static PetscErrorCode TaoComputeDual_GPCG(Tao tao, Vec DXL, Vec DXU)
{
TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, gpcg->Work);CHKERRQ(ierr);
ierr = VecCopy(gpcg->Work, DXL);CHKERRQ(ierr);
ierr = VecAXPY(DXL,-1.0,tao->gradient);CHKERRQ(ierr);
ierr = VecSet(DXU,0.0);CHKERRQ(ierr);
ierr = VecPointwiseMax(DXL,DXL,DXU);CHKERRQ(ierr);
ierr = VecCopy(tao->gradient,DXU);CHKERRQ(ierr);
ierr = VecAXPY(DXU,-1.0,gpcg->Work);CHKERRQ(ierr);
ierr = VecSet(gpcg->Work,0.0);CHKERRQ(ierr);
ierr = VecPointwiseMin(DXU,gpcg->Work,DXU);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode TaoComputeDual_TRON(Tao tao, Vec DXL, Vec DXU) {
TAO_TRON *tron = (TAO_TRON *)tao->data;
PetscErrorCode ierr;
PetscFunctionBegin;
PetscValidHeaderSpecific(tao,TAO_CLASSID,1);
PetscValidHeaderSpecific(DXL,VEC_CLASSID,2);
PetscValidHeaderSpecific(DXU,VEC_CLASSID,3);
if (!tron->Work || !tao->gradient) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Dual variables don't exist yet or no longer exist.\n");
ierr = VecBoundGradientProjection(tao->gradient,tao->solution,tao->XL,tao->XU,tron->Work);CHKERRQ(ierr);
ierr = VecCopy(tron->Work,DXL);CHKERRQ(ierr);
ierr = VecAXPY(DXL,-1.0,tao->gradient);CHKERRQ(ierr);
ierr = VecSet(DXU,0.0);CHKERRQ(ierr);
ierr = VecPointwiseMax(DXL,DXL,DXU);CHKERRQ(ierr);
ierr = VecCopy(tao->gradient,DXU);CHKERRQ(ierr);
ierr = VecAXPY(DXU,-1.0,tron->Work);CHKERRQ(ierr);
ierr = VecSet(tron->Work,0.0);CHKERRQ(ierr);
ierr = VecPointwiseMin(DXU,tron->Work,DXU);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode TaoPounders_solvequadratic(Tao tao,PetscReal *gnorm, PetscReal *qmin)
{
PetscErrorCode ierr;
#if defined(PETSC_USE_REAL_SINGLE)
PetscReal atol=1.0e-5;
#else
PetscReal atol=1.0e-10;
#endif
PetscInt info,its;
TAO_POUNDERS *mfqP = (TAO_POUNDERS*)tao->data;
PetscReal maxval;
PetscInt i,j;
PetscFunctionBegin;
ierr = VecCopy(mfqP->Gres, mfqP->subb);CHKERRQ(ierr);
ierr = VecSet(mfqP->subx,0.0);CHKERRQ(ierr);
ierr = VecSet(mfqP->subndel,-mfqP->delta);CHKERRQ(ierr);
ierr = VecSet(mfqP->subpdel,mfqP->delta);CHKERRQ(ierr);
ierr = MatCopy(mfqP->Hres,mfqP->subH,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = TaoResetStatistics(mfqP->subtao);CHKERRQ(ierr);
ierr = TaoSetTolerances(mfqP->subtao,NULL,NULL,*gnorm,*gnorm,NULL);CHKERRQ(ierr);
/* enforce bound constraints -- experimental */
if (tao->XU && tao->XL) {
ierr = VecCopy(tao->XU,mfqP->subxu);CHKERRQ(ierr);
ierr = VecAXPY(mfqP->subxu,-1.0,tao->solution);CHKERRQ(ierr);
ierr = VecScale(mfqP->subxu,1.0/mfqP->delta);CHKERRQ(ierr);
ierr = VecCopy(tao->XL,mfqP->subxl);CHKERRQ(ierr);
ierr = VecAXPY(mfqP->subxl,-1.0,tao->solution);CHKERRQ(ierr);
ierr = VecScale(mfqP->subxl,1.0/mfqP->delta);CHKERRQ(ierr);
ierr = VecPointwiseMin(mfqP->subxu,mfqP->subxu,mfqP->subpdel);CHKERRQ(ierr);
ierr = VecPointwiseMax(mfqP->subxl,mfqP->subxl,mfqP->subndel);CHKERRQ(ierr);
} else {
ierr = VecCopy(mfqP->subpdel,mfqP->subxu);CHKERRQ(ierr);
ierr = VecCopy(mfqP->subndel,mfqP->subxl);CHKERRQ(ierr);
}
/* Make sure xu > xl */
ierr = VecCopy(mfqP->subxl,mfqP->subpdel);CHKERRQ(ierr);
ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu); CHKERRQ(ierr);
ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
if (maxval > 1e-10) {
SETERRQ(PETSC_COMM_WORLD,1,"upper bound < lower bound in subproblem");
}
/* Make sure xu > tao->solution > xl */
ierr = VecCopy(mfqP->subxl,mfqP->subpdel);CHKERRQ(ierr);
ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subx); CHKERRQ(ierr);
ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
if (maxval > 1e-10) {
SETERRQ(PETSC_COMM_WORLD,1,"initial guess < lower bound in subproblem");
}
ierr = VecCopy(mfqP->subx,mfqP->subpdel);CHKERRQ(ierr);
ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu); CHKERRQ(ierr);
ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
if (maxval > 1e-10) {
SETERRQ(PETSC_COMM_WORLD,1,"initial guess > upper bound in subproblem");
}
ierr = TaoSolve(mfqP->subtao);CHKERRQ(ierr);
ierr = TaoGetSolutionStatus(mfqP->subtao,NULL,qmin,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
/* test bounds post-solution*/
ierr = VecCopy(mfqP->subxl,mfqP->subpdel);CHKERRQ(ierr);
ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subx); CHKERRQ(ierr);
ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
if (maxval > 1e-5) {
ierr = PetscInfo(tao,"subproblem solution < lower bound");CHKERRQ(ierr);
tao->reason = TAO_DIVERGED_TR_REDUCTION;
}
ierr = VecCopy(mfqP->subx,mfqP->subpdel);CHKERRQ(ierr);
ierr = VecAXPY(mfqP->subpdel,-1.0,mfqP->subxu); CHKERRQ(ierr);
ierr = VecMax(mfqP->subpdel,NULL,&maxval);CHKERRQ(ierr);
if (maxval > 1e-5) {
ierr = PetscInfo(tao,"subproblem solution > upper bound");
tao->reason = TAO_DIVERGED_TR_REDUCTION;
}
*qmin *= -1;
PetscFunctionReturn(0);
}
void PETSC_STDCALL vecpointwisemin_(Vec w,Vec x,Vec y, int *__ierr ){
*__ierr = VecPointwiseMin(
(Vec)PetscToPointer((w) ),
(Vec)PetscToPointer((x) ),
(Vec)PetscToPointer((y) ));
}
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);
}
