Actual source code: bnk.c

  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: /* Extracts from the full Hessian the part associated with the current bnk->inactive_idx and set the PCLMVM preconditioner */

 11: static PetscErrorCode TaoBNKComputeSubHessian(Tao tao)
 12: {
 13:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

 15:   PetscFunctionBegin;
 16:   PetscCall(MatDestroy(&bnk->Hpre_inactive));
 17:   PetscCall(MatDestroy(&bnk->H_inactive));
 18:   if (bnk->active_idx) {
 19:     PetscCall(MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive));
 20:     if (tao->hessian == tao->hessian_pre) {
 21:       PetscCall(PetscObjectReference((PetscObject)bnk->H_inactive));
 22:       bnk->Hpre_inactive = bnk->H_inactive;
 23:     } else {
 24:       PetscCall(MatCreateSubMatrix(tao->hessian_pre, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->Hpre_inactive));
 25:     }
 26:     if (bnk->bfgs_pre) PetscCall(PCLMVMSetIS(bnk->bfgs_pre, bnk->inactive_idx));
 27:   } else {
 28:     PetscCall(PetscObjectReference((PetscObject)tao->hessian));
 29:     bnk->H_inactive = tao->hessian;
 30:     PetscCall(PetscObjectReference((PetscObject)tao->hessian_pre));
 31:     bnk->Hpre_inactive = tao->hessian_pre;
 32:     if (bnk->bfgs_pre) PetscCall(PCLMVMClearIS(bnk->bfgs_pre));
 33:   }
 34:   PetscFunctionReturn(PETSC_SUCCESS);
 35: }

 37: /* Initializes the KSP solver, the BFGS preconditioner, and the initial trust radius estimation */

 39: PetscErrorCode TaoBNKInitialize(Tao tao, PetscInt initType, PetscBool *needH)
 40: {
 41:   TAO_BNK  *bnk = (TAO_BNK *)tao->data;
 42:   PC        pc;
 43:   PetscReal f_min, ftrial, prered, actred, kappa, sigma, resnorm;
 44:   PetscReal tau, tau_1, tau_2, tau_max, tau_min, max_radius;
 45:   PetscBool is_bfgs, is_jacobi, is_symmetric, sym_set;
 46:   PetscInt  n, N, nDiff;
 47:   PetscInt  i_max = 5;
 48:   PetscInt  j_max = 1;
 49:   PetscBool kspTR;

 51:   PetscFunctionBegin;
 52:   /* Project the current point onto the feasible set */
 53:   PetscCall(TaoComputeVariableBounds(tao));
 54:   PetscCall(TaoSetVariableBounds(bnk->bncg, tao->XL, tao->XU));
 55:   if (tao->bounded) PetscCall(TaoLineSearchSetVariableBounds(tao->linesearch, tao->XL, tao->XU));

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

 60:   /* Check convergence criteria */
 61:   PetscCall(TaoComputeObjectiveAndGradient(tao, tao->solution, &bnk->f, bnk->unprojected_gradient));
 62:   PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
 63:   PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient));
 64:   if (bnk->active_idx) PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
 65:   PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm));

 67:   /* Test the initial point for convergence */
 68:   PetscCall(VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W));
 69:   PetscCall(VecNorm(bnk->W, NORM_2, &resnorm));
 70:   PetscCheck(!PetscIsInfOrNanReal(bnk->f) && !PetscIsInfOrNanReal(resnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated infinity or NaN");
 71:   PetscCall(TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its));
 72:   PetscCall(TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, 1.0));
 73:   PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
 74:   if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(PETSC_SUCCESS);

 76:   /* Reset KSP stopping reason counters */
 77:   bnk->ksp_atol = 0;
 78:   bnk->ksp_rtol = 0;
 79:   bnk->ksp_dtol = 0;
 80:   bnk->ksp_ctol = 0;
 81:   bnk->ksp_negc = 0;
 82:   bnk->ksp_iter = 0;
 83:   bnk->ksp_othr = 0;

 85:   /* Reset accepted step type counters */
 86:   bnk->tot_cg_its = 0;
 87:   bnk->newt       = 0;
 88:   bnk->bfgs       = 0;
 89:   bnk->sgrad      = 0;
 90:   bnk->grad       = 0;

 92:   /* Initialize the Hessian perturbation */
 93:   bnk->pert = bnk->sval;

 95:   /* Reset initial steplength to zero (this helps BNCG reset its direction internally) */
 96:   PetscCall(VecSet(tao->stepdirection, 0.0));

 98:   /* Allocate the vectors needed for the BFGS approximation */
 99:   PetscCall(KSPGetPC(tao->ksp, &pc));
100:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCLMVM, &is_bfgs));
101:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCJACOBI, &is_jacobi));
102:   if (is_bfgs) {
103:     bnk->bfgs_pre = pc;
104:     PetscCall(PCLMVMGetMatLMVM(bnk->bfgs_pre, &bnk->M));
105:     PetscCall(VecGetLocalSize(tao->solution, &n));
106:     PetscCall(VecGetSize(tao->solution, &N));
107:     PetscCall(MatSetSizes(bnk->M, n, n, N, N));
108:     PetscCall(MatLMVMAllocate(bnk->M, tao->solution, bnk->unprojected_gradient));
109:     PetscCall(MatIsSymmetricKnown(bnk->M, &sym_set, &is_symmetric));
110:     PetscCheck(sym_set && is_symmetric, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_INCOMP, "LMVM matrix in the LMVM preconditioner must be symmetric.");
111:   } else if (is_jacobi) PetscCall(PCJacobiSetUseAbs(pc, PETSC_TRUE));

113:   /* Prepare the min/max vectors for safeguarding diagonal scales */
114:   PetscCall(VecSet(bnk->Diag_min, bnk->dmin));
115:   PetscCall(VecSet(bnk->Diag_max, bnk->dmax));

117:   /* Initialize trust-region radius.  The initialization is only performed
118:      when we are using Nash, Steihaug-Toint or the Generalized Lanczos method. */
119:   *needH = PETSC_TRUE;
120:   PetscCall(PetscObjectHasFunction((PetscObject)tao->ksp, "KSPCGSetRadius_C", &kspTR));
121:   if (kspTR) {
122:     switch (initType) {
123:     case BNK_INIT_CONSTANT:
124:       /* Use the initial radius specified */
125:       tao->trust = tao->trust0;
126:       break;

128:     case BNK_INIT_INTERPOLATION:
129:       /* Use interpolation based on the initial Hessian */
130:       max_radius = 0.0;
131:       tao->trust = tao->trust0;
132:       for (PetscInt j = 0; j < j_max; ++j) {
133:         f_min = bnk->f;
134:         sigma = 0.0;

136:         if (*needH) {
137:           /* Compute the Hessian at the new step, and extract the inactive subsystem */
138:           PetscCall((*bnk->computehessian)(tao));
139:           PetscCall(TaoBNKEstimateActiveSet(tao, BNK_AS_NONE));
140:           PetscCall(TaoBNKComputeSubHessian(tao));
141:           *needH = PETSC_FALSE;
142:         }

144:         for (PetscInt i = 0; i < i_max; ++i) {
145:           /* Take a steepest descent step and snap it to bounds */
146:           PetscCall(VecCopy(tao->solution, bnk->Xold));
147:           PetscCall(VecAXPY(tao->solution, -tao->trust / bnk->gnorm, tao->gradient));
148:           PetscCall(TaoBoundSolution(tao->solution, tao->XL, tao->XU, 0.0, &nDiff, tao->solution));
149:           /* Compute the step we actually accepted */
150:           PetscCall(VecCopy(tao->solution, bnk->W));
151:           PetscCall(VecAXPY(bnk->W, -1.0, bnk->Xold));
152:           /* Compute the objective at the trial */
153:           PetscCall(TaoComputeObjective(tao, tao->solution, &ftrial));
154:           PetscCheck(!PetscIsInfOrNanReal(bnk->f), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated infinity or NaN");
155:           PetscCall(VecCopy(bnk->Xold, tao->solution));
156:           if (PetscIsInfOrNanReal(ftrial)) {
157:             tau = bnk->gamma1_i;
158:           } else {
159:             if (ftrial < f_min) {
160:               f_min = ftrial;
161:               sigma = -tao->trust / bnk->gnorm;
162:             }

164:             /* Compute the predicted and actual reduction */
165:             if (bnk->active_idx) {
166:               PetscCall(VecGetSubVector(bnk->W, bnk->inactive_idx, &bnk->X_inactive));
167:               PetscCall(VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work));
168:             } else {
169:               bnk->X_inactive    = bnk->W;
170:               bnk->inactive_work = bnk->Xwork;
171:             }
172:             PetscCall(MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work));
173:             PetscCall(VecDot(bnk->X_inactive, bnk->inactive_work, &prered));
174:             if (bnk->active_idx) {
175:               PetscCall(VecRestoreSubVector(bnk->W, bnk->inactive_idx, &bnk->X_inactive));
176:               PetscCall(VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work));
177:             }
178:             prered = tao->trust * (bnk->gnorm - 0.5 * tao->trust * prered / (bnk->gnorm * bnk->gnorm));
179:             actred = bnk->f - ftrial;
180:             if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) {
181:               kappa = 1.0;
182:             } else {
183:               kappa = actred / prered;
184:             }

186:             tau_1   = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust + (1.0 - bnk->theta_i) * prered - actred);
187:             tau_2   = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust - (1.0 + bnk->theta_i) * prered + actred);
188:             tau_min = PetscMin(tau_1, tau_2);
189:             tau_max = PetscMax(tau_1, tau_2);

191:             if (PetscAbsScalar(kappa - (PetscReal)1.0) <= bnk->mu1_i) {
192:               /*  Great agreement */
193:               max_radius = PetscMax(max_radius, tao->trust);

195:               if (tau_max < 1.0) {
196:                 tau = bnk->gamma3_i;
197:               } else if (tau_max > bnk->gamma4_i) {
198:                 tau = bnk->gamma4_i;
199:               } else {
200:                 tau = tau_max;
201:               }
202:             } else if (PetscAbsScalar(kappa - (PetscReal)1.0) <= bnk->mu2_i) {
203:               /*  Good agreement */
204:               max_radius = PetscMax(max_radius, tao->trust);

206:               if (tau_max < bnk->gamma2_i) {
207:                 tau = bnk->gamma2_i;
208:               } else if (tau_max > bnk->gamma3_i) {
209:                 tau = bnk->gamma3_i;
210:               } else {
211:                 tau = tau_max;
212:               }
213:             } else {
214:               /*  Not good agreement */
215:               if (tau_min > 1.0) {
216:                 tau = bnk->gamma2_i;
217:               } else if (tau_max < bnk->gamma1_i) {
218:                 tau = bnk->gamma1_i;
219:               } else if ((tau_min < bnk->gamma1_i) && (tau_max >= 1.0)) {
220:                 tau = bnk->gamma1_i;
221:               } else if ((tau_1 >= bnk->gamma1_i) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
222:                 tau = tau_1;
223:               } else if ((tau_2 >= bnk->gamma1_i) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
224:                 tau = tau_2;
225:               } else {
226:                 tau = tau_max;
227:               }
228:             }
229:           }
230:           tao->trust = tau * tao->trust;
231:         }

233:         if (f_min < bnk->f) {
234:           /* We accidentally found a solution better than the initial, so accept it */
235:           bnk->f = f_min;
236:           PetscCall(VecCopy(tao->solution, bnk->Xold));
237:           PetscCall(VecAXPY(tao->solution, sigma, tao->gradient));
238:           PetscCall(TaoBoundSolution(tao->solution, tao->XL, tao->XU, 0.0, &nDiff, tao->solution));
239:           PetscCall(VecCopy(tao->solution, tao->stepdirection));
240:           PetscCall(VecAXPY(tao->stepdirection, -1.0, bnk->Xold));
241:           PetscCall(TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient));
242:           PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
243:           PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient));
244:           if (bnk->active_idx) PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
245:           /* Compute gradient at the new iterate and flip switch to compute the Hessian later */
246:           PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm));
247:           *needH = PETSC_TRUE;
248:           /* Test the new step for convergence */
249:           PetscCall(VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W));
250:           PetscCall(VecNorm(bnk->W, NORM_2, &resnorm));
251:           PetscCheck(!PetscIsInfOrNanReal(resnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated infinity or NaN");
252:           PetscCall(TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its));
253:           PetscCall(TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, 1.0));
254:           PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
255:           if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(PETSC_SUCCESS);
256:           /* active BNCG recycling early because we have a stepdirection computed */
257:           PetscCall(TaoSetRecycleHistory(bnk->bncg, PETSC_TRUE));
258:         }
259:       }
260:       tao->trust = PetscMax(tao->trust, max_radius);

262:       /* Ensure that the trust radius is within the limits */
263:       tao->trust = PetscMax(tao->trust, bnk->min_radius);
264:       tao->trust = PetscMin(tao->trust, bnk->max_radius);
265:       break;

267:     default:
268:       /* Norm of the first direction will initialize radius */
269:       tao->trust = 0.0;
270:       break;
271:     }
272:   }
273:   PetscFunctionReturn(PETSC_SUCCESS);
274: }

276: /* Computes the exact Hessian and extracts its subHessian */

278: PetscErrorCode TaoBNKComputeHessian(Tao tao)
279: {
280:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

282:   PetscFunctionBegin;
283:   /* Compute the Hessian */
284:   PetscCall(TaoComputeHessian(tao, tao->solution, tao->hessian, tao->hessian_pre));
285:   /* Add a correction to the BFGS preconditioner */
286:   if (bnk->M) PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
287:   /* Prepare the reduced sub-matrices for the inactive set */
288:   PetscCall(TaoBNKComputeSubHessian(tao));
289:   PetscFunctionReturn(PETSC_SUCCESS);
290: }

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

294: PetscErrorCode TaoBNKEstimateActiveSet(Tao tao, PetscInt asType)
295: {
296:   TAO_BNK  *bnk = (TAO_BNK *)tao->data;
297:   PetscBool hessComputed, diagExists, hadactive;

299:   PetscFunctionBegin;
300:   hadactive = bnk->active_idx ? PETSC_TRUE : PETSC_FALSE;
301:   switch (asType) {
302:   case BNK_AS_NONE:
303:     PetscCall(ISDestroy(&bnk->inactive_idx));
304:     PetscCall(VecWhichInactive(tao->XL, tao->solution, bnk->unprojected_gradient, tao->XU, PETSC_TRUE, &bnk->inactive_idx));
305:     PetscCall(ISDestroy(&bnk->active_idx));
306:     PetscCall(ISComplementVec(bnk->inactive_idx, tao->solution, &bnk->active_idx));
307:     break;

309:   case BNK_AS_BERTSEKAS:
310:     /* Compute the trial step vector with which we will estimate the active set at the next iteration */
311:     if (bnk->M) {
312:       /* If the BFGS matrix is available, we will construct a trial step with it */
313:       PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, bnk->W));
314:     } else {
315:       hessComputed = diagExists = PETSC_FALSE;
316:       if (tao->hessian) PetscCall(MatAssembled(tao->hessian, &hessComputed));
317:       if (hessComputed) PetscCall(MatHasOperation(tao->hessian, MATOP_GET_DIAGONAL, &diagExists));
318:       if (diagExists) {
319:         /* BFGS preconditioner doesn't exist so let's invert the absolute diagonal of the Hessian instead onto the gradient */
320:         PetscCall(MatGetDiagonal(tao->hessian, bnk->Xwork));
321:         PetscCall(VecAbs(bnk->Xwork));
322:         PetscCall(VecMedian(bnk->Diag_min, bnk->Xwork, bnk->Diag_max, bnk->Xwork));
323:         PetscCall(VecReciprocal(bnk->Xwork));
324:         PetscCall(VecPointwiseMult(bnk->W, bnk->Xwork, bnk->unprojected_gradient));
325:       } else {
326:         /* If the Hessian or its diagonal does not exist, we will simply use gradient step */
327:         PetscCall(VecCopy(bnk->unprojected_gradient, bnk->W));
328:       }
329:     }
330:     PetscCall(VecScale(bnk->W, -1.0));
331:     PetscCall(TaoEstimateActiveBounds(tao->solution, tao->XL, tao->XU, bnk->unprojected_gradient, bnk->W, bnk->Xwork, bnk->as_step, &bnk->as_tol, &bnk->active_lower, &bnk->active_upper, &bnk->active_fixed, &bnk->active_idx, &bnk->inactive_idx));
332:     break;

334:   default:
335:     break;
336:   }
337:   bnk->resetksp = (PetscBool)(bnk->active_idx || hadactive); /* inactive Hessian size may have changed, need to reset operators */
338:   PetscFunctionReturn(PETSC_SUCCESS);
339: }

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

343: PetscErrorCode TaoBNKBoundStep(Tao tao, PetscInt asType, Vec step)
344: {
345:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

347:   PetscFunctionBegin;
348:   switch (asType) {
349:   case BNK_AS_NONE:
350:     if (bnk->active_idx) PetscCall(VecISSet(step, bnk->active_idx, 0.0));
351:     break;
352:   case BNK_AS_BERTSEKAS:
353:     PetscCall(TaoBoundStep(tao->solution, tao->XL, tao->XU, bnk->active_lower, bnk->active_upper, bnk->active_fixed, 1.0, step));
354:     break;
355:   default:
356:     break;
357:   }
358:   PetscFunctionReturn(PETSC_SUCCESS);
359: }

361: /* Routine for taking a finite number of BNCG iterations to
362:    accelerate Newton convergence.

364:    In practice, this approach simply trades off Hessian evaluations
365:    for more gradient evaluations.
366: */

368: PetscErrorCode TaoBNKTakeCGSteps(Tao tao, PetscBool *terminate)
369: {
370:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

372:   PetscFunctionBegin;
373:   *terminate = PETSC_FALSE;
374:   if (bnk->max_cg_its > 0) {
375:     /* Copy the current function value (important vectors are already shared) */
376:     bnk->bncg_ctx->f = bnk->f;
377:     /* Take some small finite number of BNCG iterations */
378:     PetscCall(TaoSolve(bnk->bncg));
379:     /* Add the number of gradient and function evaluations to the total     *
380:      * Note: nfuncs are not copied as tao and subsolvers share same TaoTerm */
381:     bnk->tot_cg_its += bnk->bncg->niter;
382:     /* Extract the BNCG function value out and save it into BNK */
383:     bnk->f = bnk->bncg_ctx->f;
384:     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) {
385:       *terminate = PETSC_TRUE;
386:     } else {
387:       PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
388:     }
389:   }
390:   PetscFunctionReturn(PETSC_SUCCESS);
391: }

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

395: PetscErrorCode TaoBNKComputeStep(Tao tao, PetscBool shift, KSPConvergedReason *ksp_reason, PetscInt *step_type)
396: {
397:   TAO_BNK  *bnk         = (TAO_BNK *)tao->data;
398:   PetscInt  bfgsUpdates = 0;
399:   PetscInt  kspits;
400:   PetscBool is_lmvm;
401:   PetscBool kspTR;

403:   PetscFunctionBegin;
404:   /* If there are no inactive variables left, save some computation and return an adjusted zero step
405:      that has (l-x) and (u-x) for lower and upper bounded variables. */
406:   if (!bnk->inactive_idx) {
407:     PetscCall(VecSet(tao->stepdirection, 0.0));
408:     PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));
409:     PetscFunctionReturn(PETSC_SUCCESS);
410:   }

412:   /* Shift the reduced Hessian matrix */
413:   if (shift && bnk->pert > 0) {
414:     PetscCall(PetscObjectTypeCompare((PetscObject)tao->hessian, MATLMVM, &is_lmvm));
415:     if (is_lmvm) {
416:       PetscCall(MatShift(tao->hessian, bnk->pert));
417:     } else {
418:       PetscCall(MatShift(bnk->H_inactive, bnk->pert));
419:       if (bnk->H_inactive != bnk->Hpre_inactive) PetscCall(MatShift(bnk->Hpre_inactive, bnk->pert));
420:     }
421:   }

423:   /* Solve the Newton system of equations */
424:   tao->ksp_its = 0;
425:   PetscCall(VecSet(tao->stepdirection, 0.0));
426:   if (bnk->resetksp) {
427:     PetscCall(KSPReset(tao->ksp));
428:     PetscCall(KSPResetFromOptions(tao->ksp));
429:     bnk->resetksp = PETSC_FALSE;
430:   }
431:   PetscCall(KSPSetOperators(tao->ksp, bnk->H_inactive, bnk->Hpre_inactive));
432:   PetscCall(VecCopy(bnk->unprojected_gradient, bnk->Gwork));
433:   if (bnk->active_idx) {
434:     PetscCall(VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive));
435:     PetscCall(VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive));
436:   } else {
437:     bnk->G_inactive = bnk->unprojected_gradient;
438:     bnk->X_inactive = tao->stepdirection;
439:   }
440:   PetscCall(KSPCGSetRadius(tao->ksp, tao->trust));
441:   PetscCall(KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive));
442:   PetscCall(KSPGetIterationNumber(tao->ksp, &kspits));
443:   tao->ksp_its += kspits;
444:   tao->ksp_tot_its += kspits;
445:   PetscCall(PetscObjectHasFunction((PetscObject)tao->ksp, "KSPCGGetNormD_C", &kspTR));
446:   if (kspTR) {
447:     PetscCall(KSPCGGetNormD(tao->ksp, &bnk->dnorm));

449:     if (0.0 == tao->trust) {
450:       /* Radius was uninitialized; use the norm of the direction */
451:       if (bnk->dnorm > 0.0) {
452:         tao->trust = bnk->dnorm;

454:         /* Modify the radius if it is too large or small */
455:         tao->trust = PetscMax(tao->trust, bnk->min_radius);
456:         tao->trust = PetscMin(tao->trust, bnk->max_radius);
457:       } else {
458:         /* The direction was bad; set radius to default value and re-solve
459:            the trust-region subproblem to get a direction */
460:         tao->trust = tao->trust0;

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

466:         PetscCall(KSPCGSetRadius(tao->ksp, tao->trust));
467:         PetscCall(KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive));
468:         PetscCall(KSPGetIterationNumber(tao->ksp, &kspits));
469:         tao->ksp_its += kspits;
470:         tao->ksp_tot_its += kspits;
471:         PetscCall(KSPCGGetNormD(tao->ksp, &bnk->dnorm));

473:         PetscCheck(bnk->dnorm != 0.0, PetscObjectComm((PetscObject)tao), PETSC_ERR_PLIB, "Initial direction zero");
474:       }
475:     }
476:   }
477:   /* Restore sub vectors back */
478:   if (bnk->active_idx) {
479:     PetscCall(VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive));
480:     PetscCall(VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive));
481:   }
482:   /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
483:   PetscCall(VecScale(tao->stepdirection, -1.0));
484:   PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));

486:   /* Record convergence reasons */
487:   PetscCall(KSPGetConvergedReason(tao->ksp, ksp_reason));
488:   if (KSP_CONVERGED_ATOL == *ksp_reason) {
489:     ++bnk->ksp_atol;
490:   } else if (KSP_CONVERGED_RTOL == *ksp_reason) {
491:     ++bnk->ksp_rtol;
492:   } else if (KSP_CONVERGED_STEP_LENGTH == *ksp_reason) {
493:     ++bnk->ksp_ctol;
494:   } else if (KSP_CONVERGED_NEG_CURVE == *ksp_reason) {
495:     ++bnk->ksp_negc;
496:   } else if (KSP_DIVERGED_DTOL == *ksp_reason) {
497:     ++bnk->ksp_dtol;
498:   } else if (KSP_DIVERGED_ITS == *ksp_reason) {
499:     ++bnk->ksp_iter;
500:   } else {
501:     ++bnk->ksp_othr;
502:   }

504:   /* Make sure the BFGS preconditioner is healthy */
505:   if (bnk->M) {
506:     PetscCall(MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates));
507:     if ((KSP_DIVERGED_INDEFINITE_PC == *ksp_reason) && (bfgsUpdates > 0)) {
508:       /* Preconditioner is numerically indefinite; reset the approximation. */
509:       PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
510:       PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
511:     }
512:   }
513:   *step_type = BNK_NEWTON;
514:   PetscFunctionReturn(PETSC_SUCCESS);
515: }

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

519: PetscErrorCode TaoBNKRecomputePred(Tao tao, Vec S, PetscReal *prered)
520: {
521:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

523:   PetscFunctionBegin;
524:   /* Extract subvectors associated with the inactive set */
525:   if (bnk->active_idx) {
526:     PetscCall(VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive));
527:     PetscCall(VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work));
528:     PetscCall(VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive));
529:   } else {
530:     bnk->X_inactive    = tao->stepdirection;
531:     bnk->inactive_work = bnk->Xwork;
532:     bnk->G_inactive    = bnk->Gwork;
533:   }
534:   /* Recompute the predicted decrease based on the quadratic model */
535:   PetscCall(MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work));
536:   PetscCall(VecAYPX(bnk->inactive_work, -0.5, bnk->G_inactive));
537:   PetscCall(VecDot(bnk->inactive_work, bnk->X_inactive, prered));
538:   /* Restore the sub vectors */
539:   if (bnk->active_idx) {
540:     PetscCall(VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive));
541:     PetscCall(VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work));
542:     PetscCall(VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive));
543:   }
544:   PetscFunctionReturn(PETSC_SUCCESS);
545: }

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

549:    The step direction falls back onto BFGS, scaled gradient and gradient steps
550:    in the event that the Newton step fails the test.
551: */

553: PetscErrorCode TaoBNKSafeguardStep(Tao tao, KSPConvergedReason ksp_reason, PetscInt *stepType)
554: {
555:   TAO_BNK  *bnk = (TAO_BNK *)tao->data;
556:   PetscReal gdx, e_min;
557:   PetscInt  bfgsUpdates;

559:   PetscFunctionBegin;
560:   switch (*stepType) {
561:   case BNK_NEWTON:
562:     PetscCall(VecDot(tao->stepdirection, tao->gradient, &gdx));
563:     if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) {
564:       /* Newton step is not descent or direction produced infinity or NaN
565:         Update the perturbation for next time */
566:       if (bnk->pert <= 0.0) {
567:         PetscBool is_gltr;

569:         /* Initialize the perturbation */
570:         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
571:         PetscCall(PetscObjectTypeCompare((PetscObject)tao->ksp, KSPGLTR, &is_gltr));
572:         if (is_gltr) {
573:           PetscCall(KSPGLTRGetMinEig(tao->ksp, &e_min));
574:           bnk->pert = PetscMax(bnk->pert, -e_min);
575:         }
576:       } else {
577:         /* Increase the perturbation */
578:         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
579:       }

581:       if (!bnk->M) {
582:         /* We don't have the bfgs matrix around and updated
583:           Must use gradient direction in this case */
584:         PetscCall(VecCopy(tao->gradient, tao->stepdirection));
585:         *stepType = BNK_GRADIENT;
586:       } else {
587:         /* Attempt to use the BFGS direction */
588:         PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));

590:         /* Check for success (descent direction)
591:           NOTE: Negative gdx here means not a descent direction because
592:           the fall-back step is missing a negative sign. */
593:         PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx));
594:         if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
595:           /* BFGS direction is not descent or direction produced not a number
596:             We can assert bfgsUpdates > 1 in this case because
597:             the first solve produces the scaled gradient direction,
598:             which is guaranteed to be descent */

600:           /* Use steepest descent direction (scaled) */
601:           PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
602:           PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
603:           PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));

605:           *stepType = BNK_SCALED_GRADIENT;
606:         } else {
607:           PetscCall(MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates));
608:           if (1 == bfgsUpdates) {
609:             /* The first BFGS direction is always the scaled gradient */
610:             *stepType = BNK_SCALED_GRADIENT;
611:           } else {
612:             *stepType = BNK_BFGS;
613:           }
614:         }
615:       }
616:       /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
617:       PetscCall(VecScale(tao->stepdirection, -1.0));
618:       PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));
619:     } else {
620:       /* Computed Newton step is descent */
621:       switch (ksp_reason) {
622:       case KSP_DIVERGED_NANORINF:
623:       case KSP_DIVERGED_BREAKDOWN:
624:       case KSP_DIVERGED_INDEFINITE_MAT:
625:       case KSP_DIVERGED_INDEFINITE_PC:
626:       case KSP_CONVERGED_NEG_CURVE:
627:         /* Matrix or preconditioner is indefinite; increase perturbation */
628:         if (bnk->pert <= 0.0) {
629:           PetscBool is_gltr;

631:           /* Initialize the perturbation */
632:           bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
633:           PetscCall(PetscObjectTypeCompare((PetscObject)tao->ksp, KSPGLTR, &is_gltr));
634:           if (is_gltr) {
635:             PetscCall(KSPGLTRGetMinEig(tao->ksp, &e_min));
636:             bnk->pert = PetscMax(bnk->pert, -e_min);
637:           }
638:         } else {
639:           /* Increase the perturbation */
640:           bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
641:         }
642:         break;

644:       default:
645:         /* Newton step computation is good; decrease perturbation */
646:         bnk->pert = PetscMin(bnk->psfac * bnk->pert, bnk->pmsfac * bnk->gnorm);
647:         if (bnk->pert < bnk->pmin) bnk->pert = 0.0;
648:         break;
649:       }
650:       *stepType = BNK_NEWTON;
651:     }
652:     break;

654:   case BNK_BFGS:
655:     /* Check for success (descent direction) */
656:     PetscCall(VecDot(tao->stepdirection, tao->gradient, &gdx));
657:     if (gdx >= 0 || PetscIsInfOrNanReal(gdx)) {
658:       /* Step is not descent or solve was not successful
659:          Use steepest descent direction (scaled) */
660:       PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
661:       PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
662:       PetscCall(MatSolve(bnk->M, tao->gradient, tao->stepdirection));
663:       PetscCall(VecScale(tao->stepdirection, -1.0));
664:       PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));
665:       *stepType = BNK_SCALED_GRADIENT;
666:     } else {
667:       *stepType = BNK_BFGS;
668:     }
669:     break;

671:   case BNK_SCALED_GRADIENT:
672:     break;

674:   default:
675:     break;
676:   }
677:   PetscFunctionReturn(PETSC_SUCCESS);
678: }

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

682:   Includes fallbacks to BFGS, scaled gradient, and unscaled gradient steps if the
683:   Newton step does not produce a valid step length.
684: */

686: PetscErrorCode TaoBNKPerformLineSearch(Tao tao, PetscInt *stepType, PetscReal *steplen, TaoLineSearchConvergedReason *reason)
687: {
688:   TAO_BNK                     *bnk = (TAO_BNK *)tao->data;
689:   TaoLineSearchConvergedReason ls_reason;
690:   PetscReal                    e_min, gdx;
691:   PetscInt                     bfgsUpdates;

693:   PetscFunctionBegin;
694:   /* Perform the linesearch */
695:   PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason));
696:   PetscCall(TaoAddLineSearchCounts(tao));

698:   while (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER && *stepType != BNK_SCALED_GRADIENT && *stepType != BNK_GRADIENT) {
699:     /* Linesearch failed, revert solution */
700:     bnk->f = bnk->fold;
701:     PetscCall(VecCopy(bnk->Xold, tao->solution));
702:     PetscCall(VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient));

704:     switch (*stepType) {
705:     case BNK_NEWTON:
706:       /* Failed to obtain acceptable iterate with Newton step
707:          Update the perturbation for next time */
708:       if (bnk->pert <= 0.0) {
709:         PetscBool is_gltr;

711:         /* Initialize the perturbation */
712:         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
713:         PetscCall(PetscObjectTypeCompare((PetscObject)tao->ksp, KSPGLTR, &is_gltr));
714:         if (is_gltr) {
715:           PetscCall(KSPGLTRGetMinEig(tao->ksp, &e_min));
716:           bnk->pert = PetscMax(bnk->pert, -e_min);
717:         }
718:       } else {
719:         /* Increase the perturbation */
720:         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
721:       }

723:       if (!bnk->M) {
724:         /* We don't have the bfgs matrix around and being updated
725:            Must use gradient direction in this case */
726:         PetscCall(VecCopy(bnk->unprojected_gradient, tao->stepdirection));
727:         *stepType = BNK_GRADIENT;
728:       } else {
729:         /* Attempt to use the BFGS direction */
730:         PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));
731:         /* Check for success (descent direction)
732:            NOTE: Negative gdx means not a descent direction because the step here is missing a negative sign. */
733:         PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx));
734:         if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
735:           /* BFGS direction is not descent or direction produced not a number
736:              We can assert bfgsUpdates > 1 in this case
737:              Use steepest descent direction (scaled) */
738:           PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
739:           PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
740:           PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));

742:           bfgsUpdates = 1;
743:           *stepType   = BNK_SCALED_GRADIENT;
744:         } else {
745:           PetscCall(MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates));
746:           if (1 == bfgsUpdates) {
747:             /* The first BFGS direction is always the scaled gradient */
748:             *stepType = BNK_SCALED_GRADIENT;
749:           } else {
750:             *stepType = BNK_BFGS;
751:           }
752:         }
753:       }
754:       break;

756:     case BNK_BFGS:
757:       /* Can only enter if pc_type == BNK_PC_BFGS
758:          Failed to obtain acceptable iterate with BFGS step
759:          Attempt to use the scaled gradient direction */
760:       PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
761:       PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
762:       PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));

764:       bfgsUpdates = 1;
765:       *stepType   = BNK_SCALED_GRADIENT;
766:       break;
767:     }
768:     /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
769:     PetscCall(VecScale(tao->stepdirection, -1.0));
770:     PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));

772:     /* Perform one last line search with the fall-back step */
773:     PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason));
774:     PetscCall(TaoAddLineSearchCounts(tao));
775:   }
776:   *reason = ls_reason;
777:   PetscFunctionReturn(PETSC_SUCCESS);
778: }

780: /* Routine for updating the trust radius.

782:   Function features three different update methods:
783:   1) Line-search step length based
784:   2) Predicted decrease on the CG quadratic model
785:   3) Interpolation
786: */

788: PetscErrorCode TaoBNKUpdateTrustRadius(Tao tao, PetscReal prered, PetscReal actred, PetscInt updateType, PetscInt stepType, PetscBool *accept)
789: {
790:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

792:   PetscReal step, kappa;
793:   PetscReal gdx, tau_1, tau_2, tau_min, tau_max;

795:   PetscFunctionBegin;
796:   /* Update trust region radius */
797:   *accept = PETSC_FALSE;
798:   switch (updateType) {
799:   case BNK_UPDATE_STEP:
800:     *accept = PETSC_TRUE; /* always accept here because line search succeeded */
801:     if (stepType == BNK_NEWTON) {
802:       PetscCall(TaoLineSearchGetStepLength(tao->linesearch, &step));
803:       if (step < bnk->nu1) {
804:         /* Very bad step taken; reduce radius */
805:         tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
806:       } else if (step < bnk->nu2) {
807:         /* Reasonably bad step taken; reduce radius */
808:         tao->trust = bnk->omega2 * PetscMin(bnk->dnorm, tao->trust);
809:       } else if (step < bnk->nu3) {
810:         /*  Reasonable step was taken; leave radius alone */
811:         if (bnk->omega3 < 1.0) {
812:           tao->trust = bnk->omega3 * PetscMin(bnk->dnorm, tao->trust);
813:         } else if (bnk->omega3 > 1.0) {
814:           tao->trust = PetscMax(bnk->omega3 * bnk->dnorm, tao->trust);
815:         }
816:       } else if (step < bnk->nu4) {
817:         /*  Full step taken; increase the radius */
818:         tao->trust = PetscMax(bnk->omega4 * bnk->dnorm, tao->trust);
819:       } else {
820:         /*  More than full step taken; increase the radius */
821:         tao->trust = PetscMax(bnk->omega5 * bnk->dnorm, tao->trust);
822:       }
823:     } else {
824:       /*  Newton step was not good; reduce the radius */
825:       tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
826:     }
827:     break;

829:   case BNK_UPDATE_REDUCTION:
830:     if (stepType == BNK_NEWTON) {
831:       if ((prered < 0.0) || PetscIsInfOrNanReal(prered)) {
832:         /* The predicted reduction has the wrong sign.  This cannot
833:            happen in infinite precision arithmetic.  Step should
834:            be rejected! */
835:         tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
836:       } else {
837:         if (PetscIsInfOrNanReal(actred)) {
838:           tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
839:         } else {
840:           if ((PetscAbsScalar(actred) <= PetscMax(1.0, PetscAbsScalar(bnk->f)) * bnk->epsilon) && (PetscAbsScalar(prered) <= PetscMax(1.0, PetscAbsScalar(bnk->f)) * bnk->epsilon)) {
841:             kappa = 1.0;
842:           } else {
843:             kappa = actred / prered;
844:           }
845:           /* Accept or reject the step and update radius */
846:           if (kappa < bnk->eta1) {
847:             /* Reject the step */
848:             tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
849:           } else {
850:             /* Accept the step */
851:             *accept = PETSC_TRUE;
852:             /* Update the trust region radius only if the computed step is at the trust radius boundary */
853:             if (bnk->dnorm == tao->trust) {
854:               if (kappa < bnk->eta2) {
855:                 /* Marginal bad step */
856:                 tao->trust = bnk->alpha2 * tao->trust;
857:               } else if (kappa < bnk->eta3) {
858:                 /* Reasonable step */
859:                 tao->trust = bnk->alpha3 * tao->trust;
860:               } else if (kappa < bnk->eta4) {
861:                 /* Good step */
862:                 tao->trust = bnk->alpha4 * tao->trust;
863:               } else {
864:                 /* Very good step */
865:                 tao->trust = bnk->alpha5 * tao->trust;
866:               }
867:             }
868:           }
869:         }
870:       }
871:     } else {
872:       /*  Newton step was not good; reduce the radius */
873:       tao->trust = bnk->alpha1 * PetscMin(bnk->dnorm, tao->trust);
874:     }
875:     break;

877:   default:
878:     if (stepType == BNK_NEWTON) {
879:       if (prered < 0.0) {
880:         /*  The predicted reduction has the wrong sign.  This cannot */
881:         /*  happen in infinite precision arithmetic.  Step should */
882:         /*  be rejected! */
883:         tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
884:       } else {
885:         if (PetscIsInfOrNanReal(actred)) {
886:           tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
887:         } else {
888:           if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) {
889:             kappa = 1.0;
890:           } else {
891:             kappa = actred / prered;
892:           }

894:           PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx));
895:           tau_1   = bnk->theta * gdx / (bnk->theta * gdx - (1.0 - bnk->theta) * prered + actred);
896:           tau_2   = bnk->theta * gdx / (bnk->theta * gdx + (1.0 + bnk->theta) * prered - actred);
897:           tau_min = PetscMin(tau_1, tau_2);
898:           tau_max = PetscMax(tau_1, tau_2);

900:           if (kappa >= 1.0 - bnk->mu1) {
901:             /*  Great agreement */
902:             *accept = PETSC_TRUE;
903:             if (tau_max < 1.0) {
904:               tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
905:             } else if (tau_max > bnk->gamma4) {
906:               tao->trust = PetscMax(tao->trust, bnk->gamma4 * bnk->dnorm);
907:             } else {
908:               tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
909:             }
910:           } else if (kappa >= 1.0 - bnk->mu2) {
911:             /*  Good agreement */
912:             *accept = PETSC_TRUE;
913:             if (tau_max < bnk->gamma2) {
914:               tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
915:             } else if (tau_max > bnk->gamma3) {
916:               tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
917:             } else if (tau_max < 1.0) {
918:               tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
919:             } else {
920:               tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
921:             }
922:           } else {
923:             /*  Not good agreement */
924:             if (tau_min > 1.0) {
925:               tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
926:             } else if (tau_max < bnk->gamma1) {
927:               tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
928:             } else if ((tau_min < bnk->gamma1) && (tau_max >= 1.0)) {
929:               tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
930:             } else if ((tau_1 >= bnk->gamma1) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1) || (tau_2 >= 1.0))) {
931:               tao->trust = tau_1 * PetscMin(tao->trust, bnk->dnorm);
932:             } else if ((tau_2 >= bnk->gamma1) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1) || (tau_2 >= 1.0))) {
933:               tao->trust = tau_2 * PetscMin(tao->trust, bnk->dnorm);
934:             } else {
935:               tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
936:             }
937:           }
938:         }
939:       }
940:     } else {
941:       /*  Newton step was not good; reduce the radius */
942:       tao->trust = bnk->gamma1 * PetscMin(bnk->dnorm, tao->trust);
943:     }
944:     break;
945:   }
946:   /* Make sure the radius does not violate min and max settings */
947:   tao->trust = PetscMin(tao->trust, bnk->max_radius);
948:   tao->trust = PetscMax(tao->trust, bnk->min_radius);
949:   PetscFunctionReturn(PETSC_SUCCESS);
950: }

952: PetscErrorCode TaoBNKAddStepCounts(Tao tao, PetscInt stepType)
953: {
954:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

956:   PetscFunctionBegin;
957:   switch (stepType) {
958:   case BNK_NEWTON:
959:     ++bnk->newt;
960:     break;
961:   case BNK_BFGS:
962:     ++bnk->bfgs;
963:     break;
964:   case BNK_SCALED_GRADIENT:
965:     ++bnk->sgrad;
966:     break;
967:   case BNK_GRADIENT:
968:     ++bnk->grad;
969:     break;
970:   default:
971:     break;
972:   }
973:   PetscFunctionReturn(PETSC_SUCCESS);
974: }

976: PetscErrorCode TaoSetUp_BNK(Tao tao)
977: {
978:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

980:   PetscFunctionBegin;
981:   if (!tao->gradient) PetscCall(VecDuplicate(tao->solution, &tao->gradient));
982:   if (!tao->stepdirection) PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));
983:   if (!bnk->W) PetscCall(VecDuplicate(tao->solution, &bnk->W));
984:   if (!bnk->Xold) PetscCall(VecDuplicate(tao->solution, &bnk->Xold));
985:   if (!bnk->Gold) PetscCall(VecDuplicate(tao->solution, &bnk->Gold));
986:   if (!bnk->Xwork) PetscCall(VecDuplicate(tao->solution, &bnk->Xwork));
987:   if (!bnk->Gwork) PetscCall(VecDuplicate(tao->solution, &bnk->Gwork));
988:   if (!bnk->unprojected_gradient) PetscCall(VecDuplicate(tao->solution, &bnk->unprojected_gradient));
989:   if (!bnk->unprojected_gradient_old) PetscCall(VecDuplicate(tao->solution, &bnk->unprojected_gradient_old));
990:   if (!bnk->Diag_min) PetscCall(VecDuplicate(tao->solution, &bnk->Diag_min));
991:   if (!bnk->Diag_max) PetscCall(VecDuplicate(tao->solution, &bnk->Diag_max));
992:   PetscCall(TaoSetSolution(bnk->bncg, tao->solution));
993:   if (bnk->max_cg_its > 0) {
994:     /* Ensure that the important common vectors are shared between BNK and embedded BNCG */
995:     bnk->bncg_ctx = (TAO_BNCG *)bnk->bncg->data;
996:     PetscCall(PetscObjectReference((PetscObject)bnk->unprojected_gradient_old));
997:     PetscCall(VecDestroy(&bnk->bncg_ctx->unprojected_gradient_old));
998:     bnk->bncg_ctx->unprojected_gradient_old = bnk->unprojected_gradient_old;
999:     PetscCall(PetscObjectReference((PetscObject)bnk->unprojected_gradient));
1000:     PetscCall(VecDestroy(&bnk->bncg_ctx->unprojected_gradient));
1001:     bnk->bncg_ctx->unprojected_gradient = bnk->unprojected_gradient;
1002:     PetscCall(PetscObjectReference((PetscObject)bnk->Gold));
1003:     PetscCall(VecDestroy(&bnk->bncg_ctx->G_old));
1004:     bnk->bncg_ctx->G_old = bnk->Gold;
1005:     PetscCall(PetscObjectReference((PetscObject)tao->gradient));
1006:     PetscCall(VecDestroy(&bnk->bncg->gradient));
1007:     bnk->bncg->gradient = tao->gradient;
1008:     PetscCall(PetscObjectReference((PetscObject)tao->stepdirection));
1009:     PetscCall(VecDestroy(&bnk->bncg->stepdirection));
1010:     bnk->bncg->stepdirection = tao->stepdirection;
1011:     /* Copy over some settings from BNK into BNCG */
1012:     PetscCall(TaoSetMaximumIterations(bnk->bncg, bnk->max_cg_its));
1013:     PetscCall(TaoSetTolerances(bnk->bncg, tao->gatol, tao->grtol, tao->gttol));
1014:     PetscCall(TaoSetFunctionLowerBound(bnk->bncg, tao->fmin));
1015:     PetscCall(TaoSetConvergenceTest(bnk->bncg, tao->ops->convergencetest, tao->cnvP));
1016:     {
1017:       TaoTerm   term;
1018:       Vec       params;
1019:       PetscReal scale;
1020:       Mat       map;

1022:       // Note: tao->objective_term.term and bnk->bncg->objective_term.term will point to same address
1023:       PetscCall(TaoGetTerm(tao, &scale, &term, &params, &map));
1024:       PetscCall(TaoAddTerm(bnk->bncg, NULL, scale, term, params, map));
1025:     }
1026:     PetscCall(PetscObjectCopyFortranFunctionPointers((PetscObject)tao, (PetscObject)bnk->bncg));
1027:   }
1028:   bnk->X_inactive    = NULL;
1029:   bnk->G_inactive    = NULL;
1030:   bnk->inactive_work = NULL;
1031:   bnk->active_work   = NULL;
1032:   bnk->inactive_idx  = NULL;
1033:   bnk->active_idx    = NULL;
1034:   bnk->active_lower  = NULL;
1035:   bnk->active_upper  = NULL;
1036:   bnk->active_fixed  = NULL;
1037:   bnk->M             = NULL;
1038:   bnk->H_inactive    = NULL;
1039:   bnk->Hpre_inactive = NULL;
1040:   PetscFunctionReturn(PETSC_SUCCESS);
1041: }

1043: PetscErrorCode TaoDestroy_BNK(Tao tao)
1044: {
1045:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

1047:   PetscFunctionBegin;
1048:   PetscCall(VecDestroy(&bnk->W));
1049:   PetscCall(VecDestroy(&bnk->Xold));
1050:   PetscCall(VecDestroy(&bnk->Gold));
1051:   PetscCall(VecDestroy(&bnk->Xwork));
1052:   PetscCall(VecDestroy(&bnk->Gwork));
1053:   PetscCall(VecDestroy(&bnk->unprojected_gradient));
1054:   PetscCall(VecDestroy(&bnk->unprojected_gradient_old));
1055:   PetscCall(VecDestroy(&bnk->Diag_min));
1056:   PetscCall(VecDestroy(&bnk->Diag_max));
1057:   PetscCall(ISDestroy(&bnk->active_lower));
1058:   PetscCall(ISDestroy(&bnk->active_upper));
1059:   PetscCall(ISDestroy(&bnk->active_fixed));
1060:   PetscCall(ISDestroy(&bnk->active_idx));
1061:   PetscCall(ISDestroy(&bnk->inactive_idx));
1062:   PetscCall(MatDestroy(&bnk->Hpre_inactive));
1063:   PetscCall(MatDestroy(&bnk->H_inactive));
1064:   PetscCall(TaoDestroy(&bnk->bncg));
1065:   PetscCall(KSPDestroy(&tao->ksp));
1066:   PetscCall(PetscFree(tao->data));
1067:   PetscFunctionReturn(PETSC_SUCCESS);
1068: }

1070: PetscErrorCode TaoSetFromOptions_BNK(Tao tao, PetscOptionItems PetscOptionsObject)
1071: {
1072:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

1074:   PetscFunctionBegin;
1075:   PetscOptionsHeadBegin(PetscOptionsObject, "Newton-Krylov method for bound constrained optimization");
1076:   PetscCall(PetscOptionsEList("-tao_bnk_init_type", "radius initialization type", "", BNK_INIT, BNK_INIT_TYPES, BNK_INIT[bnk->init_type], &bnk->init_type, NULL));
1077:   PetscCall(PetscOptionsEList("-tao_bnk_update_type", "radius update type", "", BNK_UPDATE, BNK_UPDATE_TYPES, BNK_UPDATE[bnk->update_type], &bnk->update_type, NULL));
1078:   PetscCall(PetscOptionsEList("-tao_bnk_as_type", "active set estimation method", "", BNK_AS, BNK_AS_TYPES, BNK_AS[bnk->as_type], &bnk->as_type, NULL));
1079:   PetscCall(PetscOptionsReal("-tao_bnk_sval", "(developer) Hessian perturbation starting value", "", bnk->sval, &bnk->sval, NULL));
1080:   PetscCall(PetscOptionsReal("-tao_bnk_imin", "(developer) minimum initial Hessian perturbation", "", bnk->imin, &bnk->imin, NULL));
1081:   PetscCall(PetscOptionsReal("-tao_bnk_imax", "(developer) maximum initial Hessian perturbation", "", bnk->imax, &bnk->imax, NULL));
1082:   PetscCall(PetscOptionsReal("-tao_bnk_imfac", "(developer) initial merit factor for Hessian perturbation", "", bnk->imfac, &bnk->imfac, NULL));
1083:   PetscCall(PetscOptionsReal("-tao_bnk_pmin", "(developer) minimum Hessian perturbation", "", bnk->pmin, &bnk->pmin, NULL));
1084:   PetscCall(PetscOptionsReal("-tao_bnk_pmax", "(developer) maximum Hessian perturbation", "", bnk->pmax, &bnk->pmax, NULL));
1085:   PetscCall(PetscOptionsReal("-tao_bnk_pgfac", "(developer) Hessian perturbation growth factor", "", bnk->pgfac, &bnk->pgfac, NULL));
1086:   PetscCall(PetscOptionsReal("-tao_bnk_psfac", "(developer) Hessian perturbation shrink factor", "", bnk->psfac, &bnk->psfac, NULL));
1087:   PetscCall(PetscOptionsReal("-tao_bnk_pmgfac", "(developer) merit growth factor for Hessian perturbation", "", bnk->pmgfac, &bnk->pmgfac, NULL));
1088:   PetscCall(PetscOptionsReal("-tao_bnk_pmsfac", "(developer) merit shrink factor for Hessian perturbation", "", bnk->pmsfac, &bnk->pmsfac, NULL));
1089:   PetscCall(PetscOptionsReal("-tao_bnk_eta1", "(developer) threshold for rejecting step (-tao_bnk_update_type reduction)", "", bnk->eta1, &bnk->eta1, NULL));
1090:   PetscCall(PetscOptionsReal("-tao_bnk_eta2", "(developer) threshold for accepting marginal step (-tao_bnk_update_type reduction)", "", bnk->eta2, &bnk->eta2, NULL));
1091:   PetscCall(PetscOptionsReal("-tao_bnk_eta3", "(developer) threshold for accepting reasonable step (-tao_bnk_update_type reduction)", "", bnk->eta3, &bnk->eta3, NULL));
1092:   PetscCall(PetscOptionsReal("-tao_bnk_eta4", "(developer) threshold for accepting good step (-tao_bnk_update_type reduction)", "", bnk->eta4, &bnk->eta4, NULL));
1093:   PetscCall(PetscOptionsReal("-tao_bnk_alpha1", "(developer) radius reduction factor for rejected step (-tao_bnk_update_type reduction)", "", bnk->alpha1, &bnk->alpha1, NULL));
1094:   PetscCall(PetscOptionsReal("-tao_bnk_alpha2", "(developer) radius reduction factor for marginally accepted bad step (-tao_bnk_update_type reduction)", "", bnk->alpha2, &bnk->alpha2, NULL));
1095:   PetscCall(PetscOptionsReal("-tao_bnk_alpha3", "(developer) radius increase factor for reasonable accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha3, &bnk->alpha3, NULL));
1096:   PetscCall(PetscOptionsReal("-tao_bnk_alpha4", "(developer) radius increase factor for good accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha4, &bnk->alpha4, NULL));
1097:   PetscCall(PetscOptionsReal("-tao_bnk_alpha5", "(developer) radius increase factor for very good accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha5, &bnk->alpha5, NULL));
1098:   PetscCall(PetscOptionsReal("-tao_bnk_nu1", "(developer) threshold for small line-search step length (-tao_bnk_update_type step)", "", bnk->nu1, &bnk->nu1, NULL));
1099:   PetscCall(PetscOptionsReal("-tao_bnk_nu2", "(developer) threshold for reasonable line-search step length (-tao_bnk_update_type step)", "", bnk->nu2, &bnk->nu2, NULL));
1100:   PetscCall(PetscOptionsReal("-tao_bnk_nu3", "(developer) threshold for large line-search step length (-tao_bnk_update_type step)", "", bnk->nu3, &bnk->nu3, NULL));
1101:   PetscCall(PetscOptionsReal("-tao_bnk_nu4", "(developer) threshold for very large line-search step length (-tao_bnk_update_type step)", "", bnk->nu4, &bnk->nu4, NULL));
1102:   PetscCall(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));
1103:   PetscCall(PetscOptionsReal("-tao_bnk_omega2", "(developer) radius reduction factor for small line-search step length (-tao_bnk_update_type step)", "", bnk->omega2, &bnk->omega2, NULL));
1104:   PetscCall(PetscOptionsReal("-tao_bnk_omega3", "(developer) radius factor for decent line-search step length (-tao_bnk_update_type step)", "", bnk->omega3, &bnk->omega3, NULL));
1105:   PetscCall(PetscOptionsReal("-tao_bnk_omega4", "(developer) radius increase factor for large line-search step length (-tao_bnk_update_type step)", "", bnk->omega4, &bnk->omega4, NULL));
1106:   PetscCall(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));
1107:   PetscCall(PetscOptionsReal("-tao_bnk_mu1_i", "(developer) threshold for accepting very good step (-tao_bnk_init_type interpolation)", "", bnk->mu1_i, &bnk->mu1_i, NULL));
1108:   PetscCall(PetscOptionsReal("-tao_bnk_mu2_i", "(developer) threshold for accepting good step (-tao_bnk_init_type interpolation)", "", bnk->mu2_i, &bnk->mu2_i, NULL));
1109:   PetscCall(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));
1110:   PetscCall(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));
1111:   PetscCall(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));
1112:   PetscCall(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));
1113:   PetscCall(PetscOptionsReal("-tao_bnk_theta_i", "(developer) trust region interpolation factor (-tao_bnk_init_type interpolation)", "", bnk->theta_i, &bnk->theta_i, NULL));
1114:   PetscCall(PetscOptionsReal("-tao_bnk_mu1", "(developer) threshold for accepting very good step (-tao_bnk_update_type interpolation)", "", bnk->mu1, &bnk->mu1, NULL));
1115:   PetscCall(PetscOptionsReal("-tao_bnk_mu2", "(developer) threshold for accepting good step (-tao_bnk_update_type interpolation)", "", bnk->mu2, &bnk->mu2, NULL));
1116:   PetscCall(PetscOptionsReal("-tao_bnk_gamma1", "(developer) radius reduction factor for rejected very bad step (-tao_bnk_update_type interpolation)", "", bnk->gamma1, &bnk->gamma1, NULL));
1117:   PetscCall(PetscOptionsReal("-tao_bnk_gamma2", "(developer) radius reduction factor for rejected bad step (-tao_bnk_update_type interpolation)", "", bnk->gamma2, &bnk->gamma2, NULL));
1118:   PetscCall(PetscOptionsReal("-tao_bnk_gamma3", "(developer) radius increase factor for accepted good step (-tao_bnk_update_type interpolation)", "", bnk->gamma3, &bnk->gamma3, NULL));
1119:   PetscCall(PetscOptionsReal("-tao_bnk_gamma4", "(developer) radius increase factor for accepted very good step (-tao_bnk_update_type interpolation)", "", bnk->gamma4, &bnk->gamma4, NULL));
1120:   PetscCall(PetscOptionsReal("-tao_bnk_theta", "(developer) trust region interpolation factor (-tao_bnk_update_type interpolation)", "", bnk->theta, &bnk->theta, NULL));
1121:   PetscCall(PetscOptionsReal("-tao_bnk_min_radius", "(developer) lower bound on initial radius", "", bnk->min_radius, &bnk->min_radius, NULL));
1122:   PetscCall(PetscOptionsReal("-tao_bnk_max_radius", "(developer) upper bound on radius", "", bnk->max_radius, &bnk->max_radius, NULL));
1123:   PetscCall(PetscOptionsReal("-tao_bnk_epsilon", "(developer) tolerance used when computing actual and predicted reduction", "", bnk->epsilon, &bnk->epsilon, NULL));
1124:   PetscCall(PetscOptionsReal("-tao_bnk_as_tol", "(developer) initial tolerance used when estimating actively bounded variables", "", bnk->as_tol, &bnk->as_tol, NULL));
1125:   PetscCall(PetscOptionsReal("-tao_bnk_as_step", "(developer) step length used when estimating actively bounded variables", "", bnk->as_step, &bnk->as_step, NULL));
1126:   PetscCall(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));
1127:   PetscOptionsHeadEnd();

1129:   PetscCall(TaoSetOptionsPrefix(bnk->bncg, ((PetscObject)tao)->prefix));
1130:   PetscCall(TaoAppendOptionsPrefix(bnk->bncg, "tao_bnk_cg_"));
1131:   PetscCall(TaoSetFromOptions(bnk->bncg));

1133:   PetscCall(KSPSetOptionsPrefix(tao->ksp, ((PetscObject)tao)->prefix));
1134:   PetscCall(KSPAppendOptionsPrefix(tao->ksp, "tao_bnk_"));
1135:   PetscCall(KSPSetFromOptions(tao->ksp));
1136:   PetscFunctionReturn(PETSC_SUCCESS);
1137: }

1139: PetscErrorCode TaoView_BNK(Tao tao, PetscViewer viewer)
1140: {
1141:   TAO_BNK  *bnk = (TAO_BNK *)tao->data;
1142:   PetscInt  nrejects;
1143:   PetscBool isascii;

1145:   PetscFunctionBegin;
1146:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
1147:   if (isascii) {
1148:     PetscCall(PetscViewerASCIIPushTab(viewer));
1149:     PetscCall(TaoView(bnk->bncg, viewer));
1150:     if (bnk->M) {
1151:       PetscCall(MatLMVMGetRejectCount(bnk->M, &nrejects));
1152:       PetscCall(PetscViewerASCIIPrintf(viewer, "Rejected BFGS updates: %" PetscInt_FMT "\n", nrejects));
1153:     }
1154:     PetscCall(PetscViewerASCIIPrintf(viewer, "CG steps: %" PetscInt_FMT "\n", bnk->tot_cg_its));
1155:     PetscCall(PetscViewerASCIIPrintf(viewer, "Newton steps: %" PetscInt_FMT "\n", bnk->newt));
1156:     if (bnk->M) PetscCall(PetscViewerASCIIPrintf(viewer, "BFGS steps: %" PetscInt_FMT "\n", bnk->bfgs));
1157:     PetscCall(PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %" PetscInt_FMT "\n", bnk->sgrad));
1158:     PetscCall(PetscViewerASCIIPrintf(viewer, "Gradient steps: %" PetscInt_FMT "\n", bnk->grad));
1159:     PetscCall(PetscViewerASCIIPrintf(viewer, "KSP termination reasons:\n"));
1160:     PetscCall(PetscViewerASCIIPrintf(viewer, "  atol: %" PetscInt_FMT "\n", bnk->ksp_atol));
1161:     PetscCall(PetscViewerASCIIPrintf(viewer, "  rtol: %" PetscInt_FMT "\n", bnk->ksp_rtol));
1162:     PetscCall(PetscViewerASCIIPrintf(viewer, "  ctol: %" PetscInt_FMT "\n", bnk->ksp_ctol));
1163:     PetscCall(PetscViewerASCIIPrintf(viewer, "  negc: %" PetscInt_FMT "\n", bnk->ksp_negc));
1164:     PetscCall(PetscViewerASCIIPrintf(viewer, "  dtol: %" PetscInt_FMT "\n", bnk->ksp_dtol));
1165:     PetscCall(PetscViewerASCIIPrintf(viewer, "  iter: %" PetscInt_FMT "\n", bnk->ksp_iter));
1166:     PetscCall(PetscViewerASCIIPrintf(viewer, "  othr: %" PetscInt_FMT "\n", bnk->ksp_othr));
1167:     PetscCall(PetscViewerASCIIPopTab(viewer));
1168:   }
1169:   PetscFunctionReturn(PETSC_SUCCESS);
1170: }

1172: /*MC
1173:   TAOBNK - Shared base-type for Bounded Newton-Krylov type algorithms.
1174:   At each iteration, the BNK methods solve the symmetric
1175:   system of equations to obtain the step direction $d_k$:
1176:              $ H_k d_k = -g_k $
1177:   for free variables only. The step can be globalized either through
1178:   trust-region methods, or a line search, or a heuristic mixture of both.

1180:     Options Database Keys:
1181: + -tao_bnk_max_cg_its  - maximum number of bounded conjugate-gradient iterations taken in each Newton loop
1182: . -tao_bnk_init_type   - trust radius initialization method ("constant", "direction", "interpolation")
1183: . -tao_bnk_update_type - trust radius update method ("step", "direction", "interpolation")
1184: . -tao_bnk_as_type     - active-set estimation method ("none", "bertsekas")
1185: . -tao_bnk_as_tol      - (developer) initial tolerance used in estimating bounded active variables (-as_type bertsekas)
1186: . -tao_bnk_as_step     - (developer) trial step length used in estimating bounded active variables (-as_type bertsekas)
1187: . -tao_bnk_sval        - (developer) Hessian perturbation starting value
1188: . -tao_bnk_imin        - (developer) minimum initial Hessian perturbation
1189: . -tao_bnk_imax        - (developer) maximum initial Hessian perturbation
1190: . -tao_bnk_pmin        - (developer) minimum Hessian perturbation
1191: . -tao_bnk_pmax        - (developer) aximum Hessian perturbation
1192: . -tao_bnk_pgfac       - (developer) Hessian perturbation growth factor
1193: . -tao_bnk_psfac       - (developer) Hessian perturbation shrink factor
1194: . -tao_bnk_imfac       - (developer) initial merit factor for Hessian perturbation
1195: . -tao_bnk_pmgfac      - (developer) merit growth factor for Hessian perturbation
1196: . -tao_bnk_pmsfac      - (developer) merit shrink factor for Hessian perturbation
1197: . -tao_bnk_eta1        - (developer) threshold for rejecting step (-update_type reduction)
1198: . -tao_bnk_eta2        - (developer) threshold for accepting marginal step (-update_type reduction)
1199: . -tao_bnk_eta3        - (developer) threshold for accepting reasonable step (-update_type reduction)
1200: . -tao_bnk_eta4        - (developer) threshold for accepting good step (-update_type reduction)
1201: . -tao_bnk_alpha1      - (developer) radius reduction factor for rejected step (-update_type reduction)
1202: . -tao_bnk_alpha2      - (developer) radius reduction factor for marginally accepted bad step (-update_type reduction)
1203: . -tao_bnk_alpha3      - (developer) radius increase factor for reasonable accepted step (-update_type reduction)
1204: . -tao_bnk_alpha4      - (developer) radius increase factor for good accepted step (-update_type reduction)
1205: . -tao_bnk_alpha5      - (developer) radius increase factor for very good accepted step (-update_type reduction)
1206: . -tao_bnk_epsilon     - (developer) tolerance for small pred/actual ratios that trigger automatic step acceptance (-update_type reduction)
1207: . -tao_bnk_mu1         - (developer) threshold for accepting very good step (-update_type interpolation)
1208: . -tao_bnk_mu2         - (developer) threshold for accepting good step (-update_type interpolation)
1209: . -tao_bnk_gamma1      - (developer) radius reduction factor for rejected very bad step (-update_type interpolation)
1210: . -tao_bnk_gamma2      - (developer) radius reduction factor for rejected bad step (-update_type interpolation)
1211: . -tao_bnk_gamma3      - (developer) radius increase factor for accepted good step (-update_type interpolation)
1212: . -tao_bnk_gamma4      - (developer) radius increase factor for accepted very good step (-update_type interpolation)
1213: . -tao_bnk_theta       - (developer) trust region interpolation factor (-update_type interpolation)
1214: . -tao_bnk_nu1         - (developer) threshold for small line-search step length (-update_type step)
1215: . -tao_bnk_nu2         - (developer) threshold for reasonable line-search step length (-update_type step)
1216: . -tao_bnk_nu3         - (developer) threshold for large line-search step length (-update_type step)
1217: . -tao_bnk_nu4         - (developer) threshold for very large line-search step length (-update_type step)
1218: . -tao_bnk_omega1      - (developer) radius reduction factor for very small line-search step length (-update_type step)
1219: . -tao_bnk_omega2      - (developer) radius reduction factor for small line-search step length (-update_type step)
1220: . -tao_bnk_omega3      - (developer) radius factor for decent line-search step length (-update_type step)
1221: . -tao_bnk_omega4      - (developer) radius increase factor for large line-search step length (-update_type step)
1222: . -tao_bnk_omega5      - (developer) radius increase factor for very large line-search step length (-update_type step)
1223: . -tao_bnk_mu1_i       - (developer) threshold for accepting very good step (-init_type interpolation)
1224: . -tao_bnk_mu2_i       - (developer) threshold for accepting good step (-init_type interpolation)
1225: . -tao_bnk_gamma1_i    - (developer) radius reduction factor for rejected very bad step (-init_type interpolation)
1226: . -tao_bnk_gamma2_i    - (developer) radius reduction factor for rejected bad step (-init_type interpolation)
1227: . -tao_bnk_gamma3_i    - (developer) radius increase factor for accepted good step (-init_type interpolation)
1228: . -tao_bnk_gamma4_i    - (developer) radius increase factor for accepted very good step (-init_type interpolation)
1229: - -tao_bnk_theta_i     - (developer) trust region interpolation factor (-init_type interpolation)

1231:   Level: beginner

1233:   The various algorithmic factors can only be supplied via the options database

1235: .seealso: `Tao`, `TAONLS`, `TAONTL`, `TAONM`, `TaoType`, `TaoCreate()`
1236: M*/

1238: PetscErrorCode TaoCreate_BNK(Tao tao)
1239: {
1240:   TAO_BNK *bnk;
1241:   PC       pc;

1243:   PetscFunctionBegin;
1244:   PetscCall(PetscNew(&bnk));

1246:   tao->ops->setup            = TaoSetUp_BNK;
1247:   tao->ops->view             = TaoView_BNK;
1248:   tao->ops->setfromoptions   = TaoSetFromOptions_BNK;
1249:   tao->ops->destroy          = TaoDestroy_BNK;
1250:   tao->uses_gradient         = PETSC_TRUE;
1251:   tao->uses_hessian_matrices = PETSC_TRUE;

1253:   /*  Override default settings (unless already changed) */
1254:   PetscCall(TaoParametersInitialize(tao));
1255:   PetscObjectParameterSetDefault(tao, max_it, 50);
1256:   PetscObjectParameterSetDefault(tao, trust0, 100.0);

1258:   tao->data = (void *)bnk;

1260:   /*  Hessian shifting parameters */
1261:   bnk->computehessian = TaoBNKComputeHessian;
1262:   bnk->computestep    = TaoBNKComputeStep;

1264:   bnk->sval  = 0.0;
1265:   bnk->imin  = 1.0e-4;
1266:   bnk->imax  = 1.0e+2;
1267:   bnk->imfac = 1.0e-1;

1269:   bnk->pmin   = 1.0e-12;
1270:   bnk->pmax   = 1.0e+2;
1271:   bnk->pgfac  = 1.0e+1;
1272:   bnk->psfac  = 4.0e-1;
1273:   bnk->pmgfac = 1.0e-1;
1274:   bnk->pmsfac = 1.0e-1;

1276:   /*  Default values for trust-region radius update based on steplength */
1277:   bnk->nu1 = 0.25;
1278:   bnk->nu2 = 0.50;
1279:   bnk->nu3 = 1.00;
1280:   bnk->nu4 = 1.25;

1282:   bnk->omega1 = 0.25;
1283:   bnk->omega2 = 0.50;
1284:   bnk->omega3 = 1.00;
1285:   bnk->omega4 = 2.00;
1286:   bnk->omega5 = 4.00;

1288:   /*  Default values for trust-region radius update based on reduction */
1289:   bnk->eta1 = 1.0e-4;
1290:   bnk->eta2 = 0.25;
1291:   bnk->eta3 = 0.50;
1292:   bnk->eta4 = 0.90;

1294:   bnk->alpha1 = 0.25;
1295:   bnk->alpha2 = 0.50;
1296:   bnk->alpha3 = 1.00;
1297:   bnk->alpha4 = 2.00;
1298:   bnk->alpha5 = 4.00;

1300:   /*  Default values for trust-region radius update based on interpolation */
1301:   bnk->mu1 = 0.10;
1302:   bnk->mu2 = 0.50;

1304:   bnk->gamma1 = 0.25;
1305:   bnk->gamma2 = 0.50;
1306:   bnk->gamma3 = 2.00;
1307:   bnk->gamma4 = 4.00;

1309:   bnk->theta = 0.05;

1311:   /*  Default values for trust region initialization based on interpolation */
1312:   bnk->mu1_i = 0.35;
1313:   bnk->mu2_i = 0.50;

1315:   bnk->gamma1_i = 0.0625;
1316:   bnk->gamma2_i = 0.5;
1317:   bnk->gamma3_i = 2.0;
1318:   bnk->gamma4_i = 5.0;

1320:   bnk->theta_i = 0.25;

1322:   /*  Remaining parameters */
1323:   bnk->max_cg_its = 0;
1324:   bnk->min_radius = 1.0e-10;
1325:   bnk->max_radius = 1.0e10;
1326:   bnk->epsilon    = PetscPowReal(PETSC_MACHINE_EPSILON, 2.0 / 3.0);
1327:   bnk->as_tol     = 1.0e-3;
1328:   bnk->as_step    = 1.0e-3;
1329:   bnk->dmin       = 1.0e-6;
1330:   bnk->dmax       = 1.0e6;

1332:   bnk->M           = NULL;
1333:   bnk->bfgs_pre    = NULL;
1334:   bnk->init_type   = BNK_INIT_INTERPOLATION;
1335:   bnk->update_type = BNK_UPDATE_REDUCTION;
1336:   bnk->as_type     = BNK_AS_BERTSEKAS;

1338:   /* Create the embedded BNCG solver */
1339:   PetscCall(TaoCreate(PetscObjectComm((PetscObject)tao), &bnk->bncg));
1340:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)bnk->bncg, (PetscObject)tao, 1));
1341:   PetscCall(TaoSetType(bnk->bncg, TAOBNCG));

1343:   /* Create the line search */
1344:   PetscCall(TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch));
1345:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1));
1346:   PetscCall(TaoLineSearchSetType(tao->linesearch, TAOLINESEARCHMT));
1347:   PetscCall(TaoLineSearchUseTaoRoutines(tao->linesearch, tao));

1349:   /*  Set linear solver to default for symmetric matrices */
1350:   PetscCall(KSPCreate(((PetscObject)tao)->comm, &tao->ksp));
1351:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1));
1352:   PetscCall(KSPSetType(tao->ksp, KSPSTCG));
1353:   PetscCall(KSPGetPC(tao->ksp, &pc));
1354:   PetscCall(PCSetType(pc, PCLMVM));
1355:   PetscFunctionReturn(PETSC_SUCCESS);
1356: }