static PetscErrorCode TaoBQNLSComputeHessian(Tao tao) { TAO_BNK *bnk = (TAO_BNK *)tao->data; TAO_BQNK *bqnk = (TAO_BQNK*)bnk->ctx; PetscErrorCode ierr; PetscReal gnorm2, delta; PetscFunctionBegin; /* Compute the initial scaling and update the approximation */ gnorm2 = bnk->gnorm*bnk->gnorm; if (gnorm2 == 0.0) gnorm2 = PETSC_MACHINE_EPSILON; if (bnk->f == 0.0) { delta = 2.0 / gnorm2; } else { delta = 2.0 * PetscAbsScalar(bnk->f) / gnorm2; } ierr = MatSymBrdnSetDelta(bqnk->B, delta);CHKERRQ(ierr); ierr = MatLMVMUpdate(bqnk->B, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr); PetscFunctionReturn(0); }
extern PetscErrorCode MatLMVMSetPrev(Mat M, Vec x, Vec g) { MatLMVMCtx *ctx; PetscErrorCode ierr; PetscBool same; PetscFunctionBegin; PetscValidHeaderSpecific(x,VEC_CLASSID,2); PetscValidHeaderSpecific(g,VEC_CLASSID,3); ierr = PetscObjectTypeCompare((PetscObject)M,MATSHELL,&same);CHKERRQ(ierr); if (!same) SETERRQ(PETSC_COMM_SELF,1,"Matrix M is not type MatLMVM"); ierr = MatShellGetContext(M,(void**)&ctx);CHKERRQ(ierr); if (ctx->nupdates == 0) { ierr = MatLMVMUpdate(M,x,g);CHKERRQ(ierr); } else { ierr = VecCopy(x,ctx->Xprev);CHKERRQ(ierr); ierr = VecCopy(g,ctx->Gprev);CHKERRQ(ierr); /* TODO scaling specific terms */ } PetscFunctionReturn(0); }
static PetscErrorCode TaoSolve_OWLQN(Tao tao) { TAO_OWLQN *lmP = (TAO_OWLQN *)tao->data; PetscReal f, fold, gdx, gnorm; PetscReal step = 1.0; PetscReal delta; PetscErrorCode ierr; PetscInt stepType; PetscInt iter = 0; TaoConvergedReason reason = TAO_CONTINUE_ITERATING; TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING; PetscFunctionBegin; if (tao->XL || tao->XU || tao->ops->computebounds) { ierr = PetscPrintf(((PetscObject)tao)->comm,"WARNING: Variable bounds have been set but will be ignored by owlqn algorithm\n");CHKERRQ(ierr); } /* Check convergence criteria */ ierr = TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient);CHKERRQ(ierr); ierr = VecCopy(tao->gradient, lmP->GV);CHKERRQ(ierr); ierr = ComputePseudoGrad_OWLQN(tao->solution,lmP->GV,lmP->lambda);CHKERRQ(ierr); ierr = VecNorm(lmP->GV,NORM_2,&gnorm);CHKERRQ(ierr); if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN"); ierr = TaoMonitor(tao, iter, f, gnorm, 0.0, step, &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(lmP->M,delta);CHKERRQ(ierr); /* Set counter for gradient/reset steps */ lmP->bfgs = 0; lmP->sgrad = 0; lmP->grad = 0; /* Have not converged; continue with Newton method */ while (reason == TAO_CONTINUE_ITERATING) { /* Compute direction */ ierr = MatLMVMUpdate(lmP->M,tao->solution,tao->gradient);CHKERRQ(ierr); ierr = MatLMVMSolve(lmP->M, lmP->GV, lmP->D);CHKERRQ(ierr); ierr = ProjDirect_OWLQN(lmP->D,lmP->GV);CHKERRQ(ierr); ++lmP->bfgs; /* Check for success (descent direction) */ ierr = VecDot(lmP->D, lmP->GV , &gdx);CHKERRQ(ierr); if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) { /* Step is not descent or direction produced not a number We can assert bfgsUpdates > 1 in this case because the first solve produces the scaled gradient direction, which is guaranteed to be descent Use steepest descent direction (scaled) */ ++lmP->grad; if (f != 0.0) { delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm); } else { delta = 2.0 / (gnorm*gnorm); } ierr = MatLMVMSetDelta(lmP->M, delta);CHKERRQ(ierr); ierr = MatLMVMReset(lmP->M);CHKERRQ(ierr); ierr = MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);CHKERRQ(ierr); ierr = MatLMVMSolve(lmP->M,lmP->GV, lmP->D);CHKERRQ(ierr); ierr = ProjDirect_OWLQN(lmP->D,lmP->GV);CHKERRQ(ierr); lmP->bfgs = 1; ++lmP->sgrad; stepType = OWLQN_SCALED_GRADIENT; } else { if (1 == lmP->bfgs) { /* The first BFGS direction is always the scaled gradient */ ++lmP->sgrad; stepType = OWLQN_SCALED_GRADIENT; } else { ++lmP->bfgs; stepType = OWLQN_BFGS; } } ierr = VecScale(lmP->D, -1.0);CHKERRQ(ierr); /* Perform the linesearch */ fold = f; ierr = VecCopy(tao->solution, lmP->Xold);CHKERRQ(ierr); ierr = VecCopy(tao->gradient, lmP->Gold);CHKERRQ(ierr); ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f, lmP->GV, lmP->D, &step,&ls_status);CHKERRQ(ierr); ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr); while (((int)ls_status < 0) && (stepType != OWLQN_GRADIENT)) { /* Reset factors and use scaled gradient step */ f = fold; ierr = VecCopy(lmP->Xold, tao->solution);CHKERRQ(ierr); ierr = VecCopy(lmP->Gold, tao->gradient);CHKERRQ(ierr); ierr = VecCopy(tao->gradient, lmP->GV);CHKERRQ(ierr); ierr = ComputePseudoGrad_OWLQN(tao->solution,lmP->GV,lmP->lambda);CHKERRQ(ierr); switch(stepType) { case OWLQN_BFGS: /* Failed to obtain acceptable iterate with BFGS step Attempt to use the scaled gradient direction */ if (f != 0.0) { delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm); } else { delta = 2.0 / (gnorm*gnorm); } ierr = MatLMVMSetDelta(lmP->M, delta);CHKERRQ(ierr); ierr = MatLMVMReset(lmP->M);CHKERRQ(ierr); ierr = MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);CHKERRQ(ierr); ierr = MatLMVMSolve(lmP->M, lmP->GV, lmP->D);CHKERRQ(ierr); ierr = ProjDirect_OWLQN(lmP->D,lmP->GV);CHKERRQ(ierr); lmP->bfgs = 1; ++lmP->sgrad; stepType = OWLQN_SCALED_GRADIENT; break; case OWLQN_SCALED_GRADIENT: /* The scaled gradient step did not produce a new iterate; attempt to use the gradient direction. Need to make sure we are not using a different diagonal scaling */ ierr = MatLMVMSetDelta(lmP->M, 1.0);CHKERRQ(ierr); ierr = MatLMVMReset(lmP->M);CHKERRQ(ierr); ierr = MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);CHKERRQ(ierr); ierr = MatLMVMSolve(lmP->M, lmP->GV, lmP->D);CHKERRQ(ierr); ierr = ProjDirect_OWLQN(lmP->D,lmP->GV);CHKERRQ(ierr); lmP->bfgs = 1; ++lmP->grad; stepType = OWLQN_GRADIENT; break; } ierr = VecScale(lmP->D, -1.0);CHKERRQ(ierr); /* Perform the linesearch */ ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f, lmP->GV, lmP->D, &step, &ls_status);CHKERRQ(ierr); ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr); } if ((int)ls_status < 0) { /* Failed to find an improving point*/ f = fold; ierr = VecCopy(lmP->Xold, tao->solution);CHKERRQ(ierr); ierr = VecCopy(lmP->Gold, tao->gradient);CHKERRQ(ierr); ierr = VecCopy(tao->gradient, lmP->GV);CHKERRQ(ierr); step = 0.0; } else { /* a little hack here, because that gv is used to store g */ ierr = VecCopy(lmP->GV, tao->gradient);CHKERRQ(ierr); } ierr = ComputePseudoGrad_OWLQN(tao->solution,lmP->GV,lmP->lambda);CHKERRQ(ierr); /* Check for termination */ ierr = VecNorm(lmP->GV,NORM_2,&gnorm);CHKERRQ(ierr); iter++; ierr = TaoMonitor(tao,iter,f,gnorm,0.0,step,&reason);CHKERRQ(ierr); if ((int)ls_status < 0) break; } PetscFunctionReturn(0); }
static PetscErrorCode TaoSolve_NTR(Tao tao) { TAO_NTR *tr = (TAO_NTR *)tao->data; PC pc; KSPConvergedReason ksp_reason; TaoConvergedReason reason; PetscReal fmin, ftrial, prered, actred, kappa, sigma, beta; PetscReal tau, tau_1, tau_2, tau_max, tau_min, max_radius; PetscReal f, gnorm; PetscReal delta; PetscReal norm_d; PetscErrorCode ierr; PetscInt iter = 0; PetscInt bfgsUpdates = 0; PetscInt needH; PetscInt i_max = 5; PetscInt j_max = 1; PetscInt i, j, N, n, its; PetscFunctionBegin; if (tao->XL || tao->XU || tao->ops->computebounds) { ierr = PetscPrintf(((PetscObject)tao)->comm,"WARNING: Variable bounds have been set but will be ignored by ntr algorithm\n");CHKERRQ(ierr); } tao->trust = tao->trust0; /* Modify the radius if it is too large or small */ tao->trust = PetscMax(tao->trust, tr->min_radius); tao->trust = PetscMin(tao->trust, tr->max_radius); if (NTR_PC_BFGS == tr->pc_type && !tr->M) { ierr = VecGetLocalSize(tao->solution,&n);CHKERRQ(ierr); ierr = VecGetSize(tao->solution,&N);CHKERRQ(ierr); ierr = MatCreateLMVM(((PetscObject)tao)->comm,n,N,&tr->M);CHKERRQ(ierr); ierr = MatLMVMAllocateVectors(tr->M,tao->solution);CHKERRQ(ierr); } /* Check convergence criteria */ ierr = TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient);CHKERRQ(ierr); ierr = VecNorm(tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr); if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN"); needH = 1; ierr = TaoMonitor(tao, iter, f, gnorm, 0.0, 1.0, &reason);CHKERRQ(ierr); if (reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0); /* Create vectors for the limited memory preconditioner */ if ((NTR_PC_BFGS == tr->pc_type) && (BFGS_SCALE_BFGS != tr->bfgs_scale_type)) { if (!tr->Diag) { ierr = VecDuplicate(tao->solution, &tr->Diag);CHKERRQ(ierr); } } switch(tr->ksp_type) { case NTR_KSP_NASH: ierr = KSPSetType(tao->ksp, KSPNASH);CHKERRQ(ierr); if (tao->ksp->ops->setfromoptions) { (*tao->ksp->ops->setfromoptions)(tao->ksp); } break; case NTR_KSP_STCG: ierr = KSPSetType(tao->ksp, KSPSTCG);CHKERRQ(ierr); if (tao->ksp->ops->setfromoptions) { (*tao->ksp->ops->setfromoptions)(tao->ksp); } break; default: ierr = KSPSetType(tao->ksp, KSPGLTR);CHKERRQ(ierr); if (tao->ksp->ops->setfromoptions) { (*tao->ksp->ops->setfromoptions)(tao->ksp); } break; } /* Modify the preconditioner to use the bfgs approximation */ ierr = KSPGetPC(tao->ksp, &pc);CHKERRQ(ierr); switch(tr->pc_type) { case NTR_PC_NONE: ierr = PCSetType(pc, PCNONE);CHKERRQ(ierr); if (pc->ops->setfromoptions) { (*pc->ops->setfromoptions)(pc); } break; case NTR_PC_AHESS: ierr = PCSetType(pc, PCJACOBI);CHKERRQ(ierr); if (pc->ops->setfromoptions) { (*pc->ops->setfromoptions)(pc); } ierr = PCJacobiSetUseAbs(pc);CHKERRQ(ierr); break; case NTR_PC_BFGS: ierr = PCSetType(pc, PCSHELL);CHKERRQ(ierr); if (pc->ops->setfromoptions) { (*pc->ops->setfromoptions)(pc); } ierr = PCShellSetName(pc, "bfgs");CHKERRQ(ierr); ierr = PCShellSetContext(pc, tr->M);CHKERRQ(ierr); ierr = PCShellSetApply(pc, MatLMVMSolveShell);CHKERRQ(ierr); break; default: /* Use the pc method set by pc_type */ break; } /* Initialize trust-region radius */ switch(tr->init_type) { case NTR_INIT_CONSTANT: /* Use the initial radius specified */ break; case NTR_INIT_INTERPOLATION: /* Use the initial radius specified */ max_radius = 0.0; for (j = 0; j < j_max; ++j) { fmin = f; sigma = 0.0; if (needH) { ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr); needH = 0; } for (i = 0; i < i_max; ++i) { ierr = VecCopy(tao->solution, tr->W);CHKERRQ(ierr); ierr = VecAXPY(tr->W, -tao->trust/gnorm, tao->gradient);CHKERRQ(ierr); ierr = TaoComputeObjective(tao, tr->W, &ftrial);CHKERRQ(ierr); if (PetscIsInfOrNanReal(ftrial)) { tau = tr->gamma1_i; } else { if (ftrial < fmin) { fmin = ftrial; sigma = -tao->trust / gnorm; } ierr = MatMult(tao->hessian, tao->gradient, tao->stepdirection);CHKERRQ(ierr); ierr = VecDot(tao->gradient, tao->stepdirection, &prered);CHKERRQ(ierr); prered = tao->trust * (gnorm - 0.5 * tao->trust * prered / (gnorm * gnorm)); actred = f - ftrial; if ((PetscAbsScalar(actred) <= tr->epsilon) && (PetscAbsScalar(prered) <= tr->epsilon)) { kappa = 1.0; } else { kappa = actred / prered; } tau_1 = tr->theta_i * gnorm * tao->trust / (tr->theta_i * gnorm * tao->trust + (1.0 - tr->theta_i) * prered - actred); tau_2 = tr->theta_i * gnorm * tao->trust / (tr->theta_i * gnorm * tao->trust - (1.0 + tr->theta_i) * prered + actred); tau_min = PetscMin(tau_1, tau_2); tau_max = PetscMax(tau_1, tau_2); if (PetscAbsScalar(kappa - 1.0) <= tr->mu1_i) { /* Great agreement */ max_radius = PetscMax(max_radius, tao->trust); if (tau_max < 1.0) { tau = tr->gamma3_i; } else if (tau_max > tr->gamma4_i) { tau = tr->gamma4_i; } else { tau = tau_max; } } else if (PetscAbsScalar(kappa - 1.0) <= tr->mu2_i) { /* Good agreement */ max_radius = PetscMax(max_radius, tao->trust); if (tau_max < tr->gamma2_i) { tau = tr->gamma2_i; } else if (tau_max > tr->gamma3_i) { tau = tr->gamma3_i; } else { tau = tau_max; } } else { /* Not good agreement */ if (tau_min > 1.0) { tau = tr->gamma2_i; } else if (tau_max < tr->gamma1_i) { tau = tr->gamma1_i; } else if ((tau_min < tr->gamma1_i) && (tau_max >= 1.0)) { tau = tr->gamma1_i; } else if ((tau_1 >= tr->gamma1_i) && (tau_1 < 1.0) && ((tau_2 < tr->gamma1_i) || (tau_2 >= 1.0))) { tau = tau_1; } else if ((tau_2 >= tr->gamma1_i) && (tau_2 < 1.0) && ((tau_1 < tr->gamma1_i) || (tau_2 >= 1.0))) { tau = tau_2; } else { tau = tau_max; } } } tao->trust = tau * tao->trust; } if (fmin < f) { f = fmin; ierr = VecAXPY(tao->solution, sigma, tao->gradient);CHKERRQ(ierr); ierr = TaoComputeGradient(tao,tao->solution, tao->gradient);CHKERRQ(ierr); ierr = VecNorm(tao->gradient, NORM_2, &gnorm);CHKERRQ(ierr); if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN"); needH = 1; ierr = TaoMonitor(tao, iter, f, gnorm, 0.0, 1.0, &reason);CHKERRQ(ierr); if (reason != TAO_CONTINUE_ITERATING) { PetscFunctionReturn(0); } } } tao->trust = PetscMax(tao->trust, max_radius); /* Modify the radius if it is too large or small */ tao->trust = PetscMax(tao->trust, tr->min_radius); tao->trust = PetscMin(tao->trust, tr->max_radius); break; default: /* Norm of the first direction will initialize radius */ tao->trust = 0.0; break; } /* Set initial scaling for the BFGS preconditioner This step is done after computing the initial trust-region radius since the function value may have decreased */ if (NTR_PC_BFGS == tr->pc_type) { if (f != 0.0) { delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm); } else { delta = 2.0 / (gnorm*gnorm); } ierr = MatLMVMSetDelta(tr->M,delta);CHKERRQ(ierr); } /* Have not converged; continue with Newton method */ while (reason == TAO_CONTINUE_ITERATING) { ++iter; tao->ksp_its=0; /* Compute the Hessian */ if (needH) { ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr); needH = 0; } if (NTR_PC_BFGS == tr->pc_type) { if (BFGS_SCALE_AHESS == tr->bfgs_scale_type) { /* Obtain diagonal for the bfgs preconditioner */ ierr = MatGetDiagonal(tao->hessian, tr->Diag);CHKERRQ(ierr); ierr = VecAbs(tr->Diag);CHKERRQ(ierr); ierr = VecReciprocal(tr->Diag);CHKERRQ(ierr); ierr = MatLMVMSetScale(tr->M,tr->Diag);CHKERRQ(ierr); } /* Update the limited memory preconditioner */ ierr = MatLMVMUpdate(tr->M, tao->solution, tao->gradient);CHKERRQ(ierr); ++bfgsUpdates; } while (reason == TAO_CONTINUE_ITERATING) { ierr = KSPSetOperators(tao->ksp, tao->hessian, tao->hessian_pre);CHKERRQ(ierr); /* Solve the trust region subproblem */ if (NTR_KSP_NASH == tr->ksp_type) { ierr = KSPNASHSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr); ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr); ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr); tao->ksp_its+=its; tao->ksp_tot_its+=its; ierr = KSPNASHGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr); } else if (NTR_KSP_STCG == tr->ksp_type) { ierr = KSPSTCGSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr); ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr); ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr); tao->ksp_its+=its; tao->ksp_tot_its+=its; ierr = KSPSTCGGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr); } else { /* NTR_KSP_GLTR */ ierr = KSPGLTRSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr); ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr); ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr); tao->ksp_its+=its; tao->ksp_tot_its+=its; ierr = KSPGLTRGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr); } if (0.0 == tao->trust) { /* Radius was uninitialized; use the norm of the direction */ if (norm_d > 0.0) { tao->trust = norm_d; /* Modify the radius if it is too large or small */ tao->trust = PetscMax(tao->trust, tr->min_radius); tao->trust = PetscMin(tao->trust, tr->max_radius); } else { /* The direction was bad; set radius to default value and re-solve the trust-region subproblem to get a direction */ tao->trust = tao->trust0; /* Modify the radius if it is too large or small */ tao->trust = PetscMax(tao->trust, tr->min_radius); tao->trust = PetscMin(tao->trust, tr->max_radius); if (NTR_KSP_NASH == tr->ksp_type) { ierr = KSPNASHSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr); ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr); ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr); tao->ksp_its+=its; tao->ksp_tot_its+=its; ierr = KSPNASHGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr); } else if (NTR_KSP_STCG == tr->ksp_type) { ierr = KSPSTCGSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr); ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr); ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr); tao->ksp_its+=its; tao->ksp_tot_its+=its; ierr = KSPSTCGGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr); } else { /* NTR_KSP_GLTR */ ierr = KSPGLTRSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr); ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr); ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr); tao->ksp_its+=its; tao->ksp_tot_its+=its; ierr = KSPGLTRGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr); } if (norm_d == 0.0) SETERRQ(PETSC_COMM_SELF,1, "Initial direction zero"); } } ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr); ierr = KSPGetConvergedReason(tao->ksp, &ksp_reason);CHKERRQ(ierr); if ((KSP_DIVERGED_INDEFINITE_PC == ksp_reason) && (NTR_PC_BFGS == tr->pc_type) && (bfgsUpdates > 1)) { /* Preconditioner is numerically indefinite; reset the approximate if using BFGS preconditioning. */ if (f != 0.0) { delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm); } else { delta = 2.0 / (gnorm*gnorm); } ierr = MatLMVMSetDelta(tr->M, delta);CHKERRQ(ierr); ierr = MatLMVMReset(tr->M);CHKERRQ(ierr); ierr = MatLMVMUpdate(tr->M, tao->solution, tao->gradient);CHKERRQ(ierr); bfgsUpdates = 1; } if (NTR_UPDATE_REDUCTION == tr->update_type) { /* Get predicted reduction */ if (NTR_KSP_NASH == tr->ksp_type) { ierr = KSPNASHGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr); } else if (NTR_KSP_STCG == tr->ksp_type) { ierr = KSPSTCGGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr); } else { /* gltr */ ierr = KSPGLTRGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr); } if (prered >= 0.0) { /* The predicted reduction has the wrong sign. This cannot happen in infinite precision arithmetic. Step should be rejected! */ tao->trust = tr->alpha1 * PetscMin(tao->trust, norm_d); } else { /* Compute trial step and function value */ ierr = VecCopy(tao->solution,tr->W);CHKERRQ(ierr); ierr = VecAXPY(tr->W, 1.0, tao->stepdirection);CHKERRQ(ierr); ierr = TaoComputeObjective(tao, tr->W, &ftrial);CHKERRQ(ierr); if (PetscIsInfOrNanReal(ftrial)) { tao->trust = tr->alpha1 * PetscMin(tao->trust, norm_d); } else { /* Compute and actual reduction */ actred = f - ftrial; prered = -prered; if ((PetscAbsScalar(actred) <= tr->epsilon) && (PetscAbsScalar(prered) <= tr->epsilon)) { kappa = 1.0; } else { kappa = actred / prered; } /* Accept or reject the step and update radius */ if (kappa < tr->eta1) { /* Reject the step */ tao->trust = tr->alpha1 * PetscMin(tao->trust, norm_d); } else { /* Accept the step */ if (kappa < tr->eta2) { /* Marginal bad step */ tao->trust = tr->alpha2 * PetscMin(tao->trust, norm_d); } else if (kappa < tr->eta3) { /* Reasonable step */ tao->trust = tr->alpha3 * tao->trust; } else if (kappa < tr->eta4) { /* Good step */ tao->trust = PetscMax(tr->alpha4 * norm_d, tao->trust); } else { /* Very good step */ tao->trust = PetscMax(tr->alpha5 * norm_d, tao->trust); } break; } } } } else { /* Get predicted reduction */ if (NTR_KSP_NASH == tr->ksp_type) { ierr = KSPNASHGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr); } else if (NTR_KSP_STCG == tr->ksp_type) { ierr = KSPSTCGGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr); } else { /* gltr */ ierr = KSPGLTRGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr); } if (prered >= 0.0) { /* The predicted reduction has the wrong sign. This cannot happen in infinite precision arithmetic. Step should be rejected! */ tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d); } else { ierr = VecCopy(tao->solution, tr->W);CHKERRQ(ierr); ierr = VecAXPY(tr->W, 1.0, tao->stepdirection);CHKERRQ(ierr); ierr = TaoComputeObjective(tao, tr->W, &ftrial);CHKERRQ(ierr); if (PetscIsInfOrNanReal(ftrial)) { tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d); } else { ierr = VecDot(tao->gradient, tao->stepdirection, &beta);CHKERRQ(ierr); actred = f - ftrial; prered = -prered; if ((PetscAbsScalar(actred) <= tr->epsilon) && (PetscAbsScalar(prered) <= tr->epsilon)) { kappa = 1.0; } else { kappa = actred / prered; } tau_1 = tr->theta * beta / (tr->theta * beta - (1.0 - tr->theta) * prered + actred); tau_2 = tr->theta * beta / (tr->theta * beta + (1.0 + tr->theta) * prered - actred); tau_min = PetscMin(tau_1, tau_2); tau_max = PetscMax(tau_1, tau_2); if (kappa >= 1.0 - tr->mu1) { /* Great agreement; accept step and update radius */ if (tau_max < 1.0) { tao->trust = PetscMax(tao->trust, tr->gamma3 * norm_d); } else if (tau_max > tr->gamma4) { tao->trust = PetscMax(tao->trust, tr->gamma4 * norm_d); } else { tao->trust = PetscMax(tao->trust, tau_max * norm_d); } break; } else if (kappa >= 1.0 - tr->mu2) { /* Good agreement */ if (tau_max < tr->gamma2) { tao->trust = tr->gamma2 * PetscMin(tao->trust, norm_d); } else if (tau_max > tr->gamma3) { tao->trust = PetscMax(tao->trust, tr->gamma3 * norm_d); } else if (tau_max < 1.0) { tao->trust = tau_max * PetscMin(tao->trust, norm_d); } else { tao->trust = PetscMax(tao->trust, tau_max * norm_d); } break; } else { /* Not good agreement */ if (tau_min > 1.0) { tao->trust = tr->gamma2 * PetscMin(tao->trust, norm_d); } else if (tau_max < tr->gamma1) { tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d); } else if ((tau_min < tr->gamma1) && (tau_max >= 1.0)) { tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d); } else if ((tau_1 >= tr->gamma1) && (tau_1 < 1.0) && ((tau_2 < tr->gamma1) || (tau_2 >= 1.0))) { tao->trust = tau_1 * PetscMin(tao->trust, norm_d); } else if ((tau_2 >= tr->gamma1) && (tau_2 < 1.0) && ((tau_1 < tr->gamma1) || (tau_2 >= 1.0))) { tao->trust = tau_2 * PetscMin(tao->trust, norm_d); } else { tao->trust = tau_max * PetscMin(tao->trust, norm_d); } } } } } /* The step computed was not good and the radius was decreased. Monitor the radius to terminate. */ ierr = TaoMonitor(tao, iter, f, gnorm, 0.0, tao->trust, &reason);CHKERRQ(ierr); } /* The radius may have been increased; modify if it is too large */ tao->trust = PetscMin(tao->trust, tr->max_radius); if (reason == TAO_CONTINUE_ITERATING) { ierr = VecCopy(tr->W, tao->solution);CHKERRQ(ierr); f = ftrial; ierr = TaoComputeGradient(tao, tao->solution, tao->gradient); ierr = VecNorm(tao->gradient, NORM_2, &gnorm);CHKERRQ(ierr); if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN"); needH = 1; ierr = TaoMonitor(tao, iter, f, gnorm, 0.0, tao->trust, &reason);CHKERRQ(ierr); } } 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_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); }