Actual source code: bnk.c
petsc-3.10.5 2019-03-28
Report Typos and Errors

      1:  #include <petsctaolinesearch.h>
      2:  #include <../src/tao/bound/impls/bnk/bnk.h>
      3:  #include <petscksp.h>

      5: static const char *BNK_INIT[64] = {"constant", "direction", "interpolation"};
      6: static const char *BNK_UPDATE[64] = {"step", "reduction", "interpolation"};
      7: static const char *BNK_AS[64] = {"none", "bertsekas"};

      9: /*------------------------------------------------------------*/

     11: /* Routine for initializing the KSP solver, the BFGS preconditioner, and the initial trust radius estimation */

     13: PetscErrorCode TaoBNKInitialize(Tao tao, PetscInt initType, PetscBool *needH)
     14: {
     15:   PetscErrorCode               ierr;
     16:   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
     17:   PC                           pc;

     19:   PetscReal                    f_min, ftrial, prered, actred, kappa, sigma, resnorm;
     20:   PetscReal                    tau, tau_1, tau_2, tau_max, tau_min, max_radius;
     21:   PetscBool                    is_bfgs, is_jacobi, is_symmetric, sym_set;
     22:   PetscInt                     n, N, nDiff;
     23:   PetscInt                     i_max = 5;
     24:   PetscInt                     j_max = 1;
     25:   PetscInt                     i, j;

     28:   /* Project the current point onto the feasible set */
     29:   TaoComputeVariableBounds(tao);
     30:   TaoSetVariableBounds(bnk->bncg, tao->XL, tao->XU);
     31:   if (tao->bounded) {
     32:     TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);
     33:   }

     35:   /* Project the initial point onto the feasible region */
     36:   TaoBoundSolution(tao->solution, tao->XL,tao->XU, 0.0, &nDiff, tao->solution);

     38:   /* Check convergence criteria */
     39:   TaoComputeObjectiveAndGradient(tao, tao->solution, &bnk->f, bnk->unprojected_gradient);
     40:   TaoBNKEstimateActiveSet(tao, bnk->as_type);
     41:   VecCopy(bnk->unprojected_gradient, tao->gradient);
     42:   VecISSet(tao->gradient, bnk->active_idx, 0.0);
     43:   TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);

     45:   /* Test the initial point for convergence */
     46:   VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W);
     47:   VecNorm(bnk->W, NORM_2, &resnorm);
     48:   if (PetscIsInfOrNanReal(bnk->f) || PetscIsInfOrNanReal(resnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
     49:   TaoLogConvergenceHistory(tao,bnk->f,resnorm,0.0,tao->ksp_its);
     50:   TaoMonitor(tao,tao->niter,bnk->f,resnorm,0.0,1.0);
     51:   (*tao->ops->convergencetest)(tao,tao->cnvP);
     52:   if (tao->reason != TAO_CONTINUE_ITERATING) return(0);
     53:
     54:   /* Reset KSP stopping reason counters */
     55:   bnk->ksp_atol = 0;
     56:   bnk->ksp_rtol = 0;
     57:   bnk->ksp_dtol = 0;
     58:   bnk->ksp_ctol = 0;
     59:   bnk->ksp_negc = 0;
     60:   bnk->ksp_iter = 0;
     61:   bnk->ksp_othr = 0;
     62:
     63:   /* Reset accepted step type counters */
     64:   bnk->tot_cg_its = 0;
     65:   bnk->newt = 0;
     66:   bnk->bfgs = 0;
     67:   bnk->sgrad = 0;
     68:   bnk->grad = 0;
     69:
     70:   /* Initialize the Hessian perturbation */
     71:   bnk->pert = bnk->sval;
     72:
     73:   /* Reset initial steplength to zero (this helps BNCG reset its direction internally) */
     74:   VecSet(tao->stepdirection, 0.0);

     76:   /* Allocate the vectors needed for the BFGS approximation */
     77:   KSPGetPC(tao->ksp, &pc);
     78:   PetscObjectTypeCompare((PetscObject)pc, PCLMVM, &is_bfgs);
     79:   PetscObjectTypeCompare((PetscObject)pc, PCJACOBI, &is_jacobi);
     80:   if (is_bfgs) {
     81:     bnk->bfgs_pre = pc;
     82:     PCLMVMGetMatLMVM(bnk->bfgs_pre, &bnk->M);
     83:     VecGetLocalSize(tao->solution, &n);
     84:     VecGetSize(tao->solution, &N);
     85:     MatSetSizes(bnk->M, n, n, N, N);
     86:     MatLMVMAllocate(bnk->M, tao->solution, bnk->unprojected_gradient);
     87:     MatIsSymmetricKnown(bnk->M, &sym_set, &is_symmetric);
     88:     if (!sym_set || !is_symmetric) SETERRQ(PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_INCOMP, "LMVM matrix in the LMVM preconditioner must be symmetric.");
     89:   } else if (is_jacobi) {
     90:     PCJacobiSetUseAbs(pc,PETSC_TRUE);
     91:   }
     92:
     93:   /* Prepare the min/max vectors for safeguarding diagonal scales */
     94:   VecSet(bnk->Diag_min, bnk->dmin);
     95:   VecSet(bnk->Diag_max, bnk->dmax);

     97:   /* Initialize trust-region radius.  The initialization is only performed
     98:      when we are using Nash, Steihaug-Toint or the Generalized Lanczos method. */
     99:   *needH = PETSC_TRUE;
    100:   if (bnk->is_nash || bnk->is_stcg || bnk->is_gltr) {
    101:     switch(initType) {
    102:     case BNK_INIT_CONSTANT:
    103:       /* Use the initial radius specified */
    104:       tao->trust = tao->trust0;
    105:       break;

    107:     case BNK_INIT_INTERPOLATION:
    108:       /* Use interpolation based on the initial Hessian */
    109:       max_radius = 0.0;
    110:       tao->trust = tao->trust0;
    111:       for (j = 0; j < j_max; ++j) {
    112:         f_min = bnk->f;
    113:         sigma = 0.0;

    115:         if (*needH) {
    116:           /* Compute the Hessian at the new step, and extract the inactive subsystem */
    117:           bnk->computehessian(tao);
    118:           TaoBNKEstimateActiveSet(tao, BNK_AS_NONE);
    119:           MatDestroy(&bnk->H_inactive);
    120:           if (bnk->active_idx) {
    121:             MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive);
    122:           } else {
    123:             MatDuplicate(tao->hessian, MAT_COPY_VALUES, &bnk->H_inactive);
    124:           }
    125:           *needH = PETSC_FALSE;
    126:         }

    128:         for (i = 0; i < i_max; ++i) {
    129:           /* Take a steepest descent step and snap it to bounds */
    130:           VecCopy(tao->solution, bnk->Xold);
    131:           VecAXPY(tao->solution, -tao->trust/bnk->gnorm, tao->gradient);
    132:           TaoBoundSolution(tao->solution, tao->XL,tao->XU, 0.0, &nDiff, tao->solution);
    133:           /* Compute the step we actually accepted */
    134:           VecCopy(tao->solution, bnk->W);
    135:           VecAXPY(bnk->W, -1.0, bnk->Xold);
    136:           /* Compute the objective at the trial */
    137:           TaoComputeObjective(tao, tao->solution, &ftrial);
    138:           if (PetscIsInfOrNanReal(bnk->f)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
    139:           VecCopy(bnk->Xold, tao->solution);
    140:           if (PetscIsInfOrNanReal(ftrial)) {
    141:             tau = bnk->gamma1_i;
    142:           } else {
    143:             if (ftrial < f_min) {
    144:               f_min = ftrial;
    145:               sigma = -tao->trust / bnk->gnorm;
    146:             }
    147:
    148:             /* Compute the predicted and actual reduction */
    149:             if (bnk->active_idx) {
    150:               VecGetSubVector(bnk->W, bnk->inactive_idx, &bnk->X_inactive);
    151:               VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);
    152:             } else {
    153:               bnk->X_inactive = bnk->W;
    154:               bnk->inactive_work = bnk->Xwork;
    155:             }
    156:             MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work);
    157:             VecDot(bnk->X_inactive, bnk->inactive_work, &prered);
    158:             if (bnk->active_idx) {
    159:               VecRestoreSubVector(bnk->W, bnk->inactive_idx, &bnk->X_inactive);
    160:               VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);
    161:             }
    162:             prered = tao->trust * (bnk->gnorm - 0.5 * tao->trust * prered / (bnk->gnorm * bnk->gnorm));
    163:             actred = bnk->f - ftrial;
    164:             if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) {
    165:               kappa = 1.0;
    166:             } else {
    167:               kappa = actred / prered;
    168:             }

    170:             tau_1 = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust + (1.0 - bnk->theta_i) * prered - actred);
    171:             tau_2 = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust - (1.0 + bnk->theta_i) * prered + actred);
    172:             tau_min = PetscMin(tau_1, tau_2);
    173:             tau_max = PetscMax(tau_1, tau_2);

    175:             if (PetscAbsScalar(kappa - 1.0) <= bnk->mu1_i) {
    176:               /*  Great agreement */
    177:               max_radius = PetscMax(max_radius, tao->trust);

    179:               if (tau_max < 1.0) {
    180:                 tau = bnk->gamma3_i;
    181:               } else if (tau_max > bnk->gamma4_i) {
    182:                 tau = bnk->gamma4_i;
    183:               } else {
    184:                 tau = tau_max;
    185:               }
    186:             } else if (PetscAbsScalar(kappa - 1.0) <= bnk->mu2_i) {
    187:               /*  Good agreement */
    188:               max_radius = PetscMax(max_radius, tao->trust);

    190:               if (tau_max < bnk->gamma2_i) {
    191:                 tau = bnk->gamma2_i;
    192:               } else if (tau_max > bnk->gamma3_i) {
    193:                 tau = bnk->gamma3_i;
    194:               } else {
    195:                 tau = tau_max;
    196:               }
    197:             } else {
    198:               /*  Not good agreement */
    199:               if (tau_min > 1.0) {
    200:                 tau = bnk->gamma2_i;
    201:               } else if (tau_max < bnk->gamma1_i) {
    202:                 tau = bnk->gamma1_i;
    203:               } else if ((tau_min < bnk->gamma1_i) && (tau_max >= 1.0)) {
    204:                 tau = bnk->gamma1_i;
    205:               } else if ((tau_1 >= bnk->gamma1_i) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
    206:                 tau = tau_1;
    207:               } else if ((tau_2 >= bnk->gamma1_i) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
    208:                 tau = tau_2;
    209:               } else {
    210:                 tau = tau_max;
    211:               }
    212:             }
    213:           }
    214:           tao->trust = tau * tao->trust;
    215:         }

    217:         if (f_min < bnk->f) {
    218:           /* We accidentally found a solution better than the initial, so accept it */
    219:           bnk->f = f_min;
    220:           VecCopy(tao->solution, bnk->Xold);
    221:           VecAXPY(tao->solution,sigma,tao->gradient);
    222:           TaoBoundSolution(tao->solution, tao->XL,tao->XU, 0.0, &nDiff, tao->solution);
    223:           VecCopy(tao->solution, tao->stepdirection);
    224:           VecAXPY(tao->stepdirection, -1.0, bnk->Xold);
    225:           TaoComputeGradient(tao,tao->solution,bnk->unprojected_gradient);
    226:           TaoBNKEstimateActiveSet(tao, bnk->as_type);
    227:           VecCopy(bnk->unprojected_gradient, tao->gradient);
    228:           VecISSet(tao->gradient, bnk->active_idx, 0.0);
    229:           /* Compute gradient at the new iterate and flip switch to compute the Hessian later */
    230:           TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);
    231:           *needH = PETSC_TRUE;
    232:           /* Test the new step for convergence */
    233:           VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W);
    234:           VecNorm(bnk->W, NORM_2, &resnorm);
    235:           if (PetscIsInfOrNanReal(resnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
    236:           TaoLogConvergenceHistory(tao,bnk->f,resnorm,0.0,tao->ksp_its);
    237:           TaoMonitor(tao,tao->niter,bnk->f,resnorm,0.0,1.0);
    238:           (*tao->ops->convergencetest)(tao,tao->cnvP);
    239:           if (tao->reason != TAO_CONTINUE_ITERATING) return(0);
    240:           /* active BNCG recycling early because we have a stepdirection computed */
    241:           TaoBNCGSetRecycleFlag(bnk->bncg, PETSC_TRUE);
    242:         }
    243:       }
    244:       tao->trust = PetscMax(tao->trust, max_radius);
    245:
    246:       /* Ensure that the trust radius is within the limits */
    247:       tao->trust = PetscMax(tao->trust, bnk->min_radius);
    248:       tao->trust = PetscMin(tao->trust, bnk->max_radius);
    249:       break;

    251:     default:
    252:       /* Norm of the first direction will initialize radius */
    253:       tao->trust = 0.0;
    254:       break;
    255:     }
    256:   }
    257:   return(0);
    258: }

    260: /*------------------------------------------------------------*/

    262: /* Routine for computing the exact Hessian and preparing the preconditioner at the new iterate */

    264: PetscErrorCode TaoBNKComputeHessian(Tao tao)
    265: {
    266:   PetscErrorCode               ierr;
    267:   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;

    270:   /* Compute the Hessian */
    271:   TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);
    272:   /* Add a correction to the BFGS preconditioner */
    273:   if (bnk->M) {
    274:     MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);
    275:   }
    276:   /* Prepare the reduced sub-matrices for the inactive set */
    277:   if (bnk->Hpre_inactive) {
    278:     MatDestroy(&bnk->Hpre_inactive);
    279:   }
    280:   if (bnk->H_inactive) {
    281:     MatDestroy(&bnk->H_inactive);
    282:   }
    283:   if (bnk->active_idx) {
    284:     MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive);
    285:     if (tao->hessian == tao->hessian_pre) {
    286:       PetscObjectReference((PetscObject)bnk->H_inactive);
    287:       bnk->Hpre_inactive = bnk->H_inactive;
    288:     } else {
    289:       MatCreateSubMatrix(tao->hessian_pre, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->Hpre_inactive);
    290:     }
    291:     if (bnk->bfgs_pre) {
    292:       PCLMVMSetIS(bnk->bfgs_pre, bnk->inactive_idx);
    293:     }
    294:   } else {
    295:     MatDuplicate(tao->hessian, MAT_COPY_VALUES, &bnk->H_inactive);
    296:     if (tao->hessian == tao->hessian_pre) {
    297:       PetscObjectReference((PetscObject)bnk->H_inactive);
    298:       bnk->Hpre_inactive = bnk->H_inactive;
    299:     } else {
    300:       MatDuplicate(tao->hessian_pre, MAT_COPY_VALUES, &bnk->Hpre_inactive);
    301:     }
    302:     if (bnk->bfgs_pre) {
    303:       PCLMVMClearIS(bnk->bfgs_pre);
    304:     }
    305:   }
    306:   return(0);
    307: }

    309: /*------------------------------------------------------------*/

    311: /* Routine for estimating the active set */

    313: PetscErrorCode TaoBNKEstimateActiveSet(Tao tao, PetscInt asType)
    314: {
    315:   PetscErrorCode               ierr;
    316:   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
    317:   PetscBool                    hessComputed, diagExists;

    320:   switch (asType) {
    321:   case BNK_AS_NONE:
    322:     ISDestroy(&bnk->inactive_idx);
    323:     VecWhichInactive(tao->XL, tao->solution, bnk->unprojected_gradient, tao->XU, PETSC_TRUE, &bnk->inactive_idx);
    324:     ISDestroy(&bnk->active_idx);
    325:     ISComplementVec(bnk->inactive_idx, tao->solution, &bnk->active_idx);
    326:     break;

    328:   case BNK_AS_BERTSEKAS:
    329:     /* Compute the trial step vector with which we will estimate the active set at the next iteration */
    330:     if (bnk->M) {
    331:       /* If the BFGS preconditioner matrix is available, we will construct a trial step with it */
    332:       MatSolve(bnk->M, bnk->unprojected_gradient, bnk->W);
    333:     } else {
    334:       if (tao->hessian) {
    335:         MatAssembled(tao->hessian, &hessComputed);
    336:         MatHasOperation(tao->hessian, MATOP_GET_DIAGONAL, &diagExists);
    337:       } else {
    338:         hessComputed = diagExists = PETSC_FALSE;
    339:       }
    340:       if (hessComputed && diagExists) {
    341:         /* BFGS preconditioner doesn't exist so let's invert the absolute diagonal of the Hessian instead onto the gradient */
    342:         MatGetDiagonal(tao->hessian, bnk->Xwork);
    343:         VecAbs(bnk->Xwork);
    344:         VecMedian(bnk->Diag_min, bnk->Xwork, bnk->Diag_max, bnk->Xwork);
    345:         VecReciprocal(bnk->Xwork);
    346:         VecPointwiseMult(bnk->W, bnk->Xwork, bnk->unprojected_gradient);
    347:       } else {
    348:         /* If the Hessian or its diagonal does not exist, we will simply use gradient step */
    349:         VecCopy(bnk->unprojected_gradient, bnk->W);
    350:       }
    351:     }
    352:     VecScale(bnk->W, -1.0);
    353:     TaoEstimateActiveBounds(tao->solution, tao->XL, tao->XU, bnk->unprojected_gradient, bnk->W, bnk->Xwork, bnk->as_step, &bnk->as_tol,
    354:                                    &bnk->active_lower, &bnk->active_upper, &bnk->active_fixed, &bnk->active_idx, &bnk->inactive_idx);
    355:     break;
    356:
    357:   default:
    358:     break;
    359:   }
    360:   return(0);
    361: }

    363: /*------------------------------------------------------------*/

    365: /* Routine for bounding the step direction */

    367: PetscErrorCode TaoBNKBoundStep(Tao tao, PetscInt asType, Vec step)
    368: {
    369:   PetscErrorCode               ierr;
    370:   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
    371:
    373:   switch (asType) {
    374:   case BNK_AS_NONE:
    375:     VecISSet(step, bnk->active_idx, 0.0);
    376:     break;

    378:   case BNK_AS_BERTSEKAS:
    379:     TaoBoundStep(tao->solution, tao->XL, tao->XU, bnk->active_lower, bnk->active_upper, bnk->active_fixed, 1.0, step);
    380:     break;

    382:   default:
    383:     break;
    384:   }
    385:   return(0);
    386: }

    388: /*------------------------------------------------------------*/

    390: /* Routine for taking a finite number of BNCG iterations to
    391:    accelerate Newton convergence.
    392:
    393:    In practice, this approach simply trades off Hessian evaluations
    394:    for more gradient evaluations.
    395: */

    397: PetscErrorCode TaoBNKTakeCGSteps(Tao tao, PetscBool *terminate)
    398: {
    399:   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
    400:   PetscErrorCode               ierr;
    401:
    403:   *terminate = PETSC_FALSE;
    404:   if (bnk->max_cg_its > 0) {
    405:     /* Copy the current function value (important vectors are already shared) */
    406:     bnk->bncg_ctx->f = bnk->f;
    407:     /* Take some small finite number of BNCG iterations */
    408:     TaoSolve(bnk->bncg);
    409:     /* Add the number of gradient and function evaluations to the total */
    410:     tao->nfuncs += bnk->bncg->nfuncs;
    411:     tao->nfuncgrads += bnk->bncg->nfuncgrads;
    412:     tao->ngrads += bnk->bncg->ngrads;
    413:     tao->nhess += bnk->bncg->nhess;
    414:     bnk->tot_cg_its += bnk->bncg->niter;
    415:     /* Extract the BNCG function value out and save it into BNK */
    416:     bnk->f = bnk->bncg_ctx->f;
    417:     if (bnk->bncg->reason == TAO_CONVERGED_GATOL || bnk->bncg->reason == TAO_CONVERGED_GRTOL || bnk->bncg->reason == TAO_CONVERGED_GTTOL || bnk->bncg->reason == TAO_CONVERGED_MINF) {
    418:       *terminate = PETSC_TRUE;
    419:     } else {
    420:       TaoBNKEstimateActiveSet(tao, bnk->as_type);
    421:     }
    422:   }
    423:   return(0);
    424: }

    426: /*------------------------------------------------------------*/

    428: /* Routine for computing the Newton step. */

    430: PetscErrorCode TaoBNKComputeStep(Tao tao, PetscBool shift, KSPConvergedReason *ksp_reason, PetscInt *step_type)
    431: {
    432:   PetscErrorCode               ierr;
    433:   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
    434:   PetscInt                     bfgsUpdates = 0;
    435:   PetscInt                     kspits;
    436:   PetscBool                    is_lmvm;
    437:
    439:   /* If there are no inactive variables left, save some computation and return an adjusted zero step
    440:      that has (l-x) and (u-x) for lower and upper bounded variables. */
    441:   if (!bnk->inactive_idx) {
    442:     VecSet(tao->stepdirection, 0.0);
    443:     TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection);
    444:     return(0);
    445:   }
    446:
    447:   /* Shift the reduced Hessian matrix */
    448:   if ((shift) && (bnk->pert > 0)) {
    449:     PetscObjectTypeCompare((PetscObject)tao->hessian, MATLMVM, &is_lmvm);
    450:     if (is_lmvm) {
    451:       MatShift(tao->hessian, bnk->pert);
    452:     } else {
    453:       MatShift(bnk->H_inactive, bnk->pert);
    454:       if (bnk->H_inactive != bnk->Hpre_inactive) {
    455:         MatShift(bnk->Hpre_inactive, bnk->pert);
    456:       }
    457:     }
    458:   }
    459:
    460:   /* Solve the Newton system of equations */
    461:   tao->ksp_its = 0;
    462:   VecSet(tao->stepdirection, 0.0);
    463:   KSPReset(tao->ksp);
    464:   KSPSetOperators(tao->ksp,bnk->H_inactive,bnk->Hpre_inactive);
    465:   VecCopy(bnk->unprojected_gradient, bnk->Gwork);
    466:   if (bnk->active_idx) {
    467:     VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);
    468:     VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);
    469:   } else {
    470:     bnk->G_inactive = bnk->unprojected_gradient;
    471:     bnk->X_inactive = tao->stepdirection;
    472:   }
    473:   if (bnk->is_nash || bnk->is_stcg || bnk->is_gltr) {
    474:     KSPCGSetRadius(tao->ksp,tao->trust);
    475:     KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);
    476:     KSPGetIterationNumber(tao->ksp,&kspits);
    477:     tao->ksp_its+=kspits;
    478:     tao->ksp_tot_its+=kspits;
    479:     KSPCGGetNormD(tao->ksp,&bnk->dnorm);

    481:     if (0.0 == tao->trust) {
    482:       /* Radius was uninitialized; use the norm of the direction */
    483:       if (bnk->dnorm > 0.0) {
    484:         tao->trust = bnk->dnorm;

    486:         /* Modify the radius if it is too large or small */
    487:         tao->trust = PetscMax(tao->trust, bnk->min_radius);
    488:         tao->trust = PetscMin(tao->trust, bnk->max_radius);
    489:       } else {
    490:         /* The direction was bad; set radius to default value and re-solve
    491:            the trust-region subproblem to get a direction */
    492:         tao->trust = tao->trust0;

    494:         /* Modify the radius if it is too large or small */
    495:         tao->trust = PetscMax(tao->trust, bnk->min_radius);
    496:         tao->trust = PetscMin(tao->trust, bnk->max_radius);

    498:         KSPCGSetRadius(tao->ksp,tao->trust);
    499:         KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);
    500:         KSPGetIterationNumber(tao->ksp,&kspits);
    501:         tao->ksp_its+=kspits;
    502:         tao->ksp_tot_its+=kspits;
    503:         KSPCGGetNormD(tao->ksp,&bnk->dnorm);

    505:         if (bnk->dnorm == 0.0) SETERRQ(PETSC_COMM_SELF,1, "Initial direction zero");
    506:       }
    507:     }
    508:   } else {
    509:     KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);
    510:     KSPGetIterationNumber(tao->ksp, &kspits);
    511:     tao->ksp_its += kspits;
    512:     tao->ksp_tot_its+=kspits;
    513:   }
    514:   /* Restore sub vectors back */
    515:   if (bnk->active_idx) {
    516:     VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);
    517:     VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);
    518:   }
    519:   /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
    520:   VecScale(tao->stepdirection, -1.0);
    521:   TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection);
    522:
    523:   /* Record convergence reasons */
    524:   KSPGetConvergedReason(tao->ksp, ksp_reason);
    525:   if (KSP_CONVERGED_ATOL == *ksp_reason) {
    526:     ++bnk->ksp_atol;
    527:   } else if (KSP_CONVERGED_RTOL == *ksp_reason) {
    528:     ++bnk->ksp_rtol;
    529:   } else if (KSP_CONVERGED_CG_CONSTRAINED == *ksp_reason) {
    530:     ++bnk->ksp_ctol;
    531:   } else if (KSP_CONVERGED_CG_NEG_CURVE == *ksp_reason) {
    532:     ++bnk->ksp_negc;
    533:   } else if (KSP_DIVERGED_DTOL == *ksp_reason) {
    534:     ++bnk->ksp_dtol;
    535:   } else if (KSP_DIVERGED_ITS == *ksp_reason) {
    536:     ++bnk->ksp_iter;
    537:   } else {
    538:     ++bnk->ksp_othr;
    539:   }
    540:
    541:   /* Make sure the BFGS preconditioner is healthy */
    542:   if (bnk->M) {
    543:     MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates);
    544:     if ((KSP_DIVERGED_INDEFINITE_PC == *ksp_reason) && (bfgsUpdates > 0)) {
    545:       /* Preconditioner is numerically indefinite; reset the approximation. */
    546:       MatLMVMReset(bnk->M, PETSC_FALSE);
    547:       MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);
    548:     }
    549:   }
    550:   *step_type = BNK_NEWTON;
    551:   return(0);
    552: }

    554: /*------------------------------------------------------------*/

    556: /* Routine for recomputing the predicted reduction for a given step vector */

    558: PetscErrorCode TaoBNKRecomputePred(Tao tao, Vec S, PetscReal *prered)
    559: {
    560:   PetscErrorCode               ierr;
    561:   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
    562:
    564:   /* Extract subvectors associated with the inactive set */
    565:   if (bnk->active_idx){
    566:     VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);
    567:     VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);
    568:     VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);
    569:   } else {
    570:     bnk->X_inactive = tao->stepdirection;
    571:     bnk->inactive_work = bnk->Xwork;
    572:     bnk->G_inactive = bnk->Gwork;
    573:   }
    574:   /* Recompute the predicted decrease based on the quadratic model */
    575:   MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work);
    576:   VecAYPX(bnk->inactive_work, -0.5, bnk->G_inactive);
    577:   VecDot(bnk->inactive_work, bnk->X_inactive, prered);
    578:   /* Restore the sub vectors */
    579:   if (bnk->active_idx){
    580:     VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);
    581:     VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);
    582:     VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);
    583:   }
    584:   return(0);
    585: }

    587: /*------------------------------------------------------------*/

    589: /* Routine for ensuring that the Newton step is a descent direction.

    591:    The step direction falls back onto BFGS, scaled gradient and gradient steps
    592:    in the event that the Newton step fails the test.
    593: */

    595: PetscErrorCode TaoBNKSafeguardStep(Tao tao, KSPConvergedReason ksp_reason, PetscInt *stepType)
    596: {
    597:   PetscErrorCode               ierr;
    598:   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
    599:
    600:   PetscReal                    gdx, e_min;
    601:   PetscInt                     bfgsUpdates;
    602:
    604:   switch (*stepType) {
    605:   case BNK_NEWTON:
    606:     VecDot(tao->stepdirection, tao->gradient, &gdx);
    607:     if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) {
    608:       /* Newton step is not descent or direction produced Inf or NaN
    609:         Update the perturbation for next time */
    610:       if (bnk->pert <= 0.0) {
    611:         /* Initialize the perturbation */
    612:         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
    613:         if (bnk->is_gltr) {
    614:           KSPCGGLTRGetMinEig(tao->ksp,&e_min);
    615:           bnk->pert = PetscMax(bnk->pert, -e_min);
    616:         }
    617:       } else {
    618:         /* Increase the perturbation */
    619:         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
    620:       }

    622:       if (!bnk->M) {
    623:         /* We don't have the bfgs matrix around and updated
    624:           Must use gradient direction in this case */
    625:         VecCopy(tao->gradient, tao->stepdirection);
    626:         *stepType = BNK_GRADIENT;
    627:       } else {
    628:         /* Attempt to use the BFGS direction */
    629:         MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);

    631:         /* Check for success (descent direction)
    632:           NOTE: Negative gdx here means not a descent direction because
    633:           the fall-back step is missing a negative sign. */
    634:         VecDot(tao->gradient, tao->stepdirection, &gdx);
    635:         if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
    636:           /* BFGS direction is not descent or direction produced not a number
    637:             We can assert bfgsUpdates > 1 in this case because
    638:             the first solve produces the scaled gradient direction,
    639:             which is guaranteed to be descent */

    641:           /* Use steepest descent direction (scaled) */
    642:           MatLMVMReset(bnk->M, PETSC_FALSE);
    643:           MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);
    644:           MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);

    646:           *stepType = BNK_SCALED_GRADIENT;
    647:         } else {
    648:           MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates);
    649:           if (1 == bfgsUpdates) {
    650:             /* The first BFGS direction is always the scaled gradient */
    651:             *stepType = BNK_SCALED_GRADIENT;
    652:           } else {
    653:             *stepType = BNK_BFGS;
    654:           }
    655:         }
    656:       }
    657:       /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
    658:       VecScale(tao->stepdirection, -1.0);
    659:       TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection);
    660:     } else {
    661:       /* Computed Newton step is descent */
    662:       switch (ksp_reason) {
    663:       case KSP_DIVERGED_NANORINF:
    664:       case KSP_DIVERGED_BREAKDOWN:
    665:       case KSP_DIVERGED_INDEFINITE_MAT:
    666:       case KSP_DIVERGED_INDEFINITE_PC:
    667:       case KSP_CONVERGED_CG_NEG_CURVE:
    668:         /* Matrix or preconditioner is indefinite; increase perturbation */
    669:         if (bnk->pert <= 0.0) {
    670:           /* Initialize the perturbation */
    671:           bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
    672:           if (bnk->is_gltr) {
    673:             KSPCGGLTRGetMinEig(tao->ksp, &e_min);
    674:             bnk->pert = PetscMax(bnk->pert, -e_min);
    675:           }
    676:         } else {
    677:           /* Increase the perturbation */
    678:           bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
    679:         }
    680:         break;

    682:       default:
    683:         /* Newton step computation is good; decrease perturbation */
    684:         bnk->pert = PetscMin(bnk->psfac * bnk->pert, bnk->pmsfac * bnk->gnorm);
    685:         if (bnk->pert < bnk->pmin) {
    686:           bnk->pert = 0.0;
    687:         }
    688:         break;
    689:       }
    690:       *stepType = BNK_NEWTON;
    691:     }
    692:     break;
    693:
    694:   case BNK_BFGS:
    695:     /* Check for success (descent direction) */
    696:     VecDot(tao->stepdirection, tao->gradient, &gdx);
    697:     if (gdx >= 0 || PetscIsInfOrNanReal(gdx)) {
    698:       /* Step is not descent or solve was not successful
    699:          Use steepest descent direction (scaled) */
    700:       MatLMVMReset(bnk->M, PETSC_FALSE);
    701:       MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);
    702:       MatSolve(bnk->M, tao->gradient, tao->stepdirection);
    703:       VecScale(tao->stepdirection,-1.0);
    704:       TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection);
    705:       *stepType = BNK_SCALED_GRADIENT;
    706:     } else {
    707:       *stepType = BNK_BFGS;
    708:     }
    709:     break;
    710:
    711:   case BNK_SCALED_GRADIENT:
    712:     break;
    713:
    714:   default:
    715:     break;
    716:   }
    717:
    718:   return(0);
    719: }

    721: /*------------------------------------------------------------*/

    723: /* Routine for performing a bound-projected More-Thuente line search.

    725:   Includes fallbacks to BFGS, scaled gradient, and unscaled gradient steps if the
    726:   Newton step does not produce a valid step length.
    727: */

    729: PetscErrorCode TaoBNKPerformLineSearch(Tao tao, PetscInt *stepType, PetscReal *steplen, TaoLineSearchConvergedReason *reason)
    730: {
    731:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
    733:   TaoLineSearchConvergedReason ls_reason;
    734:
    735:   PetscReal      e_min, gdx;
    736:   PetscInt       bfgsUpdates;
    737:
    739:   /* Perform the linesearch */
    740:   TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason);
    741:   TaoAddLineSearchCounts(tao);

    743:   while (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER && *stepType != BNK_SCALED_GRADIENT && *stepType != BNK_GRADIENT) {
    744:     /* Linesearch failed, revert solution */
    745:     bnk->f = bnk->fold;
    746:     VecCopy(bnk->Xold, tao->solution);
    747:     VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);

    749:     switch(*stepType) {
    750:     case BNK_NEWTON:
    751:       /* Failed to obtain acceptable iterate with Newton step
    752:          Update the perturbation for next time */
    753:       if (bnk->pert <= 0.0) {
    754:         /* Initialize the perturbation */
    755:         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
    756:         if (bnk->is_gltr) {
    757:           KSPCGGLTRGetMinEig(tao->ksp,&e_min);
    758:           bnk->pert = PetscMax(bnk->pert, -e_min);
    759:         }
    760:       } else {
    761:         /* Increase the perturbation */
    762:         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
    763:       }

    765:       if (!bnk->M) {
    766:         /* We don't have the bfgs matrix around and being updated
    767:            Must use gradient direction in this case */
    768:         VecCopy(bnk->unprojected_gradient, tao->stepdirection);
    769:         *stepType = BNK_GRADIENT;
    770:       } else {
    771:         /* Attempt to use the BFGS direction */
    772:         MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);
    773:         /* Check for success (descent direction)
    774:            NOTE: Negative gdx means not a descent direction because the step here is missing a negative sign. */
    775:         VecDot(tao->gradient, tao->stepdirection, &gdx);
    776:         if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
    777:           /* BFGS direction is not descent or direction produced not a number
    778:              We can assert bfgsUpdates > 1 in this case
    779:              Use steepest descent direction (scaled) */
    780:           MatLMVMReset(bnk->M, PETSC_FALSE);
    781:           MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);
    782:           MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);

    784:           bfgsUpdates = 1;
    785:           *stepType = BNK_SCALED_GRADIENT;
    786:         } else {
    787:           MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates);
    788:           if (1 == bfgsUpdates) {
    789:             /* The first BFGS direction is always the scaled gradient */
    790:             *stepType = BNK_SCALED_GRADIENT;
    791:           } else {
    792:             *stepType = BNK_BFGS;
    793:           }
    794:         }
    795:       }
    796:       break;

    798:     case BNK_BFGS:
    799:       /* Can only enter if pc_type == BNK_PC_BFGS
    800:          Failed to obtain acceptable iterate with BFGS step
    801:          Attempt to use the scaled gradient direction */
    802:       MatLMVMReset(bnk->M, PETSC_FALSE);
    803:       MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);
    804:       MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);

    806:       bfgsUpdates = 1;
    807:       *stepType = BNK_SCALED_GRADIENT;
    808:       break;
    809:     }
    810:     /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
    811:     VecScale(tao->stepdirection, -1.0);
    812:     TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection);
    813:
    814:     /* Perform one last line search with the fall-back step */
    815:     TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason);
    816:     TaoAddLineSearchCounts(tao);
    817:   }
    818:   *reason = ls_reason;
    819:   return(0);
    820: }

    822: /*------------------------------------------------------------*/

    824: /* Routine for updating the trust radius.

    826:   Function features three different update methods:
    827:   1) Line-search step length based
    828:   2) Predicted decrease on the CG quadratic model
    829:   3) Interpolation
    830: */

    832: PetscErrorCode TaoBNKUpdateTrustRadius(Tao tao, PetscReal prered, PetscReal actred, PetscInt updateType, PetscInt stepType, PetscBool *accept)
    833: {
    834:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
    836:
    837:   PetscReal      step, kappa;
    838:   PetscReal      gdx, tau_1, tau_2, tau_min, tau_max;

    841:   /* Update trust region radius */
    842:   *accept = PETSC_FALSE;
    843:   switch(updateType) {
    844:   case BNK_UPDATE_STEP:
    845:     *accept = PETSC_TRUE; /* always accept here because line search succeeded */
    846:     if (stepType == BNK_NEWTON) {
    847:       TaoLineSearchGetStepLength(tao->linesearch, &step);
    848:       if (step < bnk->nu1) {
    849:         /* Very bad step taken; reduce radius */
    850:         tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
    851:       } else if (step < bnk->nu2) {
    852:         /* Reasonably bad step taken; reduce radius */
    853:         tao->trust = bnk->omega2 * PetscMin(bnk->dnorm, tao->trust);
    854:       } else if (step < bnk->nu3) {
    855:         /*  Reasonable step was taken; leave radius alone */
    856:         if (bnk->omega3 < 1.0) {
    857:           tao->trust = bnk->omega3 * PetscMin(bnk->dnorm, tao->trust);
    858:         } else if (bnk->omega3 > 1.0) {
    859:           tao->trust = PetscMax(bnk->omega3 * bnk->dnorm, tao->trust);
    860:         }
    861:       } else if (step < bnk->nu4) {
    862:         /*  Full step taken; increase the radius */
    863:         tao->trust = PetscMax(bnk->omega4 * bnk->dnorm, tao->trust);
    864:       } else {
    865:         /*  More than full step taken; increase the radius */
    866:         tao->trust = PetscMax(bnk->omega5 * bnk->dnorm, tao->trust);
    867:       }
    868:     } else {
    869:       /*  Newton step was not good; reduce the radius */
    870:       tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
    871:     }
    872:     break;

    874:   case BNK_UPDATE_REDUCTION:
    875:     if (stepType == BNK_NEWTON) {
    876:       if ((prered < 0.0) || PetscIsInfOrNanReal(prered)) {
    877:         /* The predicted reduction has the wrong sign.  This cannot
    878:            happen in infinite precision arithmetic.  Step should
    879:            be rejected! */
    880:         tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
    881:       } else {
    882:         if (PetscIsInfOrNanReal(actred)) {
    883:           tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
    884:         } else {
    885:           if ((PetscAbsScalar(actred) <= PetscMax(1.0, PetscAbsScalar(bnk->f))*bnk->epsilon) && (PetscAbsScalar(prered) <= PetscMax(1.0, PetscAbsScalar(bnk->f))*bnk->epsilon)) {
    886:             kappa = 1.0;
    887:           } else {
    888:             kappa = actred / prered;
    889:           }
    890:           /* Accept or reject the step and update radius */
    891:           if (kappa < bnk->eta1) {
    892:             /* Reject the step */
    893:             tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
    894:           } else {
    895:             /* Accept the step */
    896:             *accept = PETSC_TRUE;
    897:             /* Update the trust region radius only if the computed step is at the trust radius boundary */
    898:             if (bnk->dnorm == tao->trust) {
    899:               if (kappa < bnk->eta2) {
    900:                 /* Marginal bad step */
    901:                 tao->trust = bnk->alpha2 * tao->trust;
    902:               } else if (kappa < bnk->eta3) {
    903:                 /* Reasonable step */
    904:                 tao->trust = bnk->alpha3 * tao->trust;
    905:               } else if (kappa < bnk->eta4) {
    906:                 /* Good step */
    907:                 tao->trust = bnk->alpha4 * tao->trust;
    908:               } else {
    909:                 /* Very good step */
    910:                 tao->trust = bnk->alpha5 * tao->trust;
    911:               }
    912:             }
    913:           }
    914:         }
    915:       }
    916:     } else {
    917:       /*  Newton step was not good; reduce the radius */
    918:       tao->trust = bnk->alpha1 * PetscMin(bnk->dnorm, tao->trust);
    919:     }
    920:     break;

    922:   default:
    923:     if (stepType == BNK_NEWTON) {
    924:       if (prered < 0.0) {
    925:         /*  The predicted reduction has the wrong sign.  This cannot */
    926:         /*  happen in infinite precision arithmetic.  Step should */
    927:         /*  be rejected! */
    928:         tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
    929:       } else {
    930:         if (PetscIsInfOrNanReal(actred)) {
    931:           tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
    932:         } else {
    933:           if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) {
    934:             kappa = 1.0;
    935:           } else {
    936:             kappa = actred / prered;
    937:           }
    938:
    939:           VecDot(tao->gradient, tao->stepdirection, &gdx);
    940:           tau_1 = bnk->theta * gdx / (bnk->theta * gdx - (1.0 - bnk->theta) * prered + actred);
    941:           tau_2 = bnk->theta * gdx / (bnk->theta * gdx + (1.0 + bnk->theta) * prered - actred);
    942:           tau_min = PetscMin(tau_1, tau_2);
    943:           tau_max = PetscMax(tau_1, tau_2);

    945:           if (kappa >= 1.0 - bnk->mu1) {
    946:             /*  Great agreement */
    947:             *accept = PETSC_TRUE;
    948:             if (tau_max < 1.0) {
    949:               tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
    950:             } else if (tau_max > bnk->gamma4) {
    951:               tao->trust = PetscMax(tao->trust, bnk->gamma4 * bnk->dnorm);
    952:             } else {
    953:               tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
    954:             }
    955:           } else if (kappa >= 1.0 - bnk->mu2) {
    956:             /*  Good agreement */
    957:             *accept = PETSC_TRUE;
    958:             if (tau_max < bnk->gamma2) {
    959:               tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
    960:             } else if (tau_max > bnk->gamma3) {
    961:               tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
    962:             } else if (tau_max < 1.0) {
    963:               tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
    964:             } else {
    965:               tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
    966:             }
    967:           } else {
    968:             /*  Not good agreement */
    969:             if (tau_min > 1.0) {
    970:               tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
    971:             } else if (tau_max < bnk->gamma1) {
    972:               tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
    973:             } else if ((tau_min < bnk->gamma1) && (tau_max >= 1.0)) {
    974:               tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
    975:             } else if ((tau_1 >= bnk->gamma1) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1) || (tau_2 >= 1.0))) {
    976:               tao->trust = tau_1 * PetscMin(tao->trust, bnk->dnorm);
    977:             } else if ((tau_2 >= bnk->gamma1) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1) || (tau_2 >= 1.0))) {
    978:               tao->trust = tau_2 * PetscMin(tao->trust, bnk->dnorm);
    979:             } else {
    980:               tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
    981:             }
    982:           }
    983:         }
    984:       }
    985:     } else {
    986:       /*  Newton step was not good; reduce the radius */
    987:       tao->trust = bnk->gamma1 * PetscMin(bnk->dnorm, tao->trust);
    988:     }
    989:     break;
    990:   }
    991:   /* Make sure the radius does not violate min and max settings */
    992:   tao->trust = PetscMin(tao->trust, bnk->max_radius);
    993:   tao->trust = PetscMax(tao->trust, bnk->min_radius);
    994:   return(0);
    995: }

    997: /* ---------------------------------------------------------- */

    999: PetscErrorCode TaoBNKAddStepCounts(Tao tao, PetscInt stepType)
    1000: {
    1001:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
    1002:
    1004:   switch (stepType) {
    1005:   case BNK_NEWTON:
    1006:     ++bnk->newt;
    1007:     break;
    1008:   case BNK_BFGS:
    1009:     ++bnk->bfgs;
    1010:     break;
    1011:   case BNK_SCALED_GRADIENT:
    1012:     ++bnk->sgrad;
    1013:     break;
    1014:   case BNK_GRADIENT:
    1015:     ++bnk->grad;
    1016:     break;
    1017:   default:
    1018:     break;
    1019:   }
    1020:   return(0);
    1021: }

    1023: /* ---------------------------------------------------------- */

    1025: PetscErrorCode TaoSetUp_BNK(Tao tao)
    1026: {
    1027:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
    1029:   PetscInt       i;

    1032:   if (!tao->gradient) {
    1033:     VecDuplicate(tao->solution,&tao->gradient);
    1034:   }
    1035:   if (!tao->stepdirection) {
    1036:     VecDuplicate(tao->solution,&tao->stepdirection);
    1037:   }
    1038:   if (!bnk->W) {
    1039:     VecDuplicate(tao->solution,&bnk->W);
    1040:   }
    1041:   if (!bnk->Xold) {
    1042:     VecDuplicate(tao->solution,&bnk->Xold);
    1043:   }
    1044:   if (!bnk->Gold) {
    1045:     VecDuplicate(tao->solution,&bnk->Gold);
    1046:   }
    1047:   if (!bnk->Xwork) {
    1048:     VecDuplicate(tao->solution,&bnk->Xwork);
    1049:   }
    1050:   if (!bnk->Gwork) {
    1051:     VecDuplicate(tao->solution,&bnk->Gwork);
    1052:   }
    1053:   if (!bnk->unprojected_gradient) {
    1054:     VecDuplicate(tao->solution,&bnk->unprojected_gradient);
    1055:   }
    1056:   if (!bnk->unprojected_gradient_old) {
    1057:     VecDuplicate(tao->solution,&bnk->unprojected_gradient_old);
    1058:   }
    1059:   if (!bnk->Diag_min) {
    1060:     VecDuplicate(tao->solution,&bnk->Diag_min);
    1061:   }
    1062:   if (!bnk->Diag_max) {
    1063:     VecDuplicate(tao->solution,&bnk->Diag_max);
    1064:   }
    1065:   if (bnk->max_cg_its > 0) {
    1066:     /* Ensure that the important common vectors are shared between BNK and embedded BNCG */
    1067:     bnk->bncg_ctx = (TAO_BNCG *)bnk->bncg->data;
    1068:     PetscObjectReference((PetscObject)(bnk->unprojected_gradient_old));
    1069:     VecDestroy(&bnk->bncg_ctx->unprojected_gradient_old);
    1070:     bnk->bncg_ctx->unprojected_gradient_old = bnk->unprojected_gradient_old;
    1071:     PetscObjectReference((PetscObject)(bnk->unprojected_gradient));
    1072:     VecDestroy(&bnk->bncg_ctx->unprojected_gradient);
    1073:     bnk->bncg_ctx->unprojected_gradient = bnk->unprojected_gradient;
    1074:     PetscObjectReference((PetscObject)(bnk->Gold));
    1075:     VecDestroy(&bnk->bncg_ctx->G_old);
    1076:     bnk->bncg_ctx->G_old = bnk->Gold;
    1077:     PetscObjectReference((PetscObject)(tao->gradient));
    1078:     VecDestroy(&bnk->bncg->gradient);
    1079:     bnk->bncg->gradient = tao->gradient;
    1080:     PetscObjectReference((PetscObject)(tao->stepdirection));
    1081:     VecDestroy(&bnk->bncg->stepdirection);
    1082:     bnk->bncg->stepdirection = tao->stepdirection;
    1083:     TaoSetInitialVector(bnk->bncg, tao->solution);
    1084:     /* Copy over some settings from BNK into BNCG */
    1085:     TaoSetMaximumIterations(bnk->bncg, bnk->max_cg_its);
    1086:     TaoSetTolerances(bnk->bncg, tao->gatol, tao->grtol, tao->gttol);
    1087:     TaoSetFunctionLowerBound(bnk->bncg, tao->fmin);
    1088:     TaoSetConvergenceTest(bnk->bncg, tao->ops->convergencetest, tao->cnvP);
    1089:     TaoSetObjectiveRoutine(bnk->bncg, tao->ops->computeobjective, tao->user_objP);
    1090:     TaoSetGradientRoutine(bnk->bncg, tao->ops->computegradient, tao->user_gradP);
    1091:     TaoSetObjectiveAndGradientRoutine(bnk->bncg, tao->ops->computeobjectiveandgradient, tao->user_objgradP);
    1092:     PetscObjectCopyFortranFunctionPointers((PetscObject)tao, (PetscObject)(bnk->bncg));
    1093:     for (i=0; i<tao->numbermonitors; ++i) {
    1094:       TaoSetMonitor(bnk->bncg, tao->monitor[i], tao->monitorcontext[i], tao->monitordestroy[i]);
    1095:       PetscObjectReference((PetscObject)(tao->monitorcontext[i]));
    1096:     }
    1097:   }
    1098:   bnk->X_inactive = 0;
    1099:   bnk->G_inactive = 0;
    1100:   bnk->inactive_work = 0;
    1101:   bnk->active_work = 0;
    1102:   bnk->inactive_idx = 0;
    1103:   bnk->active_idx = 0;
    1104:   bnk->active_lower = 0;
    1105:   bnk->active_upper = 0;
    1106:   bnk->active_fixed = 0;
    1107:   bnk->M = 0;
    1108:   bnk->H_inactive = 0;
    1109:   bnk->Hpre_inactive = 0;
    1110:   return(0);
    1111: }

    1113: /*------------------------------------------------------------*/

    1115: PetscErrorCode TaoDestroy_BNK(Tao tao)
    1116: {
    1117:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;

    1121:   if (tao->setupcalled) {
    1122:     VecDestroy(&bnk->W);
    1123:     VecDestroy(&bnk->Xold);
    1124:     VecDestroy(&bnk->Gold);
    1125:     VecDestroy(&bnk->Xwork);
    1126:     VecDestroy(&bnk->Gwork);
    1127:     VecDestroy(&bnk->unprojected_gradient);
    1128:     VecDestroy(&bnk->unprojected_gradient_old);
    1129:     VecDestroy(&bnk->Diag_min);
    1130:     VecDestroy(&bnk->Diag_max);
    1131:   }
    1132:   ISDestroy(&bnk->active_lower);
    1133:   ISDestroy(&bnk->active_upper);
    1134:   ISDestroy(&bnk->active_fixed);
    1135:   ISDestroy(&bnk->active_idx);
    1136:   ISDestroy(&bnk->inactive_idx);
    1137:   MatDestroy(&bnk->Hpre_inactive);
    1138:   MatDestroy(&bnk->H_inactive);
    1139:   TaoDestroy(&bnk->bncg);
    1140:   PetscFree(tao->data);
    1141:   return(0);
    1142: }

    1144: /*------------------------------------------------------------*/

    1146: PetscErrorCode TaoSetFromOptions_BNK(PetscOptionItems *PetscOptionsObject,Tao tao)
    1147: {
    1148:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
    1150:   KSPType        ksp_type;

    1153:   PetscOptionsHead(PetscOptionsObject,"Newton-Krylov method for bound constrained optimization");
    1154:   PetscOptionsEList("-tao_bnk_init_type", "radius initialization type", "", BNK_INIT, BNK_INIT_TYPES, BNK_INIT[bnk->init_type], &bnk->init_type, 0);
    1155:   PetscOptionsEList("-tao_bnk_update_type", "radius update type", "", BNK_UPDATE, BNK_UPDATE_TYPES, BNK_UPDATE[bnk->update_type], &bnk->update_type, 0);
    1156:   PetscOptionsEList("-tao_bnk_as_type", "active set estimation method", "", BNK_AS, BNK_AS_TYPES, BNK_AS[bnk->as_type], &bnk->as_type, 0);
    1157:   PetscOptionsReal("-tao_bnk_sval", "(developer) Hessian perturbation starting value", "", bnk->sval, &bnk->sval,NULL);
    1158:   PetscOptionsReal("-tao_bnk_imin", "(developer) minimum initial Hessian perturbation", "", bnk->imin, &bnk->imin,NULL);
    1159:   PetscOptionsReal("-tao_bnk_imax", "(developer) maximum initial Hessian perturbation", "", bnk->imax, &bnk->imax,NULL);
    1160:   PetscOptionsReal("-tao_bnk_imfac", "(developer) initial merit factor for Hessian perturbation", "", bnk->imfac, &bnk->imfac,NULL);
    1161:   PetscOptionsReal("-tao_bnk_pmin", "(developer) minimum Hessian perturbation", "", bnk->pmin, &bnk->pmin,NULL);
    1162:   PetscOptionsReal("-tao_bnk_pmax", "(developer) maximum Hessian perturbation", "", bnk->pmax, &bnk->pmax,NULL);
    1163:   PetscOptionsReal("-tao_bnk_pgfac", "(developer) Hessian perturbation growth factor", "", bnk->pgfac, &bnk->pgfac,NULL);
    1164:   PetscOptionsReal("-tao_bnk_psfac", "(developer) Hessian perturbation shrink factor", "", bnk->psfac, &bnk->psfac,NULL);
    1165:   PetscOptionsReal("-tao_bnk_pmgfac", "(developer) merit growth factor for Hessian perturbation", "", bnk->pmgfac, &bnk->pmgfac,NULL);
    1166:   PetscOptionsReal("-tao_bnk_pmsfac", "(developer) merit shrink factor for Hessian perturbation", "", bnk->pmsfac, &bnk->pmsfac,NULL);
    1167:   PetscOptionsReal("-tao_bnk_eta1", "(developer) threshold for rejecting step (-tao_bnk_update_type reduction)", "", bnk->eta1, &bnk->eta1,NULL);
    1168:   PetscOptionsReal("-tao_bnk_eta2", "(developer) threshold for accepting marginal step (-tao_bnk_update_type reduction)", "", bnk->eta2, &bnk->eta2,NULL);
    1169:   PetscOptionsReal("-tao_bnk_eta3", "(developer) threshold for accepting reasonable step (-tao_bnk_update_type reduction)", "", bnk->eta3, &bnk->eta3,NULL);
    1170:   PetscOptionsReal("-tao_bnk_eta4", "(developer) threshold for accepting good step (-tao_bnk_update_type reduction)", "", bnk->eta4, &bnk->eta4,NULL);
    1171:   PetscOptionsReal("-tao_bnk_alpha1", "(developer) radius reduction factor for rejected step (-tao_bnk_update_type reduction)", "", bnk->alpha1, &bnk->alpha1,NULL);
    1172:   PetscOptionsReal("-tao_bnk_alpha2", "(developer) radius reduction factor for marginally accepted bad step (-tao_bnk_update_type reduction)", "", bnk->alpha2, &bnk->alpha2,NULL);
    1173:   PetscOptionsReal("-tao_bnk_alpha3", "(developer) radius increase factor for reasonable accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha3, &bnk->alpha3,NULL);
    1174:   PetscOptionsReal("-tao_bnk_alpha4", "(developer) radius increase factor for good accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha4, &bnk->alpha4,NULL);
    1175:   PetscOptionsReal("-tao_bnk_alpha5", "(developer) radius increase factor for very good accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha5, &bnk->alpha5,NULL);
    1176:   PetscOptionsReal("-tao_bnk_nu1", "(developer) threshold for small line-search step length (-tao_bnk_update_type step)", "", bnk->nu1, &bnk->nu1,NULL);
    1177:   PetscOptionsReal("-tao_bnk_nu2", "(developer) threshold for reasonable line-search step length (-tao_bnk_update_type step)", "", bnk->nu2, &bnk->nu2,NULL);
    1178:   PetscOptionsReal("-tao_bnk_nu3", "(developer) threshold for large line-search step length (-tao_bnk_update_type step)", "", bnk->nu3, &bnk->nu3,NULL);
    1179:   PetscOptionsReal("-tao_bnk_nu4", "(developer) threshold for very large line-search step length (-tao_bnk_update_type step)", "", bnk->nu4, &bnk->nu4,NULL);
    1180:   PetscOptionsReal("-tao_bnk_omega1", "(developer) radius reduction factor for very small line-search step length (-tao_bnk_update_type step)", "", bnk->omega1, &bnk->omega1,NULL);
    1181:   PetscOptionsReal("-tao_bnk_omega2", "(developer) radius reduction factor for small line-search step length (-tao_bnk_update_type step)", "", bnk->omega2, &bnk->omega2,NULL);
    1182:   PetscOptionsReal("-tao_bnk_omega3", "(developer) radius factor for decent line-search step length (-tao_bnk_update_type step)", "", bnk->omega3, &bnk->omega3,NULL);
    1183:   PetscOptionsReal("-tao_bnk_omega4", "(developer) radius increase factor for large line-search step length (-tao_bnk_update_type step)", "", bnk->omega4, &bnk->omega4,NULL);
    1184:   PetscOptionsReal("-tao_bnk_omega5", "(developer) radius increase factor for very large line-search step length (-tao_bnk_update_type step)", "", bnk->omega5, &bnk->omega5,NULL);
    1185:   PetscOptionsReal("-tao_bnk_mu1_i", "(developer) threshold for accepting very good step (-tao_bnk_init_type interpolation)", "", bnk->mu1_i, &bnk->mu1_i,NULL);
    1186:   PetscOptionsReal("-tao_bnk_mu2_i", "(developer) threshold for accepting good step (-tao_bnk_init_type interpolation)", "", bnk->mu2_i, &bnk->mu2_i,NULL);
    1187:   PetscOptionsReal("-tao_bnk_gamma1_i", "(developer) radius reduction factor for rejected very bad step (-tao_bnk_init_type interpolation)", "", bnk->gamma1_i, &bnk->gamma1_i,NULL);
    1188:   PetscOptionsReal("-tao_bnk_gamma2_i", "(developer) radius reduction factor for rejected bad step (-tao_bnk_init_type interpolation)", "", bnk->gamma2_i, &bnk->gamma2_i,NULL);
    1189:   PetscOptionsReal("-tao_bnk_gamma3_i", "(developer) radius increase factor for accepted good step (-tao_bnk_init_type interpolation)", "", bnk->gamma3_i, &bnk->gamma3_i,NULL);
    1190:   PetscOptionsReal("-tao_bnk_gamma4_i", "(developer) radius increase factor for accepted very good step (-tao_bnk_init_type interpolation)", "", bnk->gamma4_i, &bnk->gamma4_i,NULL);
    1191:   PetscOptionsReal("-tao_bnk_theta_i", "(developer) trust region interpolation factor (-tao_bnk_init_type interpolation)", "", bnk->theta_i, &bnk->theta_i,NULL);
    1192:   PetscOptionsReal("-tao_bnk_mu1", "(developer) threshold for accepting very good step (-tao_bnk_update_type interpolation)", "", bnk->mu1, &bnk->mu1,NULL);
    1193:   PetscOptionsReal("-tao_bnk_mu2", "(developer) threshold for accepting good step (-tao_bnk_update_type interpolation)", "", bnk->mu2, &bnk->mu2,NULL);
    1194:   PetscOptionsReal("-tao_bnk_gamma1", "(developer) radius reduction factor for rejected very bad step (-tao_bnk_update_type interpolation)", "", bnk->gamma1, &bnk->gamma1,NULL);
    1195:   PetscOptionsReal("-tao_bnk_gamma2", "(developer) radius reduction factor for rejected bad step (-tao_bnk_update_type interpolation)", "", bnk->gamma2, &bnk->gamma2,NULL);
    1196:   PetscOptionsReal("-tao_bnk_gamma3", "(developer) radius increase factor for accepted good step (-tao_bnk_update_type interpolation)", "", bnk->gamma3, &bnk->gamma3,NULL);
    1197:   PetscOptionsReal("-tao_bnk_gamma4", "(developer) radius increase factor for accepted very good step (-tao_bnk_update_type interpolation)", "", bnk->gamma4, &bnk->gamma4,NULL);
    1198:   PetscOptionsReal("-tao_bnk_theta", "(developer) trust region interpolation factor (-tao_bnk_update_type interpolation)", "", bnk->theta, &bnk->theta,NULL);
    1199:   PetscOptionsReal("-tao_bnk_min_radius", "(developer) lower bound on initial radius", "", bnk->min_radius, &bnk->min_radius,NULL);
    1200:   PetscOptionsReal("-tao_bnk_max_radius", "(developer) upper bound on radius", "", bnk->max_radius, &bnk->max_radius,NULL);
    1201:   PetscOptionsReal("-tao_bnk_epsilon", "(developer) tolerance used when computing actual and predicted reduction", "", bnk->epsilon, &bnk->epsilon,NULL);
    1202:   PetscOptionsReal("-tao_bnk_as_tol", "(developer) initial tolerance used when estimating actively bounded variables", "", bnk->as_tol, &bnk->as_tol,NULL);
    1203:   PetscOptionsReal("-tao_bnk_as_step", "(developer) step length used when estimating actively bounded variables", "", bnk->as_step, &bnk->as_step,NULL);
    1204:   PetscOptionsInt("-tao_bnk_max_cg_its", "number of BNCG iterations to take for each Newton step", "", bnk->max_cg_its, &bnk->max_cg_its,NULL);
    1205:   PetscOptionsTail();
    1206:   TaoSetFromOptions(bnk->bncg);
    1207:   TaoLineSearchSetFromOptions(tao->linesearch);
    1208:   KSPSetFromOptions(tao->ksp);
    1209:   KSPGetType(tao->ksp,&ksp_type);
    1210:   PetscStrcmp(ksp_type,KSPCGNASH,&bnk->is_nash);
    1211:   PetscStrcmp(ksp_type,KSPCGSTCG,&bnk->is_stcg);
    1212:   PetscStrcmp(ksp_type,KSPCGGLTR,&bnk->is_gltr);
    1213:   return(0);
    1214: }

    1216: /*------------------------------------------------------------*/

    1218: PetscErrorCode TaoView_BNK(Tao tao, PetscViewer viewer)
    1219: {
    1220:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
    1221:   PetscInt       nrejects;
    1222:   PetscBool      isascii;

    1226:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    1227:   if (isascii) {
    1228:     PetscViewerASCIIPushTab(viewer);
    1229:     if (bnk->M) {
    1230:       MatLMVMGetRejectCount(bnk->M,&nrejects);
    1231:       PetscViewerASCIIPrintf(viewer, "Rejected BFGS updates: %D\n",nrejects);
    1232:     }
    1233:     PetscViewerASCIIPrintf(viewer, "CG steps: %D\n", bnk->tot_cg_its);
    1234:     PetscViewerASCIIPrintf(viewer, "Newton steps: %D\n", bnk->newt);
    1235:     if (bnk->M) {
    1236:       PetscViewerASCIIPrintf(viewer, "BFGS steps: %D\n", bnk->bfgs);
    1237:     }
    1238:     PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %D\n", bnk->sgrad);
    1239:     PetscViewerASCIIPrintf(viewer, "Gradient steps: %D\n", bnk->grad);
    1240:     PetscViewerASCIIPrintf(viewer, "KSP termination reasons:\n");
    1241:     PetscViewerASCIIPrintf(viewer, "  atol: %D\n", bnk->ksp_atol);
    1242:     PetscViewerASCIIPrintf(viewer, "  rtol: %D\n", bnk->ksp_rtol);
    1243:     PetscViewerASCIIPrintf(viewer, "  ctol: %D\n", bnk->ksp_ctol);
    1244:     PetscViewerASCIIPrintf(viewer, "  negc: %D\n", bnk->ksp_negc);
    1245:     PetscViewerASCIIPrintf(viewer, "  dtol: %D\n", bnk->ksp_dtol);
    1246:     PetscViewerASCIIPrintf(viewer, "  iter: %D\n", bnk->ksp_iter);
    1247:     PetscViewerASCIIPrintf(viewer, "  othr: %D\n", bnk->ksp_othr);
    1248:     PetscViewerASCIIPopTab(viewer);
    1249:   }
    1250:   return(0);
    1251: }

    1253: /* ---------------------------------------------------------- */

    1255: /*MC
    1256:   TAOBNK - Shared base-type for Bounded Newton-Krylov type algorithms.
    1257:   At each iteration, the BNK methods solve the symmetric
    1258:   system of equations to obtain the step diretion dk:
    1259:               Hk dk = -gk
    1260:   for free variables only. The step can be globalized either through
    1261:   trust-region methods, or a line search, or a heuristic mixture of both.

    1263:     Options Database Keys:
    1264: + -max_cg_its - maximum number of bounded conjugate-gradient iterations taken in each Newton loop
    1265: . -init_type - trust radius initialization method ("constant", "direction", "interpolation")
    1266: . -update_type - trust radius update method ("step", "direction", "interpolation")
    1267: . -as_type - active-set estimation method ("none", "bertsekas")
    1268: . -as_tol - (developer) initial tolerance used in estimating bounded active variables (-as_type bertsekas)
    1269: . -as_step - (developer) trial step length used in estimating bounded active variables (-as_type bertsekas)
    1270: . -sval - (developer) Hessian perturbation starting value
    1271: . -imin - (developer) minimum initial Hessian perturbation
    1272: . -imax - (developer) maximum initial Hessian perturbation
    1273: . -pmin - (developer) minimum Hessian perturbation
    1274: . -pmax - (developer) aximum Hessian perturbation
    1275: . -pgfac - (developer) Hessian perturbation growth factor
    1276: . -psfac - (developer) Hessian perturbation shrink factor
    1277: . -imfac - (developer) initial merit factor for Hessian perturbation
    1278: . -pmgfac - (developer) merit growth factor for Hessian perturbation
    1279: . -pmsfac - (developer) merit shrink factor for Hessian perturbation
    1280: . -eta1 - (developer) threshold for rejecting step (-update_type reduction)
    1281: . -eta2 - (developer) threshold for accepting marginal step (-update_type reduction)
    1282: . -eta3 - (developer) threshold for accepting reasonable step (-update_type reduction)
    1283: . -eta4 - (developer) threshold for accepting good step (-update_type reduction)
    1284: . -alpha1 - (developer) radius reduction factor for rejected step (-update_type reduction)
    1285: . -alpha2 - (developer) radius reduction factor for marginally accepted bad step (-update_type reduction)
    1286: . -alpha3 - (developer) radius increase factor for reasonable accepted step (-update_type reduction)
    1287: . -alpha4 - (developer) radius increase factor for good accepted step (-update_type reduction)
    1288: . -alpha5 - (developer) radius increase factor for very good accepted step (-update_type reduction)
    1289: . -epsilon - (developer) tolerance for small pred/actual ratios that trigger automatic step acceptance (-update_type reduction)
    1290: . -mu1 - (developer) threshold for accepting very good step (-update_type interpolation)
    1291: . -mu2 - (developer) threshold for accepting good step (-update_type interpolation)
    1292: . -gamma1 - (developer) radius reduction factor for rejected very bad step (-update_type interpolation)
    1293: . -gamma2 - (developer) radius reduction factor for rejected bad step (-update_type interpolation)
    1294: . -gamma3 - (developer) radius increase factor for accepted good step (-update_type interpolation)
    1295: . -gamma4 - (developer) radius increase factor for accepted very good step (-update_type interpolation)
    1296: . -theta - (developer) trust region interpolation factor (-update_type interpolation)
    1297: . -nu1 - (developer) threshold for small line-search step length (-update_type step)
    1298: . -nu2 - (developer) threshold for reasonable line-search step length (-update_type step)
    1299: . -nu3 - (developer) threshold for large line-search step length (-update_type step)
    1300: . -nu4 - (developer) threshold for very large line-search step length (-update_type step)
    1301: . -omega1 - (developer) radius reduction factor for very small line-search step length (-update_type step)
    1302: . -omega2 - (developer) radius reduction factor for small line-search step length (-update_type step)
    1303: . -omega3 - (developer) radius factor for decent line-search step length (-update_type step)
    1304: . -omega4 - (developer) radius increase factor for large line-search step length (-update_type step)
    1305: . -omega5 - (developer) radius increase factor for very large line-search step length (-update_type step)
    1306: . -mu1_i -  (developer) threshold for accepting very good step (-init_type interpolation)
    1307: . -mu2_i -  (developer) threshold for accepting good step (-init_type interpolation)
    1308: . -gamma1_i - (developer) radius reduction factor for rejected very bad step (-init_type interpolation)
    1309: . -gamma2_i - (developer) radius reduction factor for rejected bad step (-init_type interpolation)
    1310: . -gamma3_i - (developer) radius increase factor for accepted good step (-init_type interpolation)
    1311: . -gamma4_i - (developer) radius increase factor for accepted very good step (-init_type interpolation)
    1312: - -theta_i - (developer) trust region interpolation factor (-init_type interpolation)

    1314:   Level: beginner
    1315: M*/

    1317: PetscErrorCode TaoCreate_BNK(Tao tao)
    1318: {
    1319:   TAO_BNK        *bnk;
    1320:   const char     *morethuente_type = TAOLINESEARCHMT;
    1322:   PC             pc;

    1325:   PetscNewLog(tao,&bnk);

    1327:   tao->ops->setup = TaoSetUp_BNK;
    1328:   tao->ops->view = TaoView_BNK;
    1329:   tao->ops->setfromoptions = TaoSetFromOptions_BNK;
    1330:   tao->ops->destroy = TaoDestroy_BNK;

    1332:   /*  Override default settings (unless already changed) */
    1333:   if (!tao->max_it_changed) tao->max_it = 50;
    1334:   if (!tao->trust0_changed) tao->trust0 = 100.0;

    1336:   tao->data = (void*)bnk;
    1337:
    1338:   /*  Hessian shifting parameters */
    1339:   bnk->computehessian = TaoBNKComputeHessian;
    1340:   bnk->computestep = TaoBNKComputeStep;
    1341:
    1342:   bnk->sval   = 0.0;
    1343:   bnk->imin   = 1.0e-4;
    1344:   bnk->imax   = 1.0e+2;
    1345:   bnk->imfac  = 1.0e-1;

    1347:   bnk->pmin   = 1.0e-12;
    1348:   bnk->pmax   = 1.0e+2;
    1349:   bnk->pgfac  = 1.0e+1;
    1350:   bnk->psfac  = 4.0e-1;
    1351:   bnk->pmgfac = 1.0e-1;
    1352:   bnk->pmsfac = 1.0e-1;

    1354:   /*  Default values for trust-region radius update based on steplength */
    1355:   bnk->nu1 = 0.25;
    1356:   bnk->nu2 = 0.50;
    1357:   bnk->nu3 = 1.00;
    1358:   bnk->nu4 = 1.25;

    1360:   bnk->omega1 = 0.25;
    1361:   bnk->omega2 = 0.50;
    1362:   bnk->omega3 = 1.00;
    1363:   bnk->omega4 = 2.00;
    1364:   bnk->omega5 = 4.00;

    1366:   /*  Default values for trust-region radius update based on reduction */
    1367:   bnk->eta1 = 1.0e-4;
    1368:   bnk->eta2 = 0.25;
    1369:   bnk->eta3 = 0.50;
    1370:   bnk->eta4 = 0.90;

    1372:   bnk->alpha1 = 0.25;
    1373:   bnk->alpha2 = 0.50;
    1374:   bnk->alpha3 = 1.00;
    1375:   bnk->alpha4 = 2.00;
    1376:   bnk->alpha5 = 4.00;

    1378:   /*  Default values for trust-region radius update based on interpolation */
    1379:   bnk->mu1 = 0.10;
    1380:   bnk->mu2 = 0.50;

    1382:   bnk->gamma1 = 0.25;
    1383:   bnk->gamma2 = 0.50;
    1384:   bnk->gamma3 = 2.00;
    1385:   bnk->gamma4 = 4.00;

    1387:   bnk->theta = 0.05;

    1389:   /*  Default values for trust region initialization based on interpolation */
    1390:   bnk->mu1_i = 0.35;
    1391:   bnk->mu2_i = 0.50;

    1393:   bnk->gamma1_i = 0.0625;
    1394:   bnk->gamma2_i = 0.5;
    1395:   bnk->gamma3_i = 2.0;
    1396:   bnk->gamma4_i = 5.0;

    1398:   bnk->theta_i = 0.25;

    1400:   /*  Remaining parameters */
    1401:   bnk->max_cg_its = 0;
    1402:   bnk->min_radius = 1.0e-10;
    1403:   bnk->max_radius = 1.0e10;
    1404:   bnk->epsilon = PetscPowReal(PETSC_MACHINE_EPSILON, 2.0/3.0);
    1405:   bnk->as_tol = 1.0e-3;
    1406:   bnk->as_step = 1.0e-3;
    1407:   bnk->dmin = 1.0e-6;
    1408:   bnk->dmax = 1.0e6;
    1409:
    1410:   bnk->M               = 0;
    1411:   bnk->bfgs_pre        = 0;
    1412:   bnk->init_type       = BNK_INIT_INTERPOLATION;
    1413:   bnk->update_type     = BNK_UPDATE_REDUCTION;
    1414:   bnk->as_type         = BNK_AS_BERTSEKAS;
    1415:
    1416:   /* Create the embedded BNCG solver */
    1417:   TaoCreate(PetscObjectComm((PetscObject)tao), &bnk->bncg);
    1418:   PetscObjectIncrementTabLevel((PetscObject)bnk->bncg, (PetscObject)tao, 1);
    1419:   TaoSetOptionsPrefix(bnk->bncg, "tao_bnk_");
    1420:   TaoSetType(bnk->bncg, TAOBNCG);

    1422:   /* Create the line search */
    1423:   TaoLineSearchCreate(((PetscObject)tao)->comm,&tao->linesearch);
    1424:   PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);
    1425:   TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);
    1426:   TaoLineSearchSetType(tao->linesearch,morethuente_type);
    1427:   TaoLineSearchUseTaoRoutines(tao->linesearch,tao);

    1429:   /*  Set linear solver to default for symmetric matrices */
    1430:   KSPCreate(((PetscObject)tao)->comm,&tao->ksp);
    1431:   PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1);
    1432:   KSPSetOptionsPrefix(tao->ksp,"tao_bnk_");
    1433:   KSPSetType(tao->ksp,KSPCGSTCG);
    1434:   KSPGetPC(tao->ksp, &pc);
    1435:   PCSetType(pc, PCLMVM);
    1436:   return(0);
    1437: }