(ierr);
/* Reduced Gradient dbar = d - B^t * aqwac */
ierr = MatMultTranspose(tao->jacobian_design,sqpconP->aqwac, sqpconP->dbar);CHKERRQ(ierr);
ierr = VecScale(sqpconP->dbar, -1.0);CHKERRQ(ierr);
ierr = VecAXPY(sqpconP->dbar,1.0,sqpconP->GV);CHKERRQ(ierr);
/* update reduced hessian */
ierr = MatLMVMUpdate(sqpconP->R, sqpconP->V, sqpconP->dbar);CHKERRQ(ierr);
/* Solve R*dv = -dbar using approx. hessian */
ierr = MatLMVMSolve(sqpconP->R, sqpconP->dbar, sqpconP->DV);CHKERRQ(ierr);
ierr = VecScale(sqpconP->DV, -1.0);CHKERRQ(ierr);
/* Backsolve for u = A\(g - B*dv) = tbar - A\(B*dv)*/
ierr = MatMult(tao->jacobian_design, sqpconP->DV, sqpconP->WL);CHKERRQ(ierr);
ierr = MatMult(tao->jacobian_state_inv, sqpconP->WL, sqpconP->DU);CHKERRQ(ierr);
ierr = VecScale(sqpconP->DU, -1.0);CHKERRQ(ierr);
ierr = VecAXPY(sqpconP->DU, 1.0, sqpconP->Tbar);CHKERRQ(ierr);
/* Assemble Big D */
ierr = VecScatterBegin(sqpconP->state_scatter, sqpconP->DU, tao->stepdirection, INSERT_VALUES, SCATTER_REVERSE);CHKERRQ(ierr);
ierr = VecScatterEnd(sqpconP->state_scatter, sqpconP->DU, tao->stepdirection, INSERT_VALUES, SCATTER_REVERSE);CHKERRQ(ierr);
ierr = VecScatterBegin(sqpconP->design_scatter, sqpconP->DV, tao->stepdirection, INSERT_VALUES, SCATTER_REVERSE);CHKERRQ(ierr);
ierr = VecScatterEnd(sqpconP->design_scatter, sqpconP->DV, tao->stepdirection, INSERT_VALUES, SCATTER_REVERSE);CHKERRQ(ierr);
/* Perform Line Search */
ierr = VecCopy(tao->solution, sqpconP->Xold);CHKERRQ(ierr);
ierr = VecCopy(tao->gradient, sqpconP->Gold);CHKERRQ(ierr);
fold = f;
ierr = TaoLineSearchComputeObjectiveAndGradient(tao->linesearch,tao->solution,&fm,sqpconP->GL);CHKERRQ(ierr);
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);
ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &fm, sqpconP->GL, tao->stepdirection,&step, &ls_reason);CHKERRQ(ierr);
ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
if (ls_reason < 0) {
ierr = VecCopy(sqpconP->Xold, tao->solution);
ierr = VecCopy(sqpconP->Gold, tao->gradient);
f = fold;
ierr = VecAXPY(tao->solution, 1.0, tao->stepdirection);CHKERRQ(ierr);
ierr = PetscInfo(tao,"Line Search Failed, using full step.");CHKERRQ(ierr);
use_update=PETSC_FALSE;
} else {
use_update = PETSC_TRUE;
}
/* Scatter X to U,V */
ierr = VecScatterBegin(sqpconP->state_scatter, tao->solution, sqpconP->U, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(sqpconP->state_scatter, tao->solution, sqpconP->U, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterBegin(sqpconP->design_scatter, tao->solution, sqpconP->V, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(sqpconP->design_scatter, tao->solution, sqpconP->V, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
/* Evaluate Function, Gradient, Constraints, and Jacobian */
ierr = TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);CHKERRQ(ierr);
ierr = TaoComputeConstraints(tao,tao->solution, tao->constraints);CHKERRQ(ierr);
ierr = TaoComputeJacobianState(tao,tao->solution, &tao->jacobian_state, &tao->jacobian_state_pre, &tao->jacobian_state_inv, &sqpconP->statematflag);CHKERRQ(ierr);
ierr = TaoComputeJacobianDesign(tao,tao->solution, &tao->jacobian_design, &tao->jacobian_design_pre, &sqpconP->designmatflag);CHKERRQ(ierr);
/* Scatter gradient to GU,GV */
ierr = VecScatterBegin(sqpconP->state_scatter, tao->gradient, sqpconP->GU, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(sqpconP->state_scatter, tao->gradient, sqpconP->GU, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterBegin(sqpconP->design_scatter, tao->gradient, sqpconP->GV, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(sqpconP->design_scatter, tao->gradient, sqpconP->GV, INSERT_VALUES, SCATTER_FORWARD);CHKERRQ(ierr);
/* Update approx to hessian of the Lagrangian wrt state (Q)
with u_k+1, gu_k+1 */
if (use_update) {
ierr = MatApproxUpdate(sqpconP->Q,sqpconP->U,sqpconP->GU);CHKERRQ(ierr);
}
ierr = VecNorm(sqpconP->GL, NORM_2, &mnorm);CHKERRQ(ierr);
/* Evaluate constraint norm */
ierr = VecNorm(tao->constraints, NORM_2, &cnorm);CHKERRQ(ierr);
/* Monitor convergence */
iter++;
ierr = TaoMonitor(tao, iter,f,mnorm,cnorm,step,&reason);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
static PetscErrorCode TaoSolve_GPCG(Tao tao)
{
TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;
PetscErrorCode ierr;
PetscInt its;
PetscReal actred,f,f_new,gnorm,gdx,stepsize,xtb;
PetscReal xtHx;
TaoConvergedReason reason = TAO_CONTINUE_ITERATING;
TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;
PetscFunctionBegin;
ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
ierr = VecMedian(tao->XL,tao->solution,tao->XU,tao->solution);CHKERRQ(ierr);
ierr = TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);CHKERRQ(ierr);
/* Using f = .5*x'Hx + x'b + c and g=Hx + b, compute b,c */
ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
ierr = TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);CHKERRQ(ierr);
ierr = VecCopy(tao->gradient, gpcg->B);CHKERRQ(ierr);
ierr = MatMult(tao->hessian,tao->solution,gpcg->Work);CHKERRQ(ierr);
ierr = VecDot(gpcg->Work, tao->solution, &xtHx);CHKERRQ(ierr);
ierr = VecAXPY(gpcg->B,-1.0,gpcg->Work);CHKERRQ(ierr);
ierr = VecDot(gpcg->B,tao->solution,&xtb);CHKERRQ(ierr);
gpcg->c=f-xtHx/2.0-xtb;
if (gpcg->Free_Local) {
ierr = ISDestroy(&gpcg->Free_Local);CHKERRQ(ierr);
}
ierr = VecWhichBetween(tao->XL,tao->solution,tao->XU,&gpcg->Free_Local);CHKERRQ(ierr);
/* Project the gradient and calculate the norm */
ierr = VecCopy(tao->gradient,gpcg->G_New);CHKERRQ(ierr);
ierr = VecBoundGradientProjection(tao->gradient,tao->solution,tao->XL,tao->XU,gpcg->PG);CHKERRQ(ierr);
ierr = VecNorm(gpcg->PG,NORM_2,&gpcg->gnorm);CHKERRQ(ierr);
tao->step=1.0;
gpcg->f = f;
/* Check Stopping Condition */
ierr=TaoMonitor(tao,tao->niter,f,gpcg->gnorm,0.0,tao->step,&reason);CHKERRQ(ierr);
while (reason == TAO_CONTINUE_ITERATING){
tao->ksp_its=0;
ierr = GPCGGradProjections(tao);CHKERRQ(ierr);
ierr = ISGetSize(gpcg->Free_Local,&gpcg->n_free);CHKERRQ(ierr);
f=gpcg->f; gnorm=gpcg->gnorm;
ierr = KSPReset(tao->ksp);CHKERRQ(ierr);
if (gpcg->n_free > 0){
/* Create a reduced linear system */
ierr = VecDestroy(&gpcg->R);CHKERRQ(ierr);
ierr = VecDestroy(&gpcg->DXFree);CHKERRQ(ierr);
ierr = TaoVecGetSubVec(tao->gradient,gpcg->Free_Local, tao->subset_type, 0.0, &gpcg->R);CHKERRQ(ierr);
ierr = VecScale(gpcg->R, -1.0);CHKERRQ(ierr);
ierr = TaoVecGetSubVec(tao->stepdirection,gpcg->Free_Local,tao->subset_type, 0.0, &gpcg->DXFree);CHKERRQ(ierr);
ierr = VecSet(gpcg->DXFree,0.0);CHKERRQ(ierr);
ierr = TaoMatGetSubMat(tao->hessian, gpcg->Free_Local, gpcg->Work, tao->subset_type, &gpcg->Hsub);CHKERRQ(ierr);
if (tao->hessian_pre == tao->hessian) {
ierr = MatDestroy(&gpcg->Hsub_pre);CHKERRQ(ierr);
ierr = PetscObjectReference((PetscObject)gpcg->Hsub);CHKERRQ(ierr);
gpcg->Hsub_pre = gpcg->Hsub;
} else {
ierr = TaoMatGetSubMat(tao->hessian, gpcg->Free_Local, gpcg->Work, tao->subset_type, &gpcg->Hsub_pre);CHKERRQ(ierr);
}
ierr = KSPReset(tao->ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(tao->ksp,gpcg->Hsub,gpcg->Hsub_pre);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp,gpcg->R,gpcg->DXFree);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
tao->ksp_its+=its;
tao->ksp_tot_its+=its;
ierr = VecSet(tao->stepdirection,0.0);CHKERRQ(ierr);
ierr = VecISAXPY(tao->stepdirection,gpcg->Free_Local,1.0,gpcg->DXFree);CHKERRQ(ierr);
ierr = VecDot(tao->stepdirection,tao->gradient,&gdx);CHKERRQ(ierr);
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);CHKERRQ(ierr);
f_new=f;
ierr = TaoLineSearchApply(tao->linesearch,tao->solution,&f_new,tao->gradient,tao->stepdirection,&stepsize,&ls_status);CHKERRQ(ierr);
actred = f_new - f;
/* Evaluate the function and gradient at the new point */
ierr = VecBoundGradientProjection(tao->gradient,tao->solution,tao->XL,tao->XU, gpcg->PG);CHKERRQ(ierr);
ierr = VecNorm(gpcg->PG, NORM_2, &gnorm);CHKERRQ(ierr);
f=f_new;
ierr = ISDestroy(&gpcg->Free_Local);CHKERRQ(ierr);
ierr = VecWhichBetween(tao->XL,tao->solution,tao->XU,&gpcg->Free_Local);CHKERRQ(ierr);
} else {
actred = 0; gpcg->step=1.0;
/* if there were no free variables, no cg method */
}
tao->niter++;
ierr = TaoMonitor(tao,tao->niter,f,gnorm,0.0,gpcg->step,&reason);CHKERRQ(ierr);
gpcg->f=f;gpcg->gnorm=gnorm; gpcg->actred=actred;
if (reason!=TAO_CONTINUE_ITERATING) break;
} /* END MAIN LOOP */
PetscFunctionReturn(0);
}
static PetscErrorCode TaoSolve_BLMVM(Tao tao)
{
PetscErrorCode ierr;
TAO_BLMVM *blmP = (TAO_BLMVM *)tao->data;
TaoConvergedReason reason = TAO_CONTINUE_ITERATING;
TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;
PetscReal f, fold, gdx, gnorm;
PetscReal stepsize = 1.0,delta;
PetscFunctionBegin;
/* Project initial point onto bounds */
ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
ierr = VecMedian(tao->XL,tao->solution,tao->XU,tao->solution);CHKERRQ(ierr);
ierr = TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);CHKERRQ(ierr);
/* Check convergence criteria */
ierr = TaoComputeObjectiveAndGradient(tao, tao->solution,&f,blmP->unprojected_gradient);CHKERRQ(ierr);
ierr = VecBoundGradientProjection(blmP->unprojected_gradient,tao->solution, tao->XL,tao->XU,tao->gradient);CHKERRQ(ierr);
ierr = TaoGradientNorm(tao, tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf pr NaN");
ierr = TaoMonitor(tao, tao->niter, f, gnorm, 0.0, stepsize, &reason);CHKERRQ(ierr);
if (reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
/* Set initial scaling for the function */
if (f != 0.0) {
delta = 2.0*PetscAbsScalar(f) / (gnorm*gnorm);
} else {
delta = 2.0 / (gnorm*gnorm);
}
ierr = MatLMVMSetDelta(blmP->M,delta);CHKERRQ(ierr);
/* Set counter for gradient/reset steps */
blmP->grad = 0;
blmP->reset = 0;
/* Have not converged; continue with Newton method */
while (reason == TAO_CONTINUE_ITERATING) {
/* Compute direction */
ierr = MatLMVMUpdate(blmP->M, tao->solution, tao->gradient);CHKERRQ(ierr);
ierr = MatLMVMSolve(blmP->M, blmP->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
ierr = VecBoundGradientProjection(tao->stepdirection,tao->solution,tao->XL,tao->XU,tao->gradient);CHKERRQ(ierr);
/* Check for success (descent direction) */
ierr = VecDot(blmP->unprojected_gradient, tao->gradient, &gdx);CHKERRQ(ierr);
if (gdx <= 0) {
/* Step is not descent or solve was not successful
Use steepest descent direction (scaled) */
++blmP->grad;
if (f != 0.0) {
delta = 2.0*PetscAbsScalar(f) / (gnorm*gnorm);
} else {
delta = 2.0 / (gnorm*gnorm);
}
ierr = MatLMVMSetDelta(blmP->M,delta);CHKERRQ(ierr);
ierr = MatLMVMReset(blmP->M);CHKERRQ(ierr);
ierr = MatLMVMUpdate(blmP->M, tao->solution, blmP->unprojected_gradient);CHKERRQ(ierr);
ierr = MatLMVMSolve(blmP->M,blmP->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
}
ierr = VecScale(tao->stepdirection,-1.0);CHKERRQ(ierr);
/* Perform the linesearch */
fold = f;
ierr = VecCopy(tao->solution, blmP->Xold);CHKERRQ(ierr);
ierr = VecCopy(blmP->unprojected_gradient, blmP->Gold);CHKERRQ(ierr);
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);CHKERRQ(ierr);
ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f, blmP->unprojected_gradient, tao->stepdirection, &stepsize, &ls_status);CHKERRQ(ierr);
ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER) {
/* Linesearch failed
Reset factors and use scaled (projected) gradient step */
++blmP->reset;
f = fold;
ierr = VecCopy(blmP->Xold, tao->solution);CHKERRQ(ierr);
ierr = VecCopy(blmP->Gold, blmP->unprojected_gradient);CHKERRQ(ierr);
if (f != 0.0) {
delta = 2.0* PetscAbsScalar(f) / (gnorm*gnorm);
} else {
delta = 2.0/ (gnorm*gnorm);
}
ierr = MatLMVMSetDelta(blmP->M,delta);CHKERRQ(ierr);
ierr = MatLMVMReset(blmP->M);CHKERRQ(ierr);
ierr = MatLMVMUpdate(blmP->M, tao->solution, blmP->unprojected_gradient);CHKERRQ(ierr);
ierr = MatLMVMSolve(blmP->M, blmP->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
/* This may be incorrect; linesearch has values fo stepmax and stepmin
that should be reset. */
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);CHKERRQ(ierr);
ierr = TaoLineSearchApply(tao->linesearch,tao->solution,&f, blmP->unprojected_gradient, tao->stepdirection, &stepsize, &ls_status);CHKERRQ(ierr);
ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER) {
tao->reason = TAO_DIVERGED_LS_FAILURE;
break;
}
}
/* Check for converged */
ierr = VecBoundGradientProjection(blmP->unprojected_gradient, tao->solution, tao->XL, tao->XU, tao->gradient);CHKERRQ(ierr);
ierr = TaoGradientNorm(tao, tao->gradient, NORM_2, &gnorm);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Not-a-Number");
tao->niter++;
ierr = TaoMonitor(tao, tao->niter, f, gnorm, 0.0, stepsize, &reason);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
static PetscErrorCode TaoSolve_ASILS(Tao tao)
{
TAO_SSLS *asls = (TAO_SSLS *)tao->data;
PetscReal psi,ndpsi, normd, innerd, t=0;
PetscInt iter=0, nf;
PetscErrorCode ierr;
TaoConvergedReason reason;
TaoLineSearchConvergedReason ls_reason;
PetscFunctionBegin;
/* Assume that Setup has been called!
Set the structure for the Jacobian and create a linear solver. */
ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
ierr = TaoLineSearchSetObjectiveAndGradientRoutine(tao->linesearch,Tao_ASLS_FunctionGradient,tao);CHKERRQ(ierr);
ierr = TaoLineSearchSetObjectiveRoutine(tao->linesearch,Tao_SSLS_Function,tao);CHKERRQ(ierr);
/* Calculate the function value and fischer function value at the
current iterate */
ierr = TaoLineSearchComputeObjectiveAndGradient(tao->linesearch,tao->solution,&psi,asls->dpsi);CHKERRQ(ierr);
ierr = VecNorm(asls->dpsi,NORM_2,&ndpsi);CHKERRQ(ierr);
while (1) {
/* Check the termination criteria */
ierr = PetscInfo3(tao,"iter %D, merit: %g, ||dpsi||: %g\n",iter, (double)asls->merit, (double)ndpsi);CHKERRQ(ierr);
ierr = TaoMonitor(tao, iter++, asls->merit, ndpsi, 0.0, t, &reason);CHKERRQ(ierr);
if (TAO_CONTINUE_ITERATING != reason) break;
/* We are going to solve a linear system of equations. We need to
set the tolerances for the solve so that we maintain an asymptotic
rate of convergence that is superlinear.
Note: these tolerances are for the reduced system. We really need
to make sure that the full system satisfies the full-space conditions.
This rule gives superlinear asymptotic convergence
asls->atol = min(0.5, asls->merit*sqrt(asls->merit));
asls->rtol = 0.0;
This rule gives quadratic asymptotic convergence
asls->atol = min(0.5, asls->merit*asls->merit);
asls->rtol = 0.0;
Calculate a free and fixed set of variables. The fixed set of
variables are those for the d_b is approximately equal to zero.
The definition of approximately changes as we approach the solution
to the problem.
No one rule is guaranteed to work in all cases. The following
definition is based on the norm of the Jacobian matrix. If the
norm is large, the tolerance becomes smaller. */
ierr = MatNorm(tao->jacobian,NORM_1,&asls->identifier);CHKERRQ(ierr);
asls->identifier = PetscMin(asls->merit, 1e-2) / (1 + asls->identifier);
ierr = VecSet(asls->t1,-asls->identifier);CHKERRQ(ierr);
ierr = VecSet(asls->t2, asls->identifier);CHKERRQ(ierr);
ierr = ISDestroy(&asls->fixed);CHKERRQ(ierr);
ierr = ISDestroy(&asls->free);CHKERRQ(ierr);
ierr = VecWhichBetweenOrEqual(asls->t1, asls->db, asls->t2, &asls->fixed);CHKERRQ(ierr);
ierr = ISComplementVec(asls->fixed,asls->t1, &asls->free);CHKERRQ(ierr);
ierr = ISGetSize(asls->fixed,&nf);CHKERRQ(ierr);
ierr = PetscInfo1(tao,"Number of fixed variables: %D\n", nf);CHKERRQ(ierr);
/* We now have our partition. Now calculate the direction in the
fixed variable space. */
ierr = TaoVecGetSubVec(asls->ff, asls->fixed, tao->subset_type, 0.0, &asls->r1);
ierr = TaoVecGetSubVec(asls->da, asls->fixed, tao->subset_type, 1.0, &asls->r2);
ierr = VecPointwiseDivide(asls->r1,asls->r1,asls->r2);CHKERRQ(ierr);
ierr = VecSet(tao->stepdirection,0.0);CHKERRQ(ierr);
ierr = VecISAXPY(tao->stepdirection, asls->fixed,1.0,asls->r1);CHKERRQ(ierr);
/* Our direction in the Fixed Variable Set is fixed. Calculate the
information needed for the step in the Free Variable Set. To
do this, we need to know the diagonal perturbation and the
right hand side. */
ierr = TaoVecGetSubVec(asls->da, asls->free, tao->subset_type, 0.0, &asls->r1);CHKERRQ(ierr);
ierr = TaoVecGetSubVec(asls->ff, asls->free, tao->subset_type, 0.0, &asls->r2);CHKERRQ(ierr);
ierr = TaoVecGetSubVec(asls->db, asls->free, tao->subset_type, 1.0, &asls->r3);CHKERRQ(ierr);
ierr = VecPointwiseDivide(asls->r1,asls->r1, asls->r3);CHKERRQ(ierr);
ierr = VecPointwiseDivide(asls->r2,asls->r2, asls->r3);CHKERRQ(ierr);
/* r1 is the diagonal perturbation
r2 is the right hand side
r3 is no longer needed
Now need to modify r2 for our direction choice in the fixed
variable set: calculate t1 = J*d, take the reduced vector
of t1 and modify r2. */
ierr = MatMult(tao->jacobian, tao->stepdirection, asls->t1);CHKERRQ(ierr);
ierr = TaoVecGetSubVec(asls->t1,asls->free,tao->subset_type,0.0,&asls->r3);CHKERRQ(ierr);
ierr = VecAXPY(asls->r2, -1.0, asls->r3);CHKERRQ(ierr);
/* Calculate the reduced problem matrix and the direction */
if (!asls->w && (tao->subset_type == TAO_SUBSET_MASK || tao->subset_type == TAO_SUBSET_MATRIXFREE)) {
ierr = VecDuplicate(tao->solution, &asls->w);CHKERRQ(ierr);
}
ierr = TaoMatGetSubMat(tao->jacobian, asls->free, asls->w, tao->subset_type,&asls->J_sub);CHKERRQ(ierr);
if (tao->jacobian != tao->jacobian_pre) {
ierr = TaoMatGetSubMat(tao->jacobian_pre, asls->free, asls->w, tao->subset_type, &asls->Jpre_sub);CHKERRQ(ierr);
} else {
ierr = MatDestroy(&asls->Jpre_sub);CHKERRQ(ierr);
asls->Jpre_sub = asls->J_sub;
ierr = PetscObjectReference((PetscObject)(asls->Jpre_sub));CHKERRQ(ierr);
}
ierr = MatDiagonalSet(asls->J_sub, asls->r1,ADD_VALUES);CHKERRQ(ierr);
ierr = TaoVecGetSubVec(tao->stepdirection, asls->free, tao->subset_type, 0.0, &asls->dxfree);CHKERRQ(ierr);
ierr = VecSet(asls->dxfree, 0.0);CHKERRQ(ierr);
/* Calculate the reduced direction. (Really negative of Newton
direction. Therefore, rest of the code uses -d.) */
ierr = KSPReset(tao->ksp);
ierr = KSPSetOperators(tao->ksp, asls->J_sub, asls->Jpre_sub);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp, asls->r2, asls->dxfree);CHKERRQ(ierr);
/* Add the direction in the free variables back into the real direction. */
ierr = VecISAXPY(tao->stepdirection, asls->free, 1.0,asls->dxfree);CHKERRQ(ierr);
/* Check the real direction for descent and if not, use the negative
gradient direction. */
ierr = VecNorm(tao->stepdirection, NORM_2, &normd);CHKERRQ(ierr);
ierr = VecDot(tao->stepdirection, asls->dpsi, &innerd);CHKERRQ(ierr);
if (innerd <= asls->delta*pow(normd, asls->rho)) {
ierr = PetscInfo1(tao,"Gradient direction: %5.4e.\n", (double)innerd);CHKERRQ(ierr);
ierr = PetscInfo1(tao, "Iteration %D: newton direction not descent\n", iter);CHKERRQ(ierr);
ierr = VecCopy(asls->dpsi, tao->stepdirection);CHKERRQ(ierr);
ierr = VecDot(asls->dpsi, tao->stepdirection, &innerd);CHKERRQ(ierr);
}
ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
innerd = -innerd;
/* We now have a correct descent direction. Apply a linesearch to
find the new iterate. */
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch, 1.0);CHKERRQ(ierr);
ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &psi,asls->dpsi, tao->stepdirection, &t, &ls_reason);CHKERRQ(ierr);
ierr = VecNorm(asls->dpsi, NORM_2, &ndpsi);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}