/* evaluate user info at current point */
PetscErrorCode IPMEvaluate(Tao tao)
{
TAO_IPM *ipmP = (TAO_IPM *)tao->data;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = TaoComputeObjectiveAndGradient(tao,tao->solution,&ipmP->kkt_f,tao->gradient);CHKERRQ(ierr);
ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
if (ipmP->me > 0) {
ierr = TaoComputeEqualityConstraints(tao,tao->solution,tao->constraints_equality);CHKERRQ(ierr);
ierr = TaoComputeJacobianEquality(tao,tao->solution,tao->jacobian_equality,tao->jacobian_equality_pre);CHKERRQ(ierr);
}
if (ipmP->mi > 0) {
ierr = TaoComputeInequalityConstraints(tao,tao->solution,tao->constraints_inequality);CHKERRQ(ierr);
ierr = TaoComputeJacobianInequality(tao,tao->solution,tao->jacobian_inequality,tao->jacobian_inequality_pre);CHKERRQ(ierr);
}
if (ipmP->nb > 0) {
/* Ai' = jac_ineq | I (w/lb) | -I (w/ub) */
ierr = IPMUpdateAi(tao);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
static int TaoSolve_BNLS(TAO_SOLVER tao, void*solver){
TAO_BNLS *bnls = (TAO_BNLS *)solver;
int info;
TaoInt lsflag,iter=0;
TaoTerminateReason reason=TAO_CONTINUE_ITERATING;
double f,f_full,gnorm,gdx,stepsize=1.0;
TaoTruth success;
TaoVec *XU, *XL;
TaoVec *X, *G=bnls->G, *PG=bnls->PG;
TaoVec *R=bnls->R, *DXFree=bnls->DXFree;
TaoVec *DX=bnls->DX, *Work=bnls->Work;
TaoMat *H, *Hsub=bnls->Hsub;
TaoIndexSet *FreeVariables = bnls->FreeVariables;
TaoFunctionBegin;
/* Check if upper bound greater than lower bound. */
info = TaoGetSolution(tao,&X);CHKERRQ(info); bnls->X=X;
info = TaoGetVariableBounds(tao,&XL,&XU);CHKERRQ(info);
info = TaoEvaluateVariableBounds(tao,XL,XU); CHKERRQ(info);
info = TaoGetHessian(tao,&H);CHKERRQ(info); bnls->H=H;
/* Project the current point onto the feasible set */
info = X->Median(XL,X,XU); CHKERRQ(info);
TaoLinearSolver *tls;
// Modify the linear solver to a conjugate gradient method
info = TaoGetLinearSolver(tao, &tls); CHKERRQ(info);
TaoLinearSolverPetsc *pls;
pls = dynamic_cast <TaoLinearSolverPetsc *> (tls);
// set trust radius to zero
// PETSc ignores this case and should return the negative curvature direction
// at its current default length
pls->SetTrustRadius(0.0);
if(!bnls->M) bnls->M = new TaoLMVMMat(X);
TaoLMVMMat *M = bnls->M;
KSP pksp = pls->GetKSP();
// we will want to provide an initial guess in case neg curvature on the first iteration
info = KSPSetInitialGuessNonzero(pksp,PETSC_TRUE); CHKERRQ(info);
PC ppc;
// Modify the preconditioner to use the bfgs approximation
info = KSPGetPC(pksp, &ppc); CHKERRQ(info);
PetscTruth BFGSPreconditioner=PETSC_FALSE;// debug flag
info = PetscOptionsGetTruth(PETSC_NULL,"-bnls_pc_bfgs",
&BFGSPreconditioner,PETSC_NULL); CHKERRQ(info);
if( BFGSPreconditioner)
{
info=PetscInfo(tao,"TaoSolve_BNLS: using bfgs preconditioner\n");
info = KSPSetNormType(pksp, KSP_NORM_PRECONDITIONED); CHKERRQ(info);
info = PCSetType(ppc, PCSHELL); CHKERRQ(info);
info = PCShellSetName(ppc, "bfgs"); CHKERRQ(info);
info = PCShellSetContext(ppc, M); CHKERRQ(info);
info = PCShellSetApply(ppc, bfgs_apply); CHKERRQ(info);
}
else
{// default to none
info=PetscInfo(tao,"TaoSolve_BNLS: using no preconditioner\n");
info = PCSetType(ppc, PCNONE); CHKERRQ(info);
}
info = TaoComputeMeritFunctionGradient(tao,X,&f,G);CHKERRQ(info);
info = PG->BoundGradientProjection(G,XL,X,XU);CHKERRQ(info);
info = PG->Norm2(&gnorm); CHKERRQ(info);
// Set initial scaling for the function
if (f != 0.0) {
info = M->SetDelta(2.0 * TaoAbsDouble(f) / (gnorm*gnorm)); CHKERRQ(info);
}
else {
info = M->SetDelta(2.0 / (gnorm*gnorm)); CHKERRQ(info);
}
while (reason==TAO_CONTINUE_ITERATING){
/* Project the gradient and calculate the norm */
info = PG->BoundGradientProjection(G,XL,X,XU);CHKERRQ(info);
info = PG->Norm2(&gnorm); CHKERRQ(info);
info = M->Update(X, PG); CHKERRQ(info);
PetscScalar ewAtol = PetscMin(0.5,gnorm)*gnorm;
info = KSPSetTolerances(pksp,PETSC_DEFAULT,ewAtol,
PETSC_DEFAULT, PETSC_DEFAULT); CHKERRQ(info);
info=PetscInfo1(tao,"TaoSolve_BNLS: gnorm =%g\n",gnorm);
pksp->printreason = PETSC_TRUE;
info = KSPView(pksp,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(info);
M->View();
info = TaoMonitor(tao,iter++,f,gnorm,0.0,stepsize,&reason);
CHKERRQ(info);
if (reason!=TAO_CONTINUE_ITERATING) break;
info = FreeVariables->WhichEqual(PG,G); CHKERRQ(info);
info = TaoComputeHessian(tao,X,H);CHKERRQ(info);
/* Create a reduced linear system */
info = R->SetReducedVec(G,FreeVariables);CHKERRQ(info);
info = R->Negate();CHKERRQ(info);
/* Use gradient as initial guess */
PetscTruth UseGradientIG=PETSC_FALSE;// debug flag
info = PetscOptionsGetTruth(PETSC_NULL,"-bnls_use_gradient_ig",
&UseGradientIG,PETSC_NULL); CHKERRQ(info);
if(UseGradientIG)
info = DX->CopyFrom(G);
else
{
info=PetscInfo(tao,"TaoSolve_BNLS: use bfgs init guess \n");
info = M->Solve(G, DX, &success);
}
CHKERRQ(info);
info = DXFree->SetReducedVec(DX,FreeVariables);CHKERRQ(info);
info = DXFree->Negate(); CHKERRQ(info);
info = Hsub->SetReducedMatrix(H,FreeVariables,FreeVariables);CHKERRQ(info);
bnls->gamma_factor /= 2;
success = TAO_FALSE;
while (success==TAO_FALSE) {
/* Approximately solve the reduced linear system */
info = TaoPreLinearSolve(tao,Hsub);CHKERRQ(info);
info = TaoLinearSolve(tao,Hsub,R,DXFree,&success);CHKERRQ(info);
info = DX->SetToZero(); CHKERRQ(info);
info = DX->ReducedXPY(DXFree,FreeVariables);CHKERRQ(info);
info = DX->Dot(G,&gdx); CHKERRQ(info);
if (gdx>=0 || success==TAO_FALSE) { /* use bfgs direction */
info = M->Solve(G, DX, &success); CHKERRQ(info);
info = DX->BoundGradientProjection(DX,XL,X,XU); CHKERRQ(info);
info = DX->Negate(); CHKERRQ(info);
// Check for success (descent direction)
info = DX->Dot(G,&gdx); CHKERRQ(info);
if (gdx >= 0) {
// Step is not descent or solve was not successful
// Use steepest descent direction (scaled)
if (f != 0.0) {
info = M->SetDelta(2.0 * TaoAbsDouble(f) / (gnorm*gnorm)); CHKERRQ(info);
}
else {
info = M->SetDelta(2.0 / (gnorm*gnorm)); CHKERRQ(info);
}
info = M->Reset(); CHKERRQ(info);
info = M->Update(X, G); CHKERRQ(info);
info = DX->CopyFrom(G);
info = DX->Negate(); CHKERRQ(info);
info = DX->Dot(G,&gdx); CHKERRQ(info);
info=PetscInfo1(tao,"LMVM Solve Fail use steepest descent, gdx %22.12e \n",gdx);
}
else {
info=PetscInfo1(tao,"Newton Solve Fail use BFGS direction, gdx %22.12e \n",gdx);
}
success = TAO_TRUE;
// bnls->gamma_factor *= 2;
// bnls->gamma = bnls->gamma_factor*(gnorm);
//#if !defined(PETSC_USE_COMPLEX)
// info=PetscInfo2(tao,"TaoSolve_NLS: modify diagonal (assume same nonzero structure), gamma_factor=%g, gamma=%g\n",bnls->gamma_factor,bnls->gamma);
// CHKERRQ(info);
//#else
// info=PetscInfo3(tao,"TaoSolve_NLS: modify diagonal (asuume same nonzero structure), gamma_factor=%g, gamma=%g, gdx %22.12e \n",
// bnls->gamma_factor,PetscReal(bnls->gamma),gdx);CHKERRQ(info);
//#endif
// info = Hsub->ShiftDiagonal(bnls->gamma);CHKERRQ(info);
// if (f != 0.0) {
// info = M->SetDelta(2.0 * TaoAbsDouble(f) / (gnorm*gnorm)); CHKERRQ(info);
// }
// else {
// info = M->SetDelta(2.0 / (gnorm*gnorm)); CHKERRQ(info);
// }
// info = M->Reset(); CHKERRQ(info);
// info = M->Update(X, G); CHKERRQ(info);
// success = TAO_FALSE;
} else {
info=PetscInfo1(tao,"Newton Solve is descent direction, gdx %22.12e \n",gdx);
success = TAO_TRUE;
}
}
stepsize=1.0;
info = TaoLineSearchApply(tao,X,G,DX,Work,
&f,&f_full,&stepsize,&lsflag);
CHKERRQ(info);
} /* END MAIN LOOP */
TaoFunctionReturn(0);
}
static int TaoSolve_GPCG(TAO_SOLVER tao, void *solver)
{
TAO_GPCG *gpcg = (TAO_GPCG *)solver ;
int info;
TaoInt lsflag,iter=0;
TaoTruth optimal_face=TAO_FALSE,success;
double actred,f,f_new,f_full,gnorm,gdx,stepsize;
double c;
TaoVec *XU, *XL;
TaoVec *X, *G=gpcg->G , *B=gpcg->B, *PG=gpcg->PG;
TaoVec *R=gpcg->R, *DXFree=gpcg->DXFree;
TaoVec *G_New=gpcg->G_New;
TaoVec *DX=gpcg->DX, *Work=gpcg->Work;
TaoMat *H, *Hsub=gpcg->Hsub;
TaoIndexSet *Free_Local = gpcg->Free_Local, *TIS=gpcg->TT;
TaoTerminateReason reason;
TaoFunctionBegin;
/* Check if upper bound greater than lower bound. */
info = TaoGetSolution(tao,&X);CHKERRQ(info);
info = TaoGetHessian(tao,&H);CHKERRQ(info);
info = TaoGetVariableBounds(tao,&XL,&XU);CHKERRQ(info);
info = TaoEvaluateVariableBounds(tao,XL,XU); CHKERRQ(info);
info = X->Median(XL,X,XU); CHKERRQ(info);
info = TaoComputeHessian(tao,X,H); CHKERRQ(info);
info = TaoComputeFunctionGradient(tao,X,&f,B);
CHKERRQ(info);
/* Compute quadratic representation */
info = H->Multiply(X,Work); CHKERRQ(info);
info = X->Dot(Work,&c); CHKERRQ(info);
info = B->Axpy(-1.0,Work); CHKERRQ(info);
info = X->Dot(B,&stepsize); CHKERRQ(info);
gpcg->c=f-c/2.0-stepsize;
info = Free_Local->WhichBetween(XL,X,XU); CHKERRQ(info);
info = TaoGPCGComputeFunctionGradient(tao, X, &gpcg->f , G);
/* Project the gradient and calculate the norm */
info = G_New->CopyFrom(G);CHKERRQ(info);
info = PG->BoundGradientProjection(G,XL,X,XU);CHKERRQ(info);
info = PG->Norm2(&gpcg->gnorm); CHKERRQ(info);
gpcg->step=1.0;
/* Check Stopping Condition */
info=TaoMonitor(tao,iter++,gpcg->f,gpcg->gnorm,0,gpcg->step,&reason); CHKERRQ(info);
while (reason == TAO_CONTINUE_ITERATING){
info = TaoGradProjections(tao, gpcg); CHKERRQ(info);
info = Free_Local->WhichBetween(XL,X,XU); CHKERRQ(info);
info = Free_Local->GetSize(&gpcg->n_free); CHKERRQ(info);
f=gpcg->f; gnorm=gpcg->gnorm;
if (gpcg->n_free > 0){
/* Create a reduced linear system */
info = R->SetReducedVec(G,Free_Local);CHKERRQ(info);
info = R->Negate(); CHKERRQ(info);
info = DXFree->SetReducedVec(DX,Free_Local);CHKERRQ(info);
info = DXFree->SetToZero(); CHKERRQ(info);
info = Hsub->SetReducedMatrix(H,Free_Local,Free_Local);CHKERRQ(info);
info = TaoPreLinearSolve(tao,Hsub);CHKERRQ(info);
/* Approximately solve the reduced linear system */
info = TaoLinearSolve(tao,Hsub,R,DXFree,&success);CHKERRQ(info);
info=DX->SetToZero(); CHKERRQ(info);
info=DX->ReducedXPY(DXFree,Free_Local);CHKERRQ(info);
info = G->Dot(DX,&gdx); CHKERRQ(info);
stepsize=1.0; f_new=f;
info = TaoLineSearchApply(tao,X,G,DX,Work,
&f_new,&f_full,&stepsize,&lsflag);
CHKERRQ(info);
actred = f_new - f;
/* Evaluate the function and gradient at the new point */
info = PG->BoundGradientProjection(G,XL,X,XU);
CHKERRQ(info);
info = PG->Norm2(&gnorm); CHKERRQ(info);
f=f_new;
info = GPCGCheckOptimalFace(X,XL,XU,PG,Work, Free_Local, TIS,
&optimal_face); CHKERRQ(info);
} else {
actred = 0; stepsize=1.0;
/* if there were no free variables, no cg method */
}
info = TaoMonitor(tao,iter,f,gnorm,0.0,stepsize,&reason); CHKERRQ(info);
gpcg->f=f;gpcg->gnorm=gnorm; gpcg->actred=actred;
if (reason!=TAO_CONTINUE_ITERATING) break;
iter++;
} /* END MAIN LOOP */
TaoFunctionReturn(0);
}
PetscErrorCode TaoSolve_Test(Tao tao)
{
Mat A = tao->hessian,B;
Vec x = tao->solution,g1,g2;
PetscErrorCode ierr;
PetscInt i;
PetscReal nrm,gnorm,hcnorm,fdnorm;
MPI_Comm comm;
Tao_Test *fd = (Tao_Test*)tao->data;
PetscFunctionBegin;
comm = ((PetscObject)tao)->comm;
if (fd->check_gradient) {
ierr = VecDuplicate(x,&g1);CHKERRQ(ierr);
ierr = VecDuplicate(x,&g2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Testing hand-coded gradient (hc) against finite difference gradient (fd), if the ratio ||fd - hc|| / ||hc|| is\n");CHKERRQ(ierr);
ierr = PetscPrintf(comm,"0 (1.e-8), the hand-coded gradient is probably correct.\n");CHKERRQ(ierr);
if (!fd->complete_print) {
ierr = PetscPrintf(comm,"Run with -tao_test_display to show difference\n");CHKERRQ(ierr);
ierr = PetscPrintf(comm,"between hand-coded and finite difference gradient.\n");CHKERRQ(ierr);
}
for (i=0; i<3; i++) {
if (i == 1) {ierr = VecSet(x,-1.0);CHKERRQ(ierr);}
else if (i == 2) {ierr = VecSet(x,1.0);CHKERRQ(ierr);}
/* Compute both version of gradient */
ierr = TaoComputeGradient(tao,x,g1);CHKERRQ(ierr);
ierr = TaoDefaultComputeGradient(tao,x,g2,NULL);CHKERRQ(ierr);
if (fd->complete_print) {
MPI_Comm gcomm;
PetscViewer viewer;
ierr = PetscPrintf(comm,"Finite difference gradient\n");CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)g2,&gcomm);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetStdout(gcomm,&viewer);CHKERRQ(ierr);
ierr = VecView(g2,viewer);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Hand-coded gradient\n");CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)g1,&gcomm);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetStdout(gcomm,&viewer);CHKERRQ(ierr);
ierr = VecView(g1,viewer);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"\n");CHKERRQ(ierr);
}
ierr = VecAXPY(g2,-1.0,g1);CHKERRQ(ierr);
ierr = VecNorm(g1,NORM_2,&hcnorm);CHKERRQ(ierr);
ierr = VecNorm(g2,NORM_2,&fdnorm);CHKERRQ(ierr);
if (!hcnorm) hcnorm=1.0e-20;
ierr = PetscPrintf(comm,"ratio ||fd-hc||/||hc|| = %g, difference ||fd-hc|| = %g\n", (double)(fdnorm/hcnorm), (double)fdnorm);CHKERRQ(ierr);
}
ierr = VecDestroy(&g1);CHKERRQ(ierr);
ierr = VecDestroy(&g2);CHKERRQ(ierr);
}
if (fd->check_hessian) {
if (A != tao->hessian_pre) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot test with alternative preconditioner");
ierr = PetscPrintf(comm,"Testing hand-coded Hessian (hc) against finite difference Hessian (fd). If the ratio is\n");CHKERRQ(ierr);
ierr = PetscPrintf(comm,"O (1.e-8), the hand-coded Hessian is probably correct.\n");CHKERRQ(ierr);
if (!fd->complete_print) {
ierr = PetscPrintf(comm,"Run with -tao_test_display to show difference\n");CHKERRQ(ierr);
ierr = PetscPrintf(comm,"of hand-coded and finite difference Hessian.\n");CHKERRQ(ierr);
}
for (i=0;i<3;i++) {
/* compute both versions of Hessian */
ierr = TaoComputeHessian(tao,x,A,A);CHKERRQ(ierr);
if (!i) {ierr = MatConvert(A,MATSAME,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr);}
ierr = TaoDefaultComputeHessian(tao,x,B,B,tao->user_hessP);CHKERRQ(ierr);
if (fd->complete_print) {
MPI_Comm bcomm;
PetscViewer viewer;
ierr = PetscPrintf(comm,"Finite difference Hessian\n");CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)B,&bcomm);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetStdout(bcomm,&viewer);CHKERRQ(ierr);
ierr = MatView(B,viewer);CHKERRQ(ierr);
}
/* compare */
ierr = MatAYPX(B,-1.0,A,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatNorm(B,NORM_FROBENIUS,&nrm);CHKERRQ(ierr);
ierr = MatNorm(A,NORM_FROBENIUS,&gnorm);CHKERRQ(ierr);
if (fd->complete_print) {
MPI_Comm hcomm;
PetscViewer viewer;
ierr = PetscPrintf(comm,"Hand-coded Hessian\n");CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)B,&hcomm);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetStdout(hcomm,&viewer);CHKERRQ(ierr);
ierr = MatView(A,viewer);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Hand-coded minus finite difference Hessian\n");CHKERRQ(ierr);
ierr = MatView(B,viewer);CHKERRQ(ierr);
}
if (!gnorm) gnorm = 1.0e-20;
ierr = PetscPrintf(comm,"ratio ||fd-hc||/||hc|| = %g, difference ||fd-hc|| = %g\n",(double)(nrm/gnorm),(double)nrm);CHKERRQ(ierr);
}
ierr = MatDestroy(&B);CHKERRQ(ierr);
}
tao->reason = TAO_CONVERGED_USER;
PetscFunctionReturn(0);
}
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_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_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_BQPIP(Tao tao)
{
TAO_BQPIP *qp = (TAO_BQPIP*)tao->data;
PetscErrorCode ierr;
PetscInt iter=0,its;
PetscReal d1,d2,ksptol,sigma;
PetscReal sigmamu;
PetscReal dstep,pstep,step=0;
PetscReal gap[4];
TaoConvergedReason reason;
PetscFunctionBegin;
qp->dobj = 0.0;
qp->pobj = 1.0;
qp->gap = 10.0;
qp->rgap = 1.0;
qp->mu = 1.0;
qp->sigma = 1.0;
qp->dinfeas = 1.0;
qp->psteplength = 0.0;
qp->dsteplength = 0.0;
/* Tighten infinite bounds, things break when we don't do this
-- see test_bqpip.c
*/
ierr = VecSet(qp->XU,1.0e20);CHKERRQ(ierr);
ierr = VecSet(qp->XL,-1.0e20);CHKERRQ(ierr);
ierr = VecPointwiseMax(qp->XL,qp->XL,tao->XL);CHKERRQ(ierr);
ierr = VecPointwiseMin(qp->XU,qp->XU,tao->XU);CHKERRQ(ierr);
ierr = TaoComputeObjectiveAndGradient(tao,tao->solution,&qp->c,qp->C0);CHKERRQ(ierr);
ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
ierr = MatMult(tao->hessian, tao->solution, qp->Work);CHKERRQ(ierr);
ierr = VecDot(tao->solution, qp->Work, &d1);CHKERRQ(ierr);
ierr = VecAXPY(qp->C0, -1.0, qp->Work);CHKERRQ(ierr);
ierr = VecDot(qp->C0, tao->solution, &d2);CHKERRQ(ierr);
qp->c -= (d1/2.0+d2);
ierr = MatGetDiagonal(tao->hessian, qp->HDiag);CHKERRQ(ierr);
ierr = QPIPSetInitialPoint(qp,tao);CHKERRQ(ierr);
ierr = QPIPComputeResidual(qp,tao);CHKERRQ(ierr);
/* Enter main loop */
while (1){
/* Check Stopping Condition */
ierr = TaoMonitor(tao,iter++,qp->pobj,PetscSqrtScalar(qp->gap + qp->dinfeas),
qp->pinfeas, step, &reason);CHKERRQ(ierr);
if (reason != TAO_CONTINUE_ITERATING) break;
/*
Dual Infeasibility Direction should already be in the right
hand side from computing the residuals
*/
ierr = QPIPComputeNormFromCentralPath(qp,&d1);CHKERRQ(ierr);
if (iter > 0 && (qp->rnorm>5*qp->mu || d1*d1>qp->m*qp->mu*qp->mu) ) {
sigma=1.0;sigmamu=qp->mu;
sigma=0.0;sigmamu=0;
} else {
sigma=0.0;sigmamu=0;
}
ierr = VecSet(qp->DZ, sigmamu);CHKERRQ(ierr);
ierr = VecSet(qp->DS, sigmamu);CHKERRQ(ierr);
if (sigmamu !=0){
ierr = VecPointwiseDivide(qp->DZ, qp->DZ, qp->G);CHKERRQ(ierr);
ierr = VecPointwiseDivide(qp->DS, qp->DS, qp->T);CHKERRQ(ierr);
ierr = VecCopy(qp->DZ,qp->RHS2);CHKERRQ(ierr);
ierr = VecAXPY(qp->RHS2, 1.0, qp->DS);CHKERRQ(ierr);
} else {
ierr = VecZeroEntries(qp->RHS2);CHKERRQ(ierr);
}
/*
Compute the Primal Infeasiblitiy RHS and the
Diagonal Matrix to be added to H and store in Work
*/
ierr = VecPointwiseDivide(qp->DiagAxpy, qp->Z, qp->G);CHKERRQ(ierr);
ierr = VecPointwiseMult(qp->GZwork, qp->DiagAxpy, qp->R3);CHKERRQ(ierr);
ierr = VecAXPY(qp->RHS, -1.0, qp->GZwork);CHKERRQ(ierr);
ierr = VecPointwiseDivide(qp->TSwork, qp->S, qp->T);CHKERRQ(ierr);
ierr = VecAXPY(qp->DiagAxpy, 1.0, qp->TSwork);CHKERRQ(ierr);
ierr = VecPointwiseMult(qp->TSwork, qp->TSwork, qp->R5);CHKERRQ(ierr);
ierr = VecAXPY(qp->RHS, -1.0, qp->TSwork);CHKERRQ(ierr);
ierr = VecAXPY(qp->RHS2, 1.0, qp->RHS);CHKERRQ(ierr);
/* Determine the solving tolerance */
ksptol = qp->mu/10.0;
ksptol = PetscMin(ksptol,0.001);
ierr = MatDiagonalSet(tao->hessian, qp->DiagAxpy, ADD_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(tao->hessian,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(tao->hessian,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = KSPSetOperators(tao->ksp, tao->hessian, tao->hessian_pre);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp, qp->RHS, tao->stepdirection);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
tao->ksp_its+=its;
ierr = VecScale(qp->DiagAxpy, -1.0);CHKERRQ(ierr);
ierr = MatDiagonalSet(tao->hessian, qp->DiagAxpy, ADD_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(tao->hessian,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(tao->hessian,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecScale(qp->DiagAxpy, -1.0);CHKERRQ(ierr);
ierr = QPComputeStepDirection(qp,tao);CHKERRQ(ierr);
ierr = QPStepLength(qp); CHKERRQ(ierr);
/* Calculate New Residual R1 in Work vector */
ierr = MatMult(tao->hessian, tao->stepdirection, qp->RHS2);CHKERRQ(ierr);
ierr = VecAXPY(qp->RHS2, 1.0, qp->DS);CHKERRQ(ierr);
ierr = VecAXPY(qp->RHS2, -1.0, qp->DZ);CHKERRQ(ierr);
ierr = VecAYPX(qp->RHS2, qp->dsteplength, tao->gradient);CHKERRQ(ierr);
ierr = VecNorm(qp->RHS2, NORM_2, &qp->dinfeas);CHKERRQ(ierr);
ierr = VecDot(qp->DZ, qp->DG, gap);CHKERRQ(ierr);
ierr = VecDot(qp->DS, qp->DT, gap+1);CHKERRQ(ierr);
qp->rnorm=(qp->dinfeas+qp->psteplength*qp->pinfeas)/(qp->m+qp->n);
pstep = qp->psteplength; dstep = qp->dsteplength;
step = PetscMin(qp->psteplength,qp->dsteplength);
sigmamu= ( pstep*pstep*(gap[0]+gap[1]) +
(1 - pstep + pstep*sigma)*qp->gap )/qp->m;
if (qp->predcorr && step < 0.9){
if (sigmamu < qp->mu){
sigmamu=sigmamu/qp->mu;
sigmamu=sigmamu*sigmamu*sigmamu;
} else {sigmamu = 1.0;}
sigmamu = sigmamu*qp->mu;
/* Compute Corrector Step */
ierr = VecPointwiseMult(qp->DZ, qp->DG, qp->DZ);CHKERRQ(ierr);
ierr = VecScale(qp->DZ, -1.0);CHKERRQ(ierr);
ierr = VecShift(qp->DZ, sigmamu);CHKERRQ(ierr);
ierr = VecPointwiseDivide(qp->DZ, qp->DZ, qp->G);CHKERRQ(ierr);
ierr = VecPointwiseMult(qp->DS, qp->DS, qp->DT);CHKERRQ(ierr);
ierr = VecScale(qp->DS, -1.0);CHKERRQ(ierr);
ierr = VecShift(qp->DS, sigmamu);CHKERRQ(ierr);
ierr = VecPointwiseDivide(qp->DS, qp->DS, qp->T);CHKERRQ(ierr);
ierr = VecCopy(qp->DZ, qp->RHS2);CHKERRQ(ierr);
ierr = VecAXPY(qp->RHS2, -1.0, qp->DS);CHKERRQ(ierr);
ierr = VecAXPY(qp->RHS2, 1.0, qp->RHS);CHKERRQ(ierr);
/* Approximately solve the linear system */
ierr = MatDiagonalSet(tao->hessian, qp->DiagAxpy, ADD_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(tao->hessian,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(tao->hessian,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp, qp->RHS2, tao->stepdirection);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
tao->ksp_its+=its;
ierr = MatDiagonalSet(tao->hessian, qp->HDiag, INSERT_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(tao->hessian,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(tao->hessian,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = QPComputeStepDirection(qp,tao);CHKERRQ(ierr);
ierr = QPStepLength(qp);CHKERRQ(ierr);
} /* End Corrector step */
/* Take the step */
pstep = qp->psteplength; dstep = qp->dsteplength;
ierr = VecAXPY(qp->Z, dstep, qp->DZ);CHKERRQ(ierr);
ierr = VecAXPY(qp->S, dstep, qp->DS);CHKERRQ(ierr);
ierr = VecAXPY(tao->solution, dstep, tao->stepdirection);CHKERRQ(ierr);
ierr = VecAXPY(qp->G, dstep, qp->DG);CHKERRQ(ierr);
ierr = VecAXPY(qp->T, dstep, qp->DT);CHKERRQ(ierr);
/* Compute Residuals */
ierr = QPIPComputeResidual(qp,tao);CHKERRQ(ierr);
/* Evaluate quadratic function */
ierr = MatMult(tao->hessian, tao->solution, qp->Work);CHKERRQ(ierr);
ierr = VecDot(tao->solution, qp->Work, &d1);CHKERRQ(ierr);
ierr = VecDot(tao->solution, qp->C0, &d2);CHKERRQ(ierr);
ierr = VecDot(qp->G, qp->Z, gap);CHKERRQ(ierr);
ierr = VecDot(qp->T, qp->S, gap+1);CHKERRQ(ierr);
qp->pobj=d1/2.0 + d2+qp->c;
/* Compute the duality gap */
qp->gap = (gap[0]+gap[1]);
qp->dobj = qp->pobj - qp->gap;
if (qp->m>0) qp->mu=qp->gap/(qp->m);
qp->rgap=qp->gap/( PetscAbsReal(qp->dobj) + PetscAbsReal(qp->pobj) + 1.0 );
} /* END MAIN LOOP */
PetscFunctionReturn(0);
}