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

 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(PetscObjectComm((PetscObject)tao),PETSC_ERR_USER, "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);

 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;

 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;

 70:   /* Initialize the Hessian perturbation */
 71:   bnk->pert = bnk->sval;

 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:   }

 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:             PetscObjectReference((PetscObject)tao->hessian);
124:             bnk->H_inactive = tao->hessian;
125:           }
126:           *needH = PETSC_FALSE;
127:         }

129:         for (i = 0; i < i_max; ++i) {
130:           /* Take a steepest descent step and snap it to bounds */
131:           VecCopy(tao->solution, bnk->Xold);
132:           VecAXPY(tao->solution, -tao->trust/bnk->gnorm, tao->gradient);
133:           TaoBoundSolution(tao->solution, tao->XL,tao->XU, 0.0, &nDiff, tao->solution);
134:           /* Compute the step we actually accepted */
135:           VecCopy(tao->solution, bnk->W);
136:           VecAXPY(bnk->W, -1.0, bnk->Xold);
137:           /* Compute the objective at the trial */
138:           TaoComputeObjective(tao, tao->solution, &ftrial);
139:           if (PetscIsInfOrNanReal(bnk->f)) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
140:           VecCopy(bnk->Xold, tao->solution);
141:           if (PetscIsInfOrNanReal(ftrial)) {
142:             tau = bnk->gamma1_i;
143:           } else {
144:             if (ftrial < f_min) {
145:               f_min = ftrial;
146:               sigma = -tao->trust / bnk->gnorm;
147:             }

149:             /* Compute the predicted and actual reduction */
150:             if (bnk->active_idx) {
151:               VecGetSubVector(bnk->W, bnk->inactive_idx, &bnk->X_inactive);
152:               VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);
153:             } else {
154:               bnk->X_inactive = bnk->W;
155:               bnk->inactive_work = bnk->Xwork;
156:             }
157:             MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work);
158:             VecDot(bnk->X_inactive, bnk->inactive_work, &prered);
159:             if (bnk->active_idx) {
160:               VecRestoreSubVector(bnk->W, bnk->inactive_idx, &bnk->X_inactive);
161:               VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);
162:             }
163:             prered = tao->trust * (bnk->gnorm - 0.5 * tao->trust * prered / (bnk->gnorm * bnk->gnorm));
164:             actred = bnk->f - ftrial;
165:             if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) {
166:               kappa = 1.0;
167:             } else {
168:               kappa = actred / prered;
169:             }

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

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

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

191:               if (tau_max < bnk->gamma2_i) {
192:                 tau = bnk->gamma2_i;
193:               } else if (tau_max > bnk->gamma3_i) {
194:                 tau = bnk->gamma3_i;
195:               } else {
196:                 tau = tau_max;
197:               }
198:             } else {
199:               /*  Not good agreement */
200:               if (tau_min > 1.0) {
201:                 tau = bnk->gamma2_i;
202:               } else if (tau_max < bnk->gamma1_i) {
203:                 tau = bnk->gamma1_i;
204:               } else if ((tau_min < bnk->gamma1_i) && (tau_max >= 1.0)) {
205:                 tau = bnk->gamma1_i;
206:               } else if ((tau_1 >= bnk->gamma1_i) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
207:                 tau = tau_1;
208:               } else if ((tau_2 >= bnk->gamma1_i) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
209:                 tau = tau_2;
210:               } else {
211:                 tau = tau_max;
212:               }
213:             }
214:           }
215:           tao->trust = tau * tao->trust;
216:         }

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

247:       /* Ensure that the trust radius is within the limits */
248:       tao->trust = PetscMax(tao->trust, bnk->min_radius);
249:       tao->trust = PetscMin(tao->trust, bnk->max_radius);
250:       break;

252:     default:
253:       /* Norm of the first direction will initialize radius */
254:       tao->trust = 0.0;
255:       break;
256:     }
257:   }
258:   return(0);
259: }

261: /*------------------------------------------------------------*/

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

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

271:   /* Compute the Hessian */
272:   TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);
273:   /* Add a correction to the BFGS preconditioner */
274:   if (bnk->M) {
275:     MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);
276:   }
277:   /* Prepare the reduced sub-matrices for the inactive set */
278:   if (bnk->Hpre_inactive) {
279:     MatDestroy(&bnk->Hpre_inactive);
280:   }
281:   if (bnk->H_inactive) {
282:     MatDestroy(&bnk->H_inactive);
283:   }
284:   if (bnk->active_idx) {
285:     MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive);
286:     if (tao->hessian == tao->hessian_pre) {
287:       PetscObjectReference((PetscObject)bnk->H_inactive);
288:       bnk->Hpre_inactive = bnk->H_inactive;
289:     } else {
290:       MatCreateSubMatrix(tao->hessian_pre, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->Hpre_inactive);
291:     }
292:     if (bnk->bfgs_pre) {
293:       PCLMVMSetIS(bnk->bfgs_pre, bnk->inactive_idx);
294:     }
295:   } else {
296:     PetscObjectReference((PetscObject)tao->hessian);
297:     bnk->H_inactive = tao->hessian;
298:     if (tao->hessian == tao->hessian_pre) {
299:       PetscObjectReference((PetscObject)bnk->H_inactive);
300:       bnk->Hpre_inactive = bnk->H_inactive;
301:     } else {
302:       PetscObjectReference((PetscObject)tao->hessian_pre);
303:       bnk->Hpre_inactive = tao->hessian_pre;
304:     }
305:     if (bnk->bfgs_pre) {
306:       PCLMVMClearIS(bnk->bfgs_pre);
307:     }
308:   }
309:   return(0);
310: }

312: /*------------------------------------------------------------*/

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

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

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

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

361:   default:
362:     break;
363:   }
364:   return(0);
365: }

367: /*------------------------------------------------------------*/

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

371: PetscErrorCode TaoBNKBoundStep(Tao tao, PetscInt asType, Vec step)
372: {
373:   PetscErrorCode               ierr;
374:   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;

377:   switch (asType) {
378:   case BNK_AS_NONE:
379:     VecISSet(step, bnk->active_idx, 0.0);
380:     break;

382:   case BNK_AS_BERTSEKAS:
383:     TaoBoundStep(tao->solution, tao->XL, tao->XU, bnk->active_lower, bnk->active_upper, bnk->active_fixed, 1.0, step);
384:     break;

386:   default:
387:     break;
388:   }
389:   return(0);
390: }

392: /*------------------------------------------------------------*/

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

397:    In practice, this approach simply trades off Hessian evaluations
398:    for more gradient evaluations.
399: */

401: PetscErrorCode TaoBNKTakeCGSteps(Tao tao, PetscBool *terminate)
402: {
403:   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
404:   PetscErrorCode               ierr;

407:   *terminate = PETSC_FALSE;
408:   if (bnk->max_cg_its > 0) {
409:     /* Copy the current function value (important vectors are already shared) */
410:     bnk->bncg_ctx->f = bnk->f;
411:     /* Take some small finite number of BNCG iterations */
412:     TaoSolve(bnk->bncg);
413:     /* Add the number of gradient and function evaluations to the total */
414:     tao->nfuncs += bnk->bncg->nfuncs;
415:     tao->nfuncgrads += bnk->bncg->nfuncgrads;
416:     tao->ngrads += bnk->bncg->ngrads;
417:     tao->nhess += bnk->bncg->nhess;
418:     bnk->tot_cg_its += bnk->bncg->niter;
419:     /* Extract the BNCG function value out and save it into BNK */
420:     bnk->f = bnk->bncg_ctx->f;
421:     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) {
422:       *terminate = PETSC_TRUE;
423:     } else {
424:       TaoBNKEstimateActiveSet(tao, bnk->as_type);
425:     }
426:   }
427:   return(0);
428: }

430: /*------------------------------------------------------------*/

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

434: PetscErrorCode TaoBNKComputeStep(Tao tao, PetscBool shift, KSPConvergedReason *ksp_reason, PetscInt *step_type)
435: {
436:   PetscErrorCode               ierr;
437:   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
438:   PetscInt                     bfgsUpdates = 0;
439:   PetscInt                     kspits;
440:   PetscBool                    is_lmvm;

443:   /* If there are no inactive variables left, save some computation and return an adjusted zero step
444:      that has (l-x) and (u-x) for lower and upper bounded variables. */
445:   if (!bnk->inactive_idx) {
446:     VecSet(tao->stepdirection, 0.0);
447:     TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection);
448:     return(0);
449:   }

451:   /* Shift the reduced Hessian matrix */
452:   if ((shift) && (bnk->pert > 0)) {
453:     PetscObjectTypeCompare((PetscObject)tao->hessian, MATLMVM, &is_lmvm);
454:     if (is_lmvm) {
455:       MatShift(tao->hessian, bnk->pert);
456:     } else {
457:       MatShift(bnk->H_inactive, bnk->pert);
458:       if (bnk->H_inactive != bnk->Hpre_inactive) {
459:         MatShift(bnk->Hpre_inactive, bnk->pert);
460:       }
461:     }
462:   }

464:   /* Solve the Newton system of equations */
465:   tao->ksp_its = 0;
466:   VecSet(tao->stepdirection, 0.0);
467:   KSPReset(tao->ksp);
468:   KSPResetFromOptions(tao->ksp);
469:   KSPSetOperators(tao->ksp,bnk->H_inactive,bnk->Hpre_inactive);
470:   VecCopy(bnk->unprojected_gradient, bnk->Gwork);
471:   if (bnk->active_idx) {
472:     VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);
473:     VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);
474:   } else {
475:     bnk->G_inactive = bnk->unprojected_gradient;
476:     bnk->X_inactive = tao->stepdirection;
477:   }
478:   if (bnk->is_nash || bnk->is_stcg || bnk->is_gltr) {
479:     KSPCGSetRadius(tao->ksp,tao->trust);
480:     KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);
481:     KSPGetIterationNumber(tao->ksp,&kspits);
482:     tao->ksp_its+=kspits;
483:     tao->ksp_tot_its+=kspits;
484:     KSPCGGetNormD(tao->ksp,&bnk->dnorm);

486:     if (0.0 == tao->trust) {
487:       /* Radius was uninitialized; use the norm of the direction */
488:       if (bnk->dnorm > 0.0) {
489:         tao->trust = bnk->dnorm;

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

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

503:         KSPCGSetRadius(tao->ksp,tao->trust);
504:         KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);
505:         KSPGetIterationNumber(tao->ksp,&kspits);
506:         tao->ksp_its+=kspits;
507:         tao->ksp_tot_its+=kspits;
508:         KSPCGGetNormD(tao->ksp,&bnk->dnorm);

510:         if (bnk->dnorm == 0.0) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_PLIB, "Initial direction zero");
511:       }
512:     }
513:   } else {
514:     KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);
515:     KSPGetIterationNumber(tao->ksp, &kspits);
516:     tao->ksp_its += kspits;
517:     tao->ksp_tot_its+=kspits;
518:   }
519:   /* Restore sub vectors back */
520:   if (bnk->active_idx) {
521:     VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);
522:     VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);
523:   }
524:   /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
525:   VecScale(tao->stepdirection, -1.0);
526:   TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection);

528:   /* Record convergence reasons */
529:   KSPGetConvergedReason(tao->ksp, ksp_reason);
530:   if (KSP_CONVERGED_ATOL == *ksp_reason) {
531:     ++bnk->ksp_atol;
532:   } else if (KSP_CONVERGED_RTOL == *ksp_reason) {
533:     ++bnk->ksp_rtol;
534:   } else if (KSP_CONVERGED_CG_CONSTRAINED == *ksp_reason) {
535:     ++bnk->ksp_ctol;
536:   } else if (KSP_CONVERGED_CG_NEG_CURVE == *ksp_reason) {
537:     ++bnk->ksp_negc;
538:   } else if (KSP_DIVERGED_DTOL == *ksp_reason) {
539:     ++bnk->ksp_dtol;
540:   } else if (KSP_DIVERGED_ITS == *ksp_reason) {
541:     ++bnk->ksp_iter;
542:   } else {
543:     ++bnk->ksp_othr;
544:   }

546:   /* Make sure the BFGS preconditioner is healthy */
547:   if (bnk->M) {
548:     MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates);
549:     if ((KSP_DIVERGED_INDEFINITE_PC == *ksp_reason) && (bfgsUpdates > 0)) {
550:       /* Preconditioner is numerically indefinite; reset the approximation. */
551:       MatLMVMReset(bnk->M, PETSC_FALSE);
552:       MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);
553:     }
554:   }
555:   *step_type = BNK_NEWTON;
556:   return(0);
557: }

559: /*------------------------------------------------------------*/

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

563: PetscErrorCode TaoBNKRecomputePred(Tao tao, Vec S, PetscReal *prered)
564: {
565:   PetscErrorCode               ierr;
566:   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;

569:   /* Extract subvectors associated with the inactive set */
570:   if (bnk->active_idx) {
571:     VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);
572:     VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);
573:     VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);
574:   } else {
575:     bnk->X_inactive = tao->stepdirection;
576:     bnk->inactive_work = bnk->Xwork;
577:     bnk->G_inactive = bnk->Gwork;
578:   }
579:   /* Recompute the predicted decrease based on the quadratic model */
580:   MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work);
581:   VecAYPX(bnk->inactive_work, -0.5, bnk->G_inactive);
582:   VecDot(bnk->inactive_work, bnk->X_inactive, prered);
583:   /* Restore the sub vectors */
584:   if (bnk->active_idx) {
585:     VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);
586:     VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);
587:     VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);
588:   }
589:   return(0);
590: }

592: /*------------------------------------------------------------*/

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

596:    The step direction falls back onto BFGS, scaled gradient and gradient steps
597:    in the event that the Newton step fails the test.
598: */

600: PetscErrorCode TaoBNKSafeguardStep(Tao tao, KSPConvergedReason ksp_reason, PetscInt *stepType)
601: {
602:   PetscErrorCode               ierr;
603:   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;

605:   PetscReal                    gdx, e_min;
606:   PetscInt                     bfgsUpdates;

609:   switch (*stepType) {
610:   case BNK_NEWTON:
611:     VecDot(tao->stepdirection, tao->gradient, &gdx);
612:     if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) {
613:       /* Newton step is not descent or direction produced Inf or NaN
614:         Update the perturbation for next time */
615:       if (bnk->pert <= 0.0) {
616:         /* Initialize the perturbation */
617:         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
618:         if (bnk->is_gltr) {
619:           KSPGLTRGetMinEig(tao->ksp,&e_min);
620:           bnk->pert = PetscMax(bnk->pert, -e_min);
621:         }
622:       } else {
623:         /* Increase the perturbation */
624:         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
625:       }

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

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

646:           /* Use steepest descent direction (scaled) */
647:           MatLMVMReset(bnk->M, PETSC_FALSE);
648:           MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);
649:           MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);

651:           *stepType = BNK_SCALED_GRADIENT;
652:         } else {
653:           MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates);
654:           if (1 == bfgsUpdates) {
655:             /* The first BFGS direction is always the scaled gradient */
656:             *stepType = BNK_SCALED_GRADIENT;
657:           } else {
658:             *stepType = BNK_BFGS;
659:           }
660:         }
661:       }
662:       /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
663:       VecScale(tao->stepdirection, -1.0);
664:       TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection);
665:     } else {
666:       /* Computed Newton step is descent */
667:       switch (ksp_reason) {
668:       case KSP_DIVERGED_NANORINF:
669:       case KSP_DIVERGED_BREAKDOWN:
670:       case KSP_DIVERGED_INDEFINITE_MAT:
671:       case KSP_DIVERGED_INDEFINITE_PC:
672:       case KSP_CONVERGED_CG_NEG_CURVE:
673:         /* Matrix or preconditioner is indefinite; increase perturbation */
674:         if (bnk->pert <= 0.0) {
675:           /* Initialize the perturbation */
676:           bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
677:           if (bnk->is_gltr) {
678:             KSPGLTRGetMinEig(tao->ksp, &e_min);
679:             bnk->pert = PetscMax(bnk->pert, -e_min);
680:           }
681:         } else {
682:           /* Increase the perturbation */
683:           bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
684:         }
685:         break;

687:       default:
688:         /* Newton step computation is good; decrease perturbation */
689:         bnk->pert = PetscMin(bnk->psfac * bnk->pert, bnk->pmsfac * bnk->gnorm);
690:         if (bnk->pert < bnk->pmin) {
691:           bnk->pert = 0.0;
692:         }
693:         break;
694:       }
695:       *stepType = BNK_NEWTON;
696:     }
697:     break;

699:   case BNK_BFGS:
700:     /* Check for success (descent direction) */
701:     VecDot(tao->stepdirection, tao->gradient, &gdx);
702:     if (gdx >= 0 || PetscIsInfOrNanReal(gdx)) {
703:       /* Step is not descent or solve was not successful
704:          Use steepest descent direction (scaled) */
705:       MatLMVMReset(bnk->M, PETSC_FALSE);
706:       MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);
707:       MatSolve(bnk->M, tao->gradient, tao->stepdirection);
708:       VecScale(tao->stepdirection,-1.0);
709:       TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection);
710:       *stepType = BNK_SCALED_GRADIENT;
711:     } else {
712:       *stepType = BNK_BFGS;
713:     }
714:     break;

716:   case BNK_SCALED_GRADIENT:
717:     break;

719:   default:
720:     break;
721:   }

723:   return(0);
724: }

726: /*------------------------------------------------------------*/

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

730:   Includes fallbacks to BFGS, scaled gradient, and unscaled gradient steps if the
731:   Newton step does not produce a valid step length.
732: */

734: PetscErrorCode TaoBNKPerformLineSearch(Tao tao, PetscInt *stepType, PetscReal *steplen, TaoLineSearchConvergedReason *reason)
735: {
736:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
738:   TaoLineSearchConvergedReason ls_reason;

740:   PetscReal      e_min, gdx;
741:   PetscInt       bfgsUpdates;

744:   /* Perform the linesearch */
745:   TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason);
746:   TaoAddLineSearchCounts(tao);

748:   while (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER && *stepType != BNK_SCALED_GRADIENT && *stepType != BNK_GRADIENT) {
749:     /* Linesearch failed, revert solution */
750:     bnk->f = bnk->fold;
751:     VecCopy(bnk->Xold, tao->solution);
752:     VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);

754:     switch(*stepType) {
755:     case BNK_NEWTON:
756:       /* Failed to obtain acceptable iterate with Newton step
757:          Update the perturbation for next time */
758:       if (bnk->pert <= 0.0) {
759:         /* Initialize the perturbation */
760:         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
761:         if (bnk->is_gltr) {
762:           KSPGLTRGetMinEig(tao->ksp,&e_min);
763:           bnk->pert = PetscMax(bnk->pert, -e_min);
764:         }
765:       } else {
766:         /* Increase the perturbation */
767:         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
768:       }

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

789:           bfgsUpdates = 1;
790:           *stepType = BNK_SCALED_GRADIENT;
791:         } else {
792:           MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates);
793:           if (1 == bfgsUpdates) {
794:             /* The first BFGS direction is always the scaled gradient */
795:             *stepType = BNK_SCALED_GRADIENT;
796:           } else {
797:             *stepType = BNK_BFGS;
798:           }
799:         }
800:       }
801:       break;

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

811:       bfgsUpdates = 1;
812:       *stepType = BNK_SCALED_GRADIENT;
813:       break;
814:     }
815:     /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
816:     VecScale(tao->stepdirection, -1.0);
817:     TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection);

819:     /* Perform one last line search with the fall-back step */
820:     TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason);
821:     TaoAddLineSearchCounts(tao);
822:   }
823:   *reason = ls_reason;
824:   return(0);
825: }

827: /*------------------------------------------------------------*/

829: /* Routine for updating the trust radius.

831:   Function features three different update methods:
832:   1) Line-search step length based
833:   2) Predicted decrease on the CG quadratic model
834:   3) Interpolation
835: */

837: PetscErrorCode TaoBNKUpdateTrustRadius(Tao tao, PetscReal prered, PetscReal actred, PetscInt updateType, PetscInt stepType, PetscBool *accept)
838: {
839:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;

842:   PetscReal      step, kappa;
843:   PetscReal      gdx, tau_1, tau_2, tau_min, tau_max;

846:   /* Update trust region radius */
847:   *accept = PETSC_FALSE;
848:   switch(updateType) {
849:   case BNK_UPDATE_STEP:
850:     *accept = PETSC_TRUE; /* always accept here because line search succeeded */
851:     if (stepType == BNK_NEWTON) {
852:       TaoLineSearchGetStepLength(tao->linesearch, &step);
853:       if (step < bnk->nu1) {
854:         /* Very bad step taken; reduce radius */
855:         tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
856:       } else if (step < bnk->nu2) {
857:         /* Reasonably bad step taken; reduce radius */
858:         tao->trust = bnk->omega2 * PetscMin(bnk->dnorm, tao->trust);
859:       } else if (step < bnk->nu3) {
860:         /*  Reasonable step was taken; leave radius alone */
861:         if (bnk->omega3 < 1.0) {
862:           tao->trust = bnk->omega3 * PetscMin(bnk->dnorm, tao->trust);
863:         } else if (bnk->omega3 > 1.0) {
864:           tao->trust = PetscMax(bnk->omega3 * bnk->dnorm, tao->trust);
865:         }
866:       } else if (step < bnk->nu4) {
867:         /*  Full step taken; increase the radius */
868:         tao->trust = PetscMax(bnk->omega4 * bnk->dnorm, tao->trust);
869:       } else {
870:         /*  More than full step taken; increase the radius */
871:         tao->trust = PetscMax(bnk->omega5 * bnk->dnorm, tao->trust);
872:       }
873:     } else {
874:       /*  Newton step was not good; reduce the radius */
875:       tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
876:     }
877:     break;

879:   case BNK_UPDATE_REDUCTION:
880:     if (stepType == BNK_NEWTON) {
881:       if ((prered < 0.0) || PetscIsInfOrNanReal(prered)) {
882:         /* The predicted reduction has the wrong sign.  This cannot
883:            happen in infinite precision arithmetic.  Step should
884:            be rejected! */
885:         tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
886:       } else {
887:         if (PetscIsInfOrNanReal(actred)) {
888:           tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
889:         } else {
890:           if ((PetscAbsScalar(actred) <= PetscMax(1.0, PetscAbsScalar(bnk->f))*bnk->epsilon) && (PetscAbsScalar(prered) <= PetscMax(1.0, PetscAbsScalar(bnk->f))*bnk->epsilon)) {
891:             kappa = 1.0;
892:           } else {
893:             kappa = actred / prered;
894:           }
895:           /* Accept or reject the step and update radius */
896:           if (kappa < bnk->eta1) {
897:             /* Reject the step */
898:             tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
899:           } else {
900:             /* Accept the step */
901:             *accept = PETSC_TRUE;
902:             /* Update the trust region radius only if the computed step is at the trust radius boundary */
903:             if (bnk->dnorm == tao->trust) {
904:               if (kappa < bnk->eta2) {
905:                 /* Marginal bad step */
906:                 tao->trust = bnk->alpha2 * tao->trust;
907:               } else if (kappa < bnk->eta3) {
908:                 /* Reasonable step */
909:                 tao->trust = bnk->alpha3 * tao->trust;
910:               } else if (kappa < bnk->eta4) {
911:                 /* Good step */
912:                 tao->trust = bnk->alpha4 * tao->trust;
913:               } else {
914:                 /* Very good step */
915:                 tao->trust = bnk->alpha5 * tao->trust;
916:               }
917:             }
918:           }
919:         }
920:       }
921:     } else {
922:       /*  Newton step was not good; reduce the radius */
923:       tao->trust = bnk->alpha1 * PetscMin(bnk->dnorm, tao->trust);
924:     }
925:     break;

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

944:           VecDot(tao->gradient, tao->stepdirection, &gdx);
945:           tau_1 = bnk->theta * gdx / (bnk->theta * gdx - (1.0 - bnk->theta) * prered + actred);
946:           tau_2 = bnk->theta * gdx / (bnk->theta * gdx + (1.0 + bnk->theta) * prered - actred);
947:           tau_min = PetscMin(tau_1, tau_2);
948:           tau_max = PetscMax(tau_1, tau_2);

950:           if (kappa >= 1.0 - bnk->mu1) {
951:             /*  Great agreement */
952:             *accept = PETSC_TRUE;
953:             if (tau_max < 1.0) {
954:               tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
955:             } else if (tau_max > bnk->gamma4) {
956:               tao->trust = PetscMax(tao->trust, bnk->gamma4 * bnk->dnorm);
957:             } else {
958:               tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
959:             }
960:           } else if (kappa >= 1.0 - bnk->mu2) {
961:             /*  Good agreement */
962:             *accept = PETSC_TRUE;
963:             if (tau_max < bnk->gamma2) {
964:               tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
965:             } else if (tau_max > bnk->gamma3) {
966:               tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
967:             } else if (tau_max < 1.0) {
968:               tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
969:             } else {
970:               tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
971:             }
972:           } else {
973:             /*  Not good agreement */
974:             if (tau_min > 1.0) {
975:               tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
976:             } else if (tau_max < bnk->gamma1) {
977:               tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
978:             } else if ((tau_min < bnk->gamma1) && (tau_max >= 1.0)) {
979:               tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
980:             } else if ((tau_1 >= bnk->gamma1) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1) || (tau_2 >= 1.0))) {
981:               tao->trust = tau_1 * PetscMin(tao->trust, bnk->dnorm);
982:             } else if ((tau_2 >= bnk->gamma1) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1) || (tau_2 >= 1.0))) {
983:               tao->trust = tau_2 * PetscMin(tao->trust, bnk->dnorm);
984:             } else {
985:               tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
986:             }
987:           }
988:         }
989:       }
990:     } else {
991:       /*  Newton step was not good; reduce the radius */
992:       tao->trust = bnk->gamma1 * PetscMin(bnk->dnorm, tao->trust);
993:     }
994:     break;
995:   }
996:   /* Make sure the radius does not violate min and max settings */
997:   tao->trust = PetscMin(tao->trust, bnk->max_radius);
998:   tao->trust = PetscMax(tao->trust, bnk->min_radius);
999:   return(0);
1000: }

1002: /* ---------------------------------------------------------- */

1004: PetscErrorCode TaoBNKAddStepCounts(Tao tao, PetscInt stepType)
1005: {
1006:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;

1009:   switch (stepType) {
1010:   case BNK_NEWTON:
1011:     ++bnk->newt;
1012:     break;
1013:   case BNK_BFGS:
1014:     ++bnk->bfgs;
1015:     break;
1016:   case BNK_SCALED_GRADIENT:
1017:     ++bnk->sgrad;
1018:     break;
1019:   case BNK_GRADIENT:
1020:     ++bnk->grad;
1021:     break;
1022:   default:
1023:     break;
1024:   }
1025:   return(0);
1026: }

1028: /* ---------------------------------------------------------- */

1030: PetscErrorCode TaoSetUp_BNK(Tao tao)
1031: {
1032:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1034:   PetscInt       i;
1035:   KSPType        ksp_type;

1038:   if (!tao->gradient) {
1039:     VecDuplicate(tao->solution,&tao->gradient);
1040:   }
1041:   if (!tao->stepdirection) {
1042:     VecDuplicate(tao->solution,&tao->stepdirection);
1043:   }
1044:   if (!bnk->W) {
1045:     VecDuplicate(tao->solution,&bnk->W);
1046:   }
1047:   if (!bnk->Xold) {
1048:     VecDuplicate(tao->solution,&bnk->Xold);
1049:   }
1050:   if (!bnk->Gold) {
1051:     VecDuplicate(tao->solution,&bnk->Gold);
1052:   }
1053:   if (!bnk->Xwork) {
1054:     VecDuplicate(tao->solution,&bnk->Xwork);
1055:   }
1056:   if (!bnk->Gwork) {
1057:     VecDuplicate(tao->solution,&bnk->Gwork);
1058:   }
1059:   if (!bnk->unprojected_gradient) {
1060:     VecDuplicate(tao->solution,&bnk->unprojected_gradient);
1061:   }
1062:   if (!bnk->unprojected_gradient_old) {
1063:     VecDuplicate(tao->solution,&bnk->unprojected_gradient_old);
1064:   }
1065:   if (!bnk->Diag_min) {
1066:     VecDuplicate(tao->solution,&bnk->Diag_min);
1067:   }
1068:   if (!bnk->Diag_max) {
1069:     VecDuplicate(tao->solution,&bnk->Diag_max);
1070:   }
1071:   if (bnk->max_cg_its > 0) {
1072:     /* Ensure that the important common vectors are shared between BNK and embedded BNCG */
1073:     bnk->bncg_ctx = (TAO_BNCG *)bnk->bncg->data;
1074:     PetscObjectReference((PetscObject)(bnk->unprojected_gradient_old));
1075:     VecDestroy(&bnk->bncg_ctx->unprojected_gradient_old);
1076:     bnk->bncg_ctx->unprojected_gradient_old = bnk->unprojected_gradient_old;
1077:     PetscObjectReference((PetscObject)(bnk->unprojected_gradient));
1078:     VecDestroy(&bnk->bncg_ctx->unprojected_gradient);
1079:     bnk->bncg_ctx->unprojected_gradient = bnk->unprojected_gradient;
1080:     PetscObjectReference((PetscObject)(bnk->Gold));
1081:     VecDestroy(&bnk->bncg_ctx->G_old);
1082:     bnk->bncg_ctx->G_old = bnk->Gold;
1083:     PetscObjectReference((PetscObject)(tao->gradient));
1084:     VecDestroy(&bnk->bncg->gradient);
1085:     bnk->bncg->gradient = tao->gradient;
1086:     PetscObjectReference((PetscObject)(tao->stepdirection));
1087:     VecDestroy(&bnk->bncg->stepdirection);
1088:     bnk->bncg->stepdirection = tao->stepdirection;
1089:     TaoSetInitialVector(bnk->bncg, tao->solution);
1090:     /* Copy over some settings from BNK into BNCG */
1091:     TaoSetMaximumIterations(bnk->bncg, bnk->max_cg_its);
1092:     TaoSetTolerances(bnk->bncg, tao->gatol, tao->grtol, tao->gttol);
1093:     TaoSetFunctionLowerBound(bnk->bncg, tao->fmin);
1094:     TaoSetConvergenceTest(bnk->bncg, tao->ops->convergencetest, tao->cnvP);
1095:     TaoSetObjectiveRoutine(bnk->bncg, tao->ops->computeobjective, tao->user_objP);
1096:     TaoSetGradientRoutine(bnk->bncg, tao->ops->computegradient, tao->user_gradP);
1097:     TaoSetObjectiveAndGradientRoutine(bnk->bncg, tao->ops->computeobjectiveandgradient, tao->user_objgradP);
1098:     PetscObjectCopyFortranFunctionPointers((PetscObject)tao, (PetscObject)(bnk->bncg));
1099:     for (i=0; i<tao->numbermonitors; ++i) {
1100:       TaoSetMonitor(bnk->bncg, tao->monitor[i], tao->monitorcontext[i], tao->monitordestroy[i]);
1101:       PetscObjectReference((PetscObject)(tao->monitorcontext[i]));
1102:     }
1103:   }
1104:   KSPGetType(tao->ksp,&ksp_type);
1105:   PetscStrcmp(ksp_type,KSPNASH,&bnk->is_nash);
1106:   PetscStrcmp(ksp_type,KSPSTCG,&bnk->is_stcg);
1107:   PetscStrcmp(ksp_type,KSPGLTR,&bnk->is_gltr);
1108:   bnk->X_inactive = NULL;
1109:   bnk->G_inactive = NULL;
1110:   bnk->inactive_work = NULL;
1111:   bnk->active_work = NULL;
1112:   bnk->inactive_idx = NULL;
1113:   bnk->active_idx = NULL;
1114:   bnk->active_lower = NULL;
1115:   bnk->active_upper = NULL;
1116:   bnk->active_fixed = NULL;
1117:   bnk->M = NULL;
1118:   bnk->H_inactive = NULL;
1119:   bnk->Hpre_inactive = NULL;
1120:   return(0);
1121: }

1123: /*------------------------------------------------------------*/

1125: PetscErrorCode TaoDestroy_BNK(Tao tao)
1126: {
1127:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;

1131:   if (tao->setupcalled) {
1132:     VecDestroy(&bnk->W);
1133:     VecDestroy(&bnk->Xold);
1134:     VecDestroy(&bnk->Gold);
1135:     VecDestroy(&bnk->Xwork);
1136:     VecDestroy(&bnk->Gwork);
1137:     VecDestroy(&bnk->unprojected_gradient);
1138:     VecDestroy(&bnk->unprojected_gradient_old);
1139:     VecDestroy(&bnk->Diag_min);
1140:     VecDestroy(&bnk->Diag_max);
1141:   }
1142:   ISDestroy(&bnk->active_lower);
1143:   ISDestroy(&bnk->active_upper);
1144:   ISDestroy(&bnk->active_fixed);
1145:   ISDestroy(&bnk->active_idx);
1146:   ISDestroy(&bnk->inactive_idx);
1147:   MatDestroy(&bnk->Hpre_inactive);
1148:   MatDestroy(&bnk->H_inactive);
1149:   TaoDestroy(&bnk->bncg);
1150:   PetscFree(tao->data);
1151:   return(0);
1152: }

1154: /*------------------------------------------------------------*/

1156: PetscErrorCode TaoSetFromOptions_BNK(PetscOptionItems *PetscOptionsObject,Tao tao)
1157: {
1158:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;

1162:   PetscOptionsHead(PetscOptionsObject,"Newton-Krylov method for bound constrained optimization");
1163:   PetscOptionsEList("-tao_bnk_init_type", "radius initialization type", "", BNK_INIT, BNK_INIT_TYPES, BNK_INIT[bnk->init_type], &bnk->init_type, NULL);
1164:   PetscOptionsEList("-tao_bnk_update_type", "radius update type", "", BNK_UPDATE, BNK_UPDATE_TYPES, BNK_UPDATE[bnk->update_type], &bnk->update_type, NULL);
1165:   PetscOptionsEList("-tao_bnk_as_type", "active set estimation method", "", BNK_AS, BNK_AS_TYPES, BNK_AS[bnk->as_type], &bnk->as_type, NULL);
1166:   PetscOptionsReal("-tao_bnk_sval", "(developer) Hessian perturbation starting value", "", bnk->sval, &bnk->sval,NULL);
1167:   PetscOptionsReal("-tao_bnk_imin", "(developer) minimum initial Hessian perturbation", "", bnk->imin, &bnk->imin,NULL);
1168:   PetscOptionsReal("-tao_bnk_imax", "(developer) maximum initial Hessian perturbation", "", bnk->imax, &bnk->imax,NULL);
1169:   PetscOptionsReal("-tao_bnk_imfac", "(developer) initial merit factor for Hessian perturbation", "", bnk->imfac, &bnk->imfac,NULL);
1170:   PetscOptionsReal("-tao_bnk_pmin", "(developer) minimum Hessian perturbation", "", bnk->pmin, &bnk->pmin,NULL);
1171:   PetscOptionsReal("-tao_bnk_pmax", "(developer) maximum Hessian perturbation", "", bnk->pmax, &bnk->pmax,NULL);
1172:   PetscOptionsReal("-tao_bnk_pgfac", "(developer) Hessian perturbation growth factor", "", bnk->pgfac, &bnk->pgfac,NULL);
1173:   PetscOptionsReal("-tao_bnk_psfac", "(developer) Hessian perturbation shrink factor", "", bnk->psfac, &bnk->psfac,NULL);
1174:   PetscOptionsReal("-tao_bnk_pmgfac", "(developer) merit growth factor for Hessian perturbation", "", bnk->pmgfac, &bnk->pmgfac,NULL);
1175:   PetscOptionsReal("-tao_bnk_pmsfac", "(developer) merit shrink factor for Hessian perturbation", "", bnk->pmsfac, &bnk->pmsfac,NULL);
1176:   PetscOptionsReal("-tao_bnk_eta1", "(developer) threshold for rejecting step (-tao_bnk_update_type reduction)", "", bnk->eta1, &bnk->eta1,NULL);
1177:   PetscOptionsReal("-tao_bnk_eta2", "(developer) threshold for accepting marginal step (-tao_bnk_update_type reduction)", "", bnk->eta2, &bnk->eta2,NULL);
1178:   PetscOptionsReal("-tao_bnk_eta3", "(developer) threshold for accepting reasonable step (-tao_bnk_update_type reduction)", "", bnk->eta3, &bnk->eta3,NULL);
1179:   PetscOptionsReal("-tao_bnk_eta4", "(developer) threshold for accepting good step (-tao_bnk_update_type reduction)", "", bnk->eta4, &bnk->eta4,NULL);
1180:   PetscOptionsReal("-tao_bnk_alpha1", "(developer) radius reduction factor for rejected step (-tao_bnk_update_type reduction)", "", bnk->alpha1, &bnk->alpha1,NULL);
1181:   PetscOptionsReal("-tao_bnk_alpha2", "(developer) radius reduction factor for marginally accepted bad step (-tao_bnk_update_type reduction)", "", bnk->alpha2, &bnk->alpha2,NULL);
1182:   PetscOptionsReal("-tao_bnk_alpha3", "(developer) radius increase factor for reasonable accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha3, &bnk->alpha3,NULL);
1183:   PetscOptionsReal("-tao_bnk_alpha4", "(developer) radius increase factor for good accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha4, &bnk->alpha4,NULL);
1184:   PetscOptionsReal("-tao_bnk_alpha5", "(developer) radius increase factor for very good accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha5, &bnk->alpha5,NULL);
1185:   PetscOptionsReal("-tao_bnk_nu1", "(developer) threshold for small line-search step length (-tao_bnk_update_type step)", "", bnk->nu1, &bnk->nu1,NULL);
1186:   PetscOptionsReal("-tao_bnk_nu2", "(developer) threshold for reasonable line-search step length (-tao_bnk_update_type step)", "", bnk->nu2, &bnk->nu2,NULL);
1187:   PetscOptionsReal("-tao_bnk_nu3", "(developer) threshold for large line-search step length (-tao_bnk_update_type step)", "", bnk->nu3, &bnk->nu3,NULL);
1188:   PetscOptionsReal("-tao_bnk_nu4", "(developer) threshold for very large line-search step length (-tao_bnk_update_type step)", "", bnk->nu4, &bnk->nu4,NULL);
1189:   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);
1190:   PetscOptionsReal("-tao_bnk_omega2", "(developer) radius reduction factor for small line-search step length (-tao_bnk_update_type step)", "", bnk->omega2, &bnk->omega2,NULL);
1191:   PetscOptionsReal("-tao_bnk_omega3", "(developer) radius factor for decent line-search step length (-tao_bnk_update_type step)", "", bnk->omega3, &bnk->omega3,NULL);
1192:   PetscOptionsReal("-tao_bnk_omega4", "(developer) radius increase factor for large line-search step length (-tao_bnk_update_type step)", "", bnk->omega4, &bnk->omega4,NULL);
1193:   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);
1194:   PetscOptionsReal("-tao_bnk_mu1_i", "(developer) threshold for accepting very good step (-tao_bnk_init_type interpolation)", "", bnk->mu1_i, &bnk->mu1_i,NULL);
1195:   PetscOptionsReal("-tao_bnk_mu2_i", "(developer) threshold for accepting good step (-tao_bnk_init_type interpolation)", "", bnk->mu2_i, &bnk->mu2_i,NULL);
1196:   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);
1197:   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);
1198:   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);
1199:   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);
1200:   PetscOptionsReal("-tao_bnk_theta_i", "(developer) trust region interpolation factor (-tao_bnk_init_type interpolation)", "", bnk->theta_i, &bnk->theta_i,NULL);
1201:   PetscOptionsReal("-tao_bnk_mu1", "(developer) threshold for accepting very good step (-tao_bnk_update_type interpolation)", "", bnk->mu1, &bnk->mu1,NULL);
1202:   PetscOptionsReal("-tao_bnk_mu2", "(developer) threshold for accepting good step (-tao_bnk_update_type interpolation)", "", bnk->mu2, &bnk->mu2,NULL);
1203:   PetscOptionsReal("-tao_bnk_gamma1", "(developer) radius reduction factor for rejected very bad step (-tao_bnk_update_type interpolation)", "", bnk->gamma1, &bnk->gamma1,NULL);
1204:   PetscOptionsReal("-tao_bnk_gamma2", "(developer) radius reduction factor for rejected bad step (-tao_bnk_update_type interpolation)", "", bnk->gamma2, &bnk->gamma2,NULL);
1205:   PetscOptionsReal("-tao_bnk_gamma3", "(developer) radius increase factor for accepted good step (-tao_bnk_update_type interpolation)", "", bnk->gamma3, &bnk->gamma3,NULL);
1206:   PetscOptionsReal("-tao_bnk_gamma4", "(developer) radius increase factor for accepted very good step (-tao_bnk_update_type interpolation)", "", bnk->gamma4, &bnk->gamma4,NULL);
1207:   PetscOptionsReal("-tao_bnk_theta", "(developer) trust region interpolation factor (-tao_bnk_update_type interpolation)", "", bnk->theta, &bnk->theta,NULL);
1208:   PetscOptionsReal("-tao_bnk_min_radius", "(developer) lower bound on initial radius", "", bnk->min_radius, &bnk->min_radius,NULL);
1209:   PetscOptionsReal("-tao_bnk_max_radius", "(developer) upper bound on radius", "", bnk->max_radius, &bnk->max_radius,NULL);
1210:   PetscOptionsReal("-tao_bnk_epsilon", "(developer) tolerance used when computing actual and predicted reduction", "", bnk->epsilon, &bnk->epsilon,NULL);
1211:   PetscOptionsReal("-tao_bnk_as_tol", "(developer) initial tolerance used when estimating actively bounded variables", "", bnk->as_tol, &bnk->as_tol,NULL);
1212:   PetscOptionsReal("-tao_bnk_as_step", "(developer) step length used when estimating actively bounded variables", "", bnk->as_step, &bnk->as_step,NULL);
1213:   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);
1214:   PetscOptionsTail();
1215:   TaoSetFromOptions(bnk->bncg);
1216:   TaoLineSearchSetFromOptions(tao->linesearch);
1217:   KSPSetFromOptions(tao->ksp);
1218:   return(0);
1219: }

1221: /*------------------------------------------------------------*/

1223: PetscErrorCode TaoView_BNK(Tao tao, PetscViewer viewer)
1224: {
1225:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1226:   PetscInt       nrejects;
1227:   PetscBool      isascii;

1231:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
1232:   if (isascii) {
1233:     PetscViewerASCIIPushTab(viewer);
1234:     if (bnk->M) {
1235:       MatLMVMGetRejectCount(bnk->M,&nrejects);
1236:       PetscViewerASCIIPrintf(viewer, "Rejected BFGS updates: %D\n",nrejects);
1237:     }
1238:     PetscViewerASCIIPrintf(viewer, "CG steps: %D\n", bnk->tot_cg_its);
1239:     PetscViewerASCIIPrintf(viewer, "Newton steps: %D\n", bnk->newt);
1240:     if (bnk->M) {
1241:       PetscViewerASCIIPrintf(viewer, "BFGS steps: %D\n", bnk->bfgs);
1242:     }
1243:     PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %D\n", bnk->sgrad);
1244:     PetscViewerASCIIPrintf(viewer, "Gradient steps: %D\n", bnk->grad);
1245:     PetscViewerASCIIPrintf(viewer, "KSP termination reasons:\n");
1246:     PetscViewerASCIIPrintf(viewer, "  atol: %D\n", bnk->ksp_atol);
1247:     PetscViewerASCIIPrintf(viewer, "  rtol: %D\n", bnk->ksp_rtol);
1248:     PetscViewerASCIIPrintf(viewer, "  ctol: %D\n", bnk->ksp_ctol);
1249:     PetscViewerASCIIPrintf(viewer, "  negc: %D\n", bnk->ksp_negc);
1250:     PetscViewerASCIIPrintf(viewer, "  dtol: %D\n", bnk->ksp_dtol);
1251:     PetscViewerASCIIPrintf(viewer, "  iter: %D\n", bnk->ksp_iter);
1252:     PetscViewerASCIIPrintf(viewer, "  othr: %D\n", bnk->ksp_othr);
1253:     PetscViewerASCIIPopTab(viewer);
1254:   }
1255:   return(0);
1256: }

1258: /* ---------------------------------------------------------- */

1260: /*MC
1261:   TAOBNK - Shared base-type for Bounded Newton-Krylov type algorithms.
1262:   At each iteration, the BNK methods solve the symmetric
1263:   system of equations to obtain the step diretion dk:
1264:               Hk dk = -gk
1265:   for free variables only. The step can be globalized either through
1266:   trust-region methods, or a line search, or a heuristic mixture of both.

1268:     Options Database Keys:
1269: + -max_cg_its - maximum number of bounded conjugate-gradient iterations taken in each Newton loop
1270: . -init_type - trust radius initialization method ("constant", "direction", "interpolation")
1271: . -update_type - trust radius update method ("step", "direction", "interpolation")
1272: . -as_type - active-set estimation method ("none", "bertsekas")
1273: . -as_tol - (developer) initial tolerance used in estimating bounded active variables (-as_type bertsekas)
1274: . -as_step - (developer) trial step length used in estimating bounded active variables (-as_type bertsekas)
1275: . -sval - (developer) Hessian perturbation starting value
1276: . -imin - (developer) minimum initial Hessian perturbation
1277: . -imax - (developer) maximum initial Hessian perturbation
1278: . -pmin - (developer) minimum Hessian perturbation
1279: . -pmax - (developer) aximum Hessian perturbation
1280: . -pgfac - (developer) Hessian perturbation growth factor
1281: . -psfac - (developer) Hessian perturbation shrink factor
1282: . -imfac - (developer) initial merit factor for Hessian perturbation
1283: . -pmgfac - (developer) merit growth factor for Hessian perturbation
1284: . -pmsfac - (developer) merit shrink factor for Hessian perturbation
1285: . -eta1 - (developer) threshold for rejecting step (-update_type reduction)
1286: . -eta2 - (developer) threshold for accepting marginal step (-update_type reduction)
1287: . -eta3 - (developer) threshold for accepting reasonable step (-update_type reduction)
1288: . -eta4 - (developer) threshold for accepting good step (-update_type reduction)
1289: . -alpha1 - (developer) radius reduction factor for rejected step (-update_type reduction)
1290: . -alpha2 - (developer) radius reduction factor for marginally accepted bad step (-update_type reduction)
1291: . -alpha3 - (developer) radius increase factor for reasonable accepted step (-update_type reduction)
1292: . -alpha4 - (developer) radius increase factor for good accepted step (-update_type reduction)
1293: . -alpha5 - (developer) radius increase factor for very good accepted step (-update_type reduction)
1294: . -epsilon - (developer) tolerance for small pred/actual ratios that trigger automatic step acceptance (-update_type reduction)
1295: . -mu1 - (developer) threshold for accepting very good step (-update_type interpolation)
1296: . -mu2 - (developer) threshold for accepting good step (-update_type interpolation)
1297: . -gamma1 - (developer) radius reduction factor for rejected very bad step (-update_type interpolation)
1298: . -gamma2 - (developer) radius reduction factor for rejected bad step (-update_type interpolation)
1299: . -gamma3 - (developer) radius increase factor for accepted good step (-update_type interpolation)
1300: . -gamma4 - (developer) radius increase factor for accepted very good step (-update_type interpolation)
1301: . -theta - (developer) trust region interpolation factor (-update_type interpolation)
1302: . -nu1 - (developer) threshold for small line-search step length (-update_type step)
1303: . -nu2 - (developer) threshold for reasonable line-search step length (-update_type step)
1304: . -nu3 - (developer) threshold for large line-search step length (-update_type step)
1305: . -nu4 - (developer) threshold for very large line-search step length (-update_type step)
1306: . -omega1 - (developer) radius reduction factor for very small line-search step length (-update_type step)
1307: . -omega2 - (developer) radius reduction factor for small line-search step length (-update_type step)
1308: . -omega3 - (developer) radius factor for decent line-search step length (-update_type step)
1309: . -omega4 - (developer) radius increase factor for large line-search step length (-update_type step)
1310: . -omega5 - (developer) radius increase factor for very large line-search step length (-update_type step)
1311: . -mu1_i -  (developer) threshold for accepting very good step (-init_type interpolation)
1312: . -mu2_i -  (developer) threshold for accepting good step (-init_type interpolation)
1313: . -gamma1_i - (developer) radius reduction factor for rejected very bad step (-init_type interpolation)
1314: . -gamma2_i - (developer) radius reduction factor for rejected bad step (-init_type interpolation)
1315: . -gamma3_i - (developer) radius increase factor for accepted good step (-init_type interpolation)
1316: . -gamma4_i - (developer) radius increase factor for accepted very good step (-init_type interpolation)
1317: - -theta_i - (developer) trust region interpolation factor (-init_type interpolation)

1319:   Level: beginner
1320: M*/

1322: PetscErrorCode TaoCreate_BNK(Tao tao)
1323: {
1324:   TAO_BNK        *bnk;
1325:   const char     *morethuente_type = TAOLINESEARCHMT;
1327:   PC             pc;

1330:   PetscNewLog(tao,&bnk);

1332:   tao->ops->setup = TaoSetUp_BNK;
1333:   tao->ops->view = TaoView_BNK;
1334:   tao->ops->setfromoptions = TaoSetFromOptions_BNK;
1335:   tao->ops->destroy = TaoDestroy_BNK;

1337:   /*  Override default settings (unless already changed) */
1338:   if (!tao->max_it_changed) tao->max_it = 50;
1339:   if (!tao->trust0_changed) tao->trust0 = 100.0;

1341:   tao->data = (void*)bnk;

1343:   /*  Hessian shifting parameters */
1344:   bnk->computehessian = TaoBNKComputeHessian;
1345:   bnk->computestep = TaoBNKComputeStep;

1347:   bnk->sval   = 0.0;
1348:   bnk->imin   = 1.0e-4;
1349:   bnk->imax   = 1.0e+2;
1350:   bnk->imfac  = 1.0e-1;

1352:   bnk->pmin   = 1.0e-12;
1353:   bnk->pmax   = 1.0e+2;
1354:   bnk->pgfac  = 1.0e+1;
1355:   bnk->psfac  = 4.0e-1;
1356:   bnk->pmgfac = 1.0e-1;
1357:   bnk->pmsfac = 1.0e-1;

1359:   /*  Default values for trust-region radius update based on steplength */
1360:   bnk->nu1 = 0.25;
1361:   bnk->nu2 = 0.50;
1362:   bnk->nu3 = 1.00;
1363:   bnk->nu4 = 1.25;

1365:   bnk->omega1 = 0.25;
1366:   bnk->omega2 = 0.50;
1367:   bnk->omega3 = 1.00;
1368:   bnk->omega4 = 2.00;
1369:   bnk->omega5 = 4.00;

1371:   /*  Default values for trust-region radius update based on reduction */
1372:   bnk->eta1 = 1.0e-4;
1373:   bnk->eta2 = 0.25;
1374:   bnk->eta3 = 0.50;
1375:   bnk->eta4 = 0.90;

1377:   bnk->alpha1 = 0.25;
1378:   bnk->alpha2 = 0.50;
1379:   bnk->alpha3 = 1.00;
1380:   bnk->alpha4 = 2.00;
1381:   bnk->alpha5 = 4.00;

1383:   /*  Default values for trust-region radius update based on interpolation */
1384:   bnk->mu1 = 0.10;
1385:   bnk->mu2 = 0.50;

1387:   bnk->gamma1 = 0.25;
1388:   bnk->gamma2 = 0.50;
1389:   bnk->gamma3 = 2.00;
1390:   bnk->gamma4 = 4.00;

1392:   bnk->theta = 0.05;

1394:   /*  Default values for trust region initialization based on interpolation */
1395:   bnk->mu1_i = 0.35;
1396:   bnk->mu2_i = 0.50;

1398:   bnk->gamma1_i = 0.0625;
1399:   bnk->gamma2_i = 0.5;
1400:   bnk->gamma3_i = 2.0;
1401:   bnk->gamma4_i = 5.0;

1403:   bnk->theta_i = 0.25;

1405:   /*  Remaining parameters */
1406:   bnk->max_cg_its = 0;
1407:   bnk->min_radius = 1.0e-10;
1408:   bnk->max_radius = 1.0e10;
1409:   bnk->epsilon = PetscPowReal(PETSC_MACHINE_EPSILON, 2.0/3.0);
1410:   bnk->as_tol = 1.0e-3;
1411:   bnk->as_step = 1.0e-3;
1412:   bnk->dmin = 1.0e-6;
1413:   bnk->dmax = 1.0e6;

1415:   bnk->M               = NULL;
1416:   bnk->bfgs_pre        = NULL;
1417:   bnk->init_type       = BNK_INIT_INTERPOLATION;
1418:   bnk->update_type     = BNK_UPDATE_REDUCTION;
1419:   bnk->as_type         = BNK_AS_BERTSEKAS;

1421:   bnk->is_stcg         = PETSC_FALSE;
1422:   bnk->is_gltr         = PETSC_FALSE;
1423:   bnk->is_nash         = PETSC_FALSE;

1425:   /* Create the embedded BNCG solver */
1426:   TaoCreate(PetscObjectComm((PetscObject)tao), &bnk->bncg);
1427:   PetscObjectIncrementTabLevel((PetscObject)bnk->bncg, (PetscObject)tao, 1);
1428:   TaoSetOptionsPrefix(bnk->bncg, "tao_bnk_");
1429:   TaoSetType(bnk->bncg, TAOBNCG);

1431:   /* Create the line search */
1432:   TaoLineSearchCreate(((PetscObject)tao)->comm,&tao->linesearch);
1433:   PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);
1434:   TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);
1435:   TaoLineSearchSetType(tao->linesearch,morethuente_type);
1436:   TaoLineSearchUseTaoRoutines(tao->linesearch,tao);

1438:   /*  Set linear solver to default for symmetric matrices */
1439:   KSPCreate(((PetscObject)tao)->comm,&tao->ksp);
1440:   PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1);
1441:   KSPSetOptionsPrefix(tao->ksp,"tao_bnk_");
1442:   KSPSetType(tao->ksp,KSPSTCG);
1443:   KSPGetPC(tao->ksp, &pc);
1444:   PCSetType(pc, PCLMVM);
1445:   return(0);
1446: }