Actual source code: ntl.c

petsc-master 2019-12-13
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  1:  #include <../src/tao/unconstrained/impls/ntl/ntlimpl.h>

  3:  #include <petscksp.h>

  5: #define NTL_INIT_CONSTANT         0
  6: #define NTL_INIT_DIRECTION        1
  7: #define NTL_INIT_INTERPOLATION    2
  8: #define NTL_INIT_TYPES            3

 10: #define NTL_UPDATE_REDUCTION      0
 11: #define NTL_UPDATE_INTERPOLATION  1
 12: #define NTL_UPDATE_TYPES          2

 14: static const char *NTL_INIT[64] = {"constant","direction","interpolation"};

 16: static const char *NTL_UPDATE[64] = {"reduction","interpolation"};

 18: /* Implements Newton's Method with a trust-region, line-search approach for
 19:    solving unconstrained minimization problems.  A More'-Thuente line search
 20:    is used to guarantee that the bfgs preconditioner remains positive
 21:    definite. */

 23: #define NTL_NEWTON              0
 24: #define NTL_BFGS                1
 25: #define NTL_SCALED_GRADIENT     2
 26: #define NTL_GRADIENT            3

 28: static PetscErrorCode TaoSolve_NTL(Tao tao)
 29: {
 30:   TAO_NTL                      *tl = (TAO_NTL *)tao->data;
 31:   KSPType                      ksp_type;
 32:   PetscBool                    is_nash,is_stcg,is_gltr,is_bfgs,is_jacobi,is_symmetric,sym_set;
 33:   KSPConvergedReason           ksp_reason;
 34:   PC                           pc;
 35:   TaoLineSearchConvergedReason ls_reason;

 37:   PetscReal                    fmin, ftrial, prered, actred, kappa, sigma;
 38:   PetscReal                    tau, tau_1, tau_2, tau_max, tau_min, max_radius;
 39:   PetscReal                    f, fold, gdx, gnorm;
 40:   PetscReal                    step = 1.0;

 42:   PetscReal                    norm_d = 0.0;
 43:   PetscErrorCode               ierr;
 44:   PetscInt                     stepType;
 45:   PetscInt                     its;

 47:   PetscInt                     bfgsUpdates = 0;
 48:   PetscInt                     needH;

 50:   PetscInt                     i_max = 5;
 51:   PetscInt                     j_max = 1;
 52:   PetscInt                     i, j, n, N;

 54:   PetscInt                     tr_reject;

 57:   if (tao->XL || tao->XU || tao->ops->computebounds) {
 58:     PetscInfo(tao,"WARNING: Variable bounds have been set but will be ignored by ntl algorithm\n");
 59:   }

 61:   KSPGetType(tao->ksp,&ksp_type);
 62:   PetscStrcmp(ksp_type,KSPNASH,&is_nash);
 63:   PetscStrcmp(ksp_type,KSPSTCG,&is_stcg);
 64:   PetscStrcmp(ksp_type,KSPGLTR,&is_gltr);
 65:   if (!is_nash && !is_stcg && !is_gltr) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_SUP,"TAO_NTR requires nash, stcg, or gltr for the KSP");

 67:   /* Initialize the radius and modify if it is too large or small */
 68:   tao->trust = tao->trust0;
 69:   tao->trust = PetscMax(tao->trust, tl->min_radius);
 70:   tao->trust = PetscMin(tao->trust, tl->max_radius);

 72:   /* Allocate the vectors needed for the BFGS approximation */
 73:   KSPGetPC(tao->ksp, &pc);
 74:   PetscObjectTypeCompare((PetscObject)pc, PCLMVM, &is_bfgs);
 75:   PetscObjectTypeCompare((PetscObject)pc, PCJACOBI, &is_jacobi);
 76:   if (is_bfgs) {
 77:     tl->bfgs_pre = pc;
 78:     PCLMVMGetMatLMVM(tl->bfgs_pre, &tl->M);
 79:     VecGetLocalSize(tao->solution, &n);
 80:     VecGetSize(tao->solution, &N);
 81:     MatSetSizes(tl->M, n, n, N, N);
 82:     MatLMVMAllocate(tl->M, tao->solution, tao->gradient);
 83:     MatIsSymmetricKnown(tl->M, &sym_set, &is_symmetric);
 84:     if (!sym_set || !is_symmetric) SETERRQ(PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_INCOMP, "LMVM matrix in the LMVM preconditioner must be symmetric.");
 85:   } else if (is_jacobi) {
 86:     PCJacobiSetUseAbs(pc,PETSC_TRUE);
 87:   }

 89:   /* Check convergence criteria */
 90:   TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient);
 91:   VecNorm(tao->gradient, NORM_2, &gnorm);
 92: if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
 93:   needH = 1;

 95:   tao->reason = TAO_CONTINUE_ITERATING;
 96:   TaoLogConvergenceHistory(tao,f,gnorm,0.0,tao->ksp_its);
 97:   TaoMonitor(tao,tao->niter,f,gnorm,0.0,step);
 98:   (*tao->ops->convergencetest)(tao,tao->cnvP);
 99:   if (tao->reason != TAO_CONTINUE_ITERATING) return(0);

101:   /* Initialize trust-region radius */
102:   switch(tl->init_type) {
103:   case NTL_INIT_CONSTANT:
104:     /* Use the initial radius specified */
105:     break;

107:   case NTL_INIT_INTERPOLATION:
108:     /* Use the initial radius specified */
109:     max_radius = 0.0;

111:     for (j = 0; j < j_max; ++j) {
112:       fmin = f;
113:       sigma = 0.0;

115:       if (needH) {
116:         TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);
117:         needH = 0;
118:       }

120:       for (i = 0; i < i_max; ++i) {
121:         VecCopy(tao->solution, tl->W);
122:         VecAXPY(tl->W, -tao->trust/gnorm, tao->gradient);

124:         TaoComputeObjective(tao, tl->W, &ftrial);
125:         if (PetscIsInfOrNanReal(ftrial)) {
126:           tau = tl->gamma1_i;
127:         } else {
128:           if (ftrial < fmin) {
129:             fmin = ftrial;
130:             sigma = -tao->trust / gnorm;
131:           }

133:           MatMult(tao->hessian, tao->gradient, tao->stepdirection);
134:           VecDot(tao->gradient, tao->stepdirection, &prered);

136:           prered = tao->trust * (gnorm - 0.5 * tao->trust * prered / (gnorm * gnorm));
137:           actred = f - ftrial;
138:           if ((PetscAbsScalar(actred) <= tl->epsilon) && (PetscAbsScalar(prered) <= tl->epsilon)) {
139:             kappa = 1.0;
140:           } else {
141:             kappa = actred / prered;
142:           }

144:           tau_1 = tl->theta_i * gnorm * tao->trust / (tl->theta_i * gnorm * tao->trust + (1.0 - tl->theta_i) * prered - actred);
145:           tau_2 = tl->theta_i * gnorm * tao->trust / (tl->theta_i * gnorm * tao->trust - (1.0 + tl->theta_i) * prered + actred);
146:           tau_min = PetscMin(tau_1, tau_2);
147:           tau_max = PetscMax(tau_1, tau_2);

149:           if (PetscAbsScalar(kappa - (PetscReal)1.0) <= tl->mu1_i) {
150:             /* Great agreement */
151:             max_radius = PetscMax(max_radius, tao->trust);

153:             if (tau_max < 1.0) {
154:               tau = tl->gamma3_i;
155:             } else if (tau_max > tl->gamma4_i) {
156:               tau = tl->gamma4_i;
157:             } else if (tau_1 >= 1.0 && tau_1 <= tl->gamma4_i && tau_2 < 1.0) {
158:               tau = tau_1;
159:             } else if (tau_2 >= 1.0 && tau_2 <= tl->gamma4_i && tau_1 < 1.0) {
160:               tau = tau_2;
161:             } else {
162:               tau = tau_max;
163:             }
164:           } else if (PetscAbsScalar(kappa - (PetscReal)1.0) <= tl->mu2_i) {
165:             /* Good agreement */
166:             max_radius = PetscMax(max_radius, tao->trust);

168:             if (tau_max < tl->gamma2_i) {
169:               tau = tl->gamma2_i;
170:             } else if (tau_max > tl->gamma3_i) {
171:               tau = tl->gamma3_i;
172:             } else {
173:               tau = tau_max;
174:             }
175:           } else {
176:             /* Not good agreement */
177:             if (tau_min > 1.0) {
178:               tau = tl->gamma2_i;
179:             } else if (tau_max < tl->gamma1_i) {
180:               tau = tl->gamma1_i;
181:             } else if ((tau_min < tl->gamma1_i) && (tau_max >= 1.0)) {
182:               tau = tl->gamma1_i;
183:             } else if ((tau_1 >= tl->gamma1_i) && (tau_1 < 1.0) &&  ((tau_2 < tl->gamma1_i) || (tau_2 >= 1.0))) {
184:               tau = tau_1;
185:             } else if ((tau_2 >= tl->gamma1_i) && (tau_2 < 1.0) &&  ((tau_1 < tl->gamma1_i) || (tau_2 >= 1.0))) {
186:               tau = tau_2;
187:             } else {
188:               tau = tau_max;
189:             }
190:           }
191:         }
192:         tao->trust = tau * tao->trust;
193:       }

195:       if (fmin < f) {
196:         f = fmin;
197:         VecAXPY(tao->solution, sigma, tao->gradient);
198:         TaoComputeGradient(tao, tao->solution, tao->gradient);

200:         VecNorm(tao->gradient, NORM_2, &gnorm);
201:         if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
202:         needH = 1;

204:         TaoLogConvergenceHistory(tao,f,gnorm,0.0,tao->ksp_its);
205:         TaoMonitor(tao,tao->niter,f,gnorm,0.0,step);
206:         (*tao->ops->convergencetest)(tao,tao->cnvP);
207:         if (tao->reason != TAO_CONTINUE_ITERATING) return(0);
208:       }
209:     }
210:     tao->trust = PetscMax(tao->trust, max_radius);

212:     /* Modify the radius if it is too large or small */
213:     tao->trust = PetscMax(tao->trust, tl->min_radius);
214:     tao->trust = PetscMin(tao->trust, tl->max_radius);
215:     break;

217:   default:
218:     /* Norm of the first direction will initialize radius */
219:     tao->trust = 0.0;
220:     break;
221:   }

223:   /* Set counter for gradient/reset steps */
224:   tl->ntrust = 0;
225:   tl->newt = 0;
226:   tl->bfgs = 0;
227:   tl->grad = 0;

229:   /* Have not converged; continue with Newton method */
230:   while (tao->reason == TAO_CONTINUE_ITERATING) {
231:     /* Call general purpose update function */
232:     if (tao->ops->update) {
233:       (*tao->ops->update)(tao, tao->niter, tao->user_update);
234:     }
235:     ++tao->niter;
236:     tao->ksp_its=0;
237:     /* Compute the Hessian */
238:     if (needH) {
239:       TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);
240:     }

242:     if (tl->bfgs_pre) {
243:       /* Update the limited memory preconditioner */
244:       MatLMVMUpdate(tl->M,tao->solution, tao->gradient);
245:       ++bfgsUpdates;
246:     }
247:     KSPSetOperators(tao->ksp, tao->hessian, tao->hessian_pre);
248:     /* Solve the Newton system of equations */
249:     KSPCGSetRadius(tao->ksp,tl->max_radius);
250:     KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);
251:     KSPGetIterationNumber(tao->ksp,&its);
252:     tao->ksp_its+=its;
253:     tao->ksp_tot_its+=its;
254:     KSPCGGetNormD(tao->ksp, &norm_d);

256:     if (0.0 == tao->trust) {
257:       /* Radius was uninitialized; use the norm of the direction */
258:       if (norm_d > 0.0) {
259:         tao->trust = norm_d;

261:         /* Modify the radius if it is too large or small */
262:         tao->trust = PetscMax(tao->trust, tl->min_radius);
263:         tao->trust = PetscMin(tao->trust, tl->max_radius);
264:       } else {
265:         /* The direction was bad; set radius to default value and re-solve
266:            the trust-region subproblem to get a direction */
267:         tao->trust = tao->trust0;

269:         /* Modify the radius if it is too large or small */
270:         tao->trust = PetscMax(tao->trust, tl->min_radius);
271:         tao->trust = PetscMin(tao->trust, tl->max_radius);

273:         KSPCGSetRadius(tao->ksp,tl->max_radius);
274:         KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);
275:         KSPGetIterationNumber(tao->ksp,&its);
276:         tao->ksp_its+=its;
277:         tao->ksp_tot_its+=its;
278:         KSPCGGetNormD(tao->ksp, &norm_d);

280:         if (norm_d == 0.0) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_PLIB, "Initial direction zero");
281:       }
282:     }

284:     VecScale(tao->stepdirection, -1.0);
285:     KSPGetConvergedReason(tao->ksp, &ksp_reason);
286:     if ((KSP_DIVERGED_INDEFINITE_PC == ksp_reason) && (tl->bfgs_pre)) {
287:       /* Preconditioner is numerically indefinite; reset the
288:          approximate if using BFGS preconditioning. */
289:       MatLMVMReset(tl->M, PETSC_FALSE);
290:       MatLMVMUpdate(tl->M, tao->solution, tao->gradient);
291:       bfgsUpdates = 1;
292:     }

294:     /* Check trust-region reduction conditions */
295:     tr_reject = 0;
296:     if (NTL_UPDATE_REDUCTION == tl->update_type) {
297:       /* Get predicted reduction */
298:       KSPCGGetObjFcn(tao->ksp,&prered);
299:       if (prered >= 0.0) {
300:         /* The predicted reduction has the wrong sign.  This cannot
301:            happen in infinite precision arithmetic.  Step should
302:            be rejected! */
303:         tao->trust = tl->alpha1 * PetscMin(tao->trust, norm_d);
304:         tr_reject = 1;
305:       } else {
306:         /* Compute trial step and function value */
307:         VecCopy(tao->solution, tl->W);
308:         VecAXPY(tl->W, 1.0, tao->stepdirection);
309:         TaoComputeObjective(tao, tl->W, &ftrial);

311:         if (PetscIsInfOrNanReal(ftrial)) {
312:           tao->trust = tl->alpha1 * PetscMin(tao->trust, norm_d);
313:           tr_reject = 1;
314:         } else {
315:           /* Compute and actual reduction */
316:           actred = f - ftrial;
317:           prered = -prered;
318:           if ((PetscAbsScalar(actred) <= tl->epsilon) &&
319:               (PetscAbsScalar(prered) <= tl->epsilon)) {
320:             kappa = 1.0;
321:           } else {
322:             kappa = actred / prered;
323:           }

325:           /* Accept of reject the step and update radius */
326:           if (kappa < tl->eta1) {
327:             /* Reject the step */
328:             tao->trust = tl->alpha1 * PetscMin(tao->trust, norm_d);
329:             tr_reject = 1;
330:           } else {
331:             /* Accept the step */
332:             if (kappa < tl->eta2) {
333:               /* Marginal bad step */
334:               tao->trust = tl->alpha2 * PetscMin(tao->trust, norm_d);
335:             } else if (kappa < tl->eta3) {
336:               /* Reasonable step */
337:               tao->trust = tl->alpha3 * tao->trust;
338:             } else if (kappa < tl->eta4) {
339:               /* Good step */
340:               tao->trust = PetscMax(tl->alpha4 * norm_d, tao->trust);
341:             } else {
342:               /* Very good step */
343:               tao->trust = PetscMax(tl->alpha5 * norm_d, tao->trust);
344:             }
345:           }
346:         }
347:       }
348:     } else {
349:       /* Get predicted reduction */
350:       KSPCGGetObjFcn(tao->ksp,&prered);
351:       if (prered >= 0.0) {
352:         /* The predicted reduction has the wrong sign.  This cannot
353:            happen in infinite precision arithmetic.  Step should
354:            be rejected! */
355:         tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d);
356:         tr_reject = 1;
357:       } else {
358:         VecCopy(tao->solution, tl->W);
359:         VecAXPY(tl->W, 1.0, tao->stepdirection);
360:         TaoComputeObjective(tao, tl->W, &ftrial);
361:         if (PetscIsInfOrNanReal(ftrial)) {
362:           tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d);
363:           tr_reject = 1;
364:         } else {
365:           VecDot(tao->gradient, tao->stepdirection, &gdx);

367:           actred = f - ftrial;
368:           prered = -prered;
369:           if ((PetscAbsScalar(actred) <= tl->epsilon) &&
370:               (PetscAbsScalar(prered) <= tl->epsilon)) {
371:             kappa = 1.0;
372:           } else {
373:             kappa = actred / prered;
374:           }

376:           tau_1 = tl->theta * gdx / (tl->theta * gdx - (1.0 - tl->theta) * prered + actred);
377:           tau_2 = tl->theta * gdx / (tl->theta * gdx + (1.0 + tl->theta) * prered - actred);
378:           tau_min = PetscMin(tau_1, tau_2);
379:           tau_max = PetscMax(tau_1, tau_2);

381:           if (kappa >= 1.0 - tl->mu1) {
382:             /* Great agreement; accept step and update radius */
383:             if (tau_max < 1.0) {
384:               tao->trust = PetscMax(tao->trust, tl->gamma3 * norm_d);
385:             } else if (tau_max > tl->gamma4) {
386:               tao->trust = PetscMax(tao->trust, tl->gamma4 * norm_d);
387:             } else {
388:               tao->trust = PetscMax(tao->trust, tau_max * norm_d);
389:             }
390:           } else if (kappa >= 1.0 - tl->mu2) {
391:             /* Good agreement */

393:             if (tau_max < tl->gamma2) {
394:               tao->trust = tl->gamma2 * PetscMin(tao->trust, norm_d);
395:             } else if (tau_max > tl->gamma3) {
396:               tao->trust = PetscMax(tao->trust, tl->gamma3 * norm_d);
397:             } else if (tau_max < 1.0) {
398:               tao->trust = tau_max * PetscMin(tao->trust, norm_d);
399:             } else {
400:               tao->trust = PetscMax(tao->trust, tau_max * norm_d);
401:             }
402:           } else {
403:             /* Not good agreement */
404:             if (tau_min > 1.0) {
405:               tao->trust = tl->gamma2 * PetscMin(tao->trust, norm_d);
406:             } else if (tau_max < tl->gamma1) {
407:               tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d);
408:             } else if ((tau_min < tl->gamma1) && (tau_max >= 1.0)) {
409:               tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d);
410:             } else if ((tau_1 >= tl->gamma1) && (tau_1 < 1.0) && ((tau_2 < tl->gamma1) || (tau_2 >= 1.0))) {
411:               tao->trust = tau_1 * PetscMin(tao->trust, norm_d);
412:             } else if ((tau_2 >= tl->gamma1) && (tau_2 < 1.0) && ((tau_1 < tl->gamma1) || (tau_2 >= 1.0))) {
413:               tao->trust = tau_2 * PetscMin(tao->trust, norm_d);
414:             } else {
415:               tao->trust = tau_max * PetscMin(tao->trust, norm_d);
416:             }
417:             tr_reject = 1;
418:           }
419:         }
420:       }
421:     }

423:     if (tr_reject) {
424:       /* The trust-region constraints rejected the step.  Apply a linesearch.
425:          Check for descent direction. */
426:       VecDot(tao->stepdirection, tao->gradient, &gdx);
427:       if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) {
428:         /* Newton step is not descent or direction produced Inf or NaN */

430:         if (!tl->bfgs_pre) {
431:           /* We don't have the bfgs matrix around and updated
432:              Must use gradient direction in this case */
433:           VecCopy(tao->gradient, tao->stepdirection);
434:           VecScale(tao->stepdirection, -1.0);
435:           ++tl->grad;
436:           stepType = NTL_GRADIENT;
437:         } else {
438:           /* Attempt to use the BFGS direction */
439:           MatSolve(tl->M, tao->gradient, tao->stepdirection);
440:           VecScale(tao->stepdirection, -1.0);

442:           /* Check for success (descent direction) */
443:           VecDot(tao->stepdirection, tao->gradient, &gdx);
444:           if ((gdx >= 0) || PetscIsInfOrNanReal(gdx)) {
445:             /* BFGS direction is not descent or direction produced not a number
446:                We can assert bfgsUpdates > 1 in this case because
447:                the first solve produces the scaled gradient direction,
448:                which is guaranteed to be descent */

450:             /* Use steepest descent direction (scaled) */
451:             MatLMVMReset(tl->M, PETSC_FALSE);
452:             MatLMVMUpdate(tl->M, tao->solution, tao->gradient);
453:             MatSolve(tl->M, tao->gradient, tao->stepdirection);
454:             VecScale(tao->stepdirection, -1.0);

456:             bfgsUpdates = 1;
457:             ++tl->grad;
458:             stepType = NTL_GRADIENT;
459:           } else {
460:             MatLMVMGetUpdateCount(tl->M, &bfgsUpdates);
461:             if (1 == bfgsUpdates) {
462:               /* The first BFGS direction is always the scaled gradient */
463:               ++tl->grad;
464:               stepType = NTL_GRADIENT;
465:             } else {
466:               ++tl->bfgs;
467:               stepType = NTL_BFGS;
468:             }
469:           }
470:         }
471:       } else {
472:         /* Computed Newton step is descent */
473:         ++tl->newt;
474:         stepType = NTL_NEWTON;
475:       }

477:       /* Perform the linesearch */
478:       fold = f;
479:       VecCopy(tao->solution, tl->Xold);
480:       VecCopy(tao->gradient, tl->Gold);

482:       step = 1.0;
483:       TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, tao->stepdirection, &step, &ls_reason);
484:       TaoAddLineSearchCounts(tao);

486:       while (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER && stepType != NTL_GRADIENT) {      /* Linesearch failed */
487:         /* Linesearch failed */
488:         f = fold;
489:         VecCopy(tl->Xold, tao->solution);
490:         VecCopy(tl->Gold, tao->gradient);

492:         switch(stepType) {
493:         case NTL_NEWTON:
494:           /* Failed to obtain acceptable iterate with Newton step */

496:           if (tl->bfgs_pre) {
497:             /* We don't have the bfgs matrix around and being updated
498:                Must use gradient direction in this case */
499:             VecCopy(tao->gradient, tao->stepdirection);
500:             ++tl->grad;
501:             stepType = NTL_GRADIENT;
502:           } else {
503:             /* Attempt to use the BFGS direction */
504:             MatSolve(tl->M, tao->gradient, tao->stepdirection);


507:             /* Check for success (descent direction) */
508:             VecDot(tao->stepdirection, tao->gradient, &gdx);
509:             if ((gdx <= 0) || PetscIsInfOrNanReal(gdx)) {
510:               /* BFGS direction is not descent or direction produced
511:                  not a number.  We can assert bfgsUpdates > 1 in this case
512:                  Use steepest descent direction (scaled) */
513:               MatLMVMReset(tl->M, PETSC_FALSE);
514:               MatLMVMUpdate(tl->M, tao->solution, tao->gradient);
515:               MatSolve(tl->M, tao->gradient, tao->stepdirection);

517:               bfgsUpdates = 1;
518:               ++tl->grad;
519:               stepType = NTL_GRADIENT;
520:             } else {
521:               MatLMVMGetUpdateCount(tl->M, &bfgsUpdates);
522:               if (1 == bfgsUpdates) {
523:                 /* The first BFGS direction is always the scaled gradient */
524:                 ++tl->grad;
525:                 stepType = NTL_GRADIENT;
526:               } else {
527:                 ++tl->bfgs;
528:                 stepType = NTL_BFGS;
529:               }
530:             }
531:           }
532:           break;

534:         case NTL_BFGS:
535:           /* Can only enter if pc_type == NTL_PC_BFGS
536:              Failed to obtain acceptable iterate with BFGS step
537:              Attempt to use the scaled gradient direction */
538:           MatLMVMReset(tl->M, PETSC_FALSE);
539:           MatLMVMUpdate(tl->M, tao->solution, tao->gradient);
540:           MatSolve(tl->M, tao->gradient, tao->stepdirection);

542:           bfgsUpdates = 1;
543:           ++tl->grad;
544:           stepType = NTL_GRADIENT;
545:           break;
546:         }
547:         VecScale(tao->stepdirection, -1.0);

549:         /* This may be incorrect; linesearch has values for stepmax and stepmin
550:            that should be reset. */
551:         step = 1.0;
552:         TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, tao->stepdirection, &step, &ls_reason);
553:         TaoAddLineSearchCounts(tao);
554:       }

556:       if (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER) {
557:         /* Failed to find an improving point */
558:         f = fold;
559:         VecCopy(tl->Xold, tao->solution);
560:         VecCopy(tl->Gold, tao->gradient);
561:         tao->trust = 0.0;
562:         step = 0.0;
563:         tao->reason = TAO_DIVERGED_LS_FAILURE;
564:         break;
565:       } else if (stepType == NTL_NEWTON) {
566:         if (step < tl->nu1) {
567:           /* Very bad step taken; reduce radius */
568:           tao->trust = tl->omega1 * PetscMin(norm_d, tao->trust);
569:         } else if (step < tl->nu2) {
570:           /* Reasonably bad step taken; reduce radius */
571:           tao->trust = tl->omega2 * PetscMin(norm_d, tao->trust);
572:         } else if (step < tl->nu3) {
573:           /* Reasonable step was taken; leave radius alone */
574:           if (tl->omega3 < 1.0) {
575:             tao->trust = tl->omega3 * PetscMin(norm_d, tao->trust);
576:           } else if (tl->omega3 > 1.0) {
577:             tao->trust = PetscMax(tl->omega3 * norm_d, tao->trust);
578:           }
579:         } else if (step < tl->nu4) {
580:           /* Full step taken; increase the radius */
581:           tao->trust = PetscMax(tl->omega4 * norm_d, tao->trust);
582:         } else {
583:           /* More than full step taken; increase the radius */
584:           tao->trust = PetscMax(tl->omega5 * norm_d, tao->trust);
585:         }
586:       } else {
587:         /* Newton step was not good; reduce the radius */
588:         tao->trust = tl->omega1 * PetscMin(norm_d, tao->trust);
589:       }
590:     } else {
591:       /* Trust-region step is accepted */
592:       VecCopy(tl->W, tao->solution);
593:       f = ftrial;
594:       TaoComputeGradient(tao, tao->solution, tao->gradient);
595:       ++tl->ntrust;
596:     }

598:     /* The radius may have been increased; modify if it is too large */
599:     tao->trust = PetscMin(tao->trust, tl->max_radius);

601:     /* Check for converged */
602:     VecNorm(tao->gradient, NORM_2, &gnorm);
603:     if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_USER,"User provided compute function generated Not-a-Number");
604:     needH = 1;

606:     TaoLogConvergenceHistory(tao,f,gnorm,0.0,tao->ksp_its);
607:     TaoMonitor(tao,tao->niter,f,gnorm,0.0,step);
608:     (*tao->ops->convergencetest)(tao,tao->cnvP);
609:   }
610:   return(0);
611: }

613: /* ---------------------------------------------------------- */
614: static PetscErrorCode TaoSetUp_NTL(Tao tao)
615: {
616:   TAO_NTL        *tl = (TAO_NTL *)tao->data;

620:   if (!tao->gradient) {VecDuplicate(tao->solution, &tao->gradient); }
621:   if (!tao->stepdirection) {VecDuplicate(tao->solution, &tao->stepdirection);}
622:   if (!tl->W) { VecDuplicate(tao->solution, &tl->W);}
623:   if (!tl->Xold) { VecDuplicate(tao->solution, &tl->Xold);}
624:   if (!tl->Gold) { VecDuplicate(tao->solution, &tl->Gold);}
625:   tl->bfgs_pre = 0;
626:   tl->M = 0;
627:   return(0);
628: }

630: /*------------------------------------------------------------*/
631: static PetscErrorCode TaoDestroy_NTL(Tao tao)
632: {
633:   TAO_NTL        *tl = (TAO_NTL *)tao->data;

637:   if (tao->setupcalled) {
638:     VecDestroy(&tl->W);
639:     VecDestroy(&tl->Xold);
640:     VecDestroy(&tl->Gold);
641:   }
642:   PetscFree(tao->data);
643:   return(0);
644: }

646: /*------------------------------------------------------------*/
647: static PetscErrorCode TaoSetFromOptions_NTL(PetscOptionItems *PetscOptionsObject,Tao tao)
648: {
649:   TAO_NTL        *tl = (TAO_NTL *)tao->data;

653:   PetscOptionsHead(PetscOptionsObject,"Newton trust region with line search method for unconstrained optimization");
654:   PetscOptionsEList("-tao_ntl_init_type", "radius initialization type", "", NTL_INIT, NTL_INIT_TYPES, NTL_INIT[tl->init_type], &tl->init_type,NULL);
655:   PetscOptionsEList("-tao_ntl_update_type", "radius update type", "", NTL_UPDATE, NTL_UPDATE_TYPES, NTL_UPDATE[tl->update_type], &tl->update_type,NULL);
656:   PetscOptionsReal("-tao_ntl_eta1", "poor steplength; reduce radius", "", tl->eta1, &tl->eta1,NULL);
657:   PetscOptionsReal("-tao_ntl_eta2", "reasonable steplength; leave radius alone", "", tl->eta2, &tl->eta2,NULL);
658:   PetscOptionsReal("-tao_ntl_eta3", "good steplength; increase radius", "", tl->eta3, &tl->eta3,NULL);
659:   PetscOptionsReal("-tao_ntl_eta4", "excellent steplength; greatly increase radius", "", tl->eta4, &tl->eta4,NULL);
660:   PetscOptionsReal("-tao_ntl_alpha1", "", "", tl->alpha1, &tl->alpha1,NULL);
661:   PetscOptionsReal("-tao_ntl_alpha2", "", "", tl->alpha2, &tl->alpha2,NULL);
662:   PetscOptionsReal("-tao_ntl_alpha3", "", "", tl->alpha3, &tl->alpha3,NULL);
663:   PetscOptionsReal("-tao_ntl_alpha4", "", "", tl->alpha4, &tl->alpha4,NULL);
664:   PetscOptionsReal("-tao_ntl_alpha5", "", "", tl->alpha5, &tl->alpha5,NULL);
665:   PetscOptionsReal("-tao_ntl_nu1", "poor steplength; reduce radius", "", tl->nu1, &tl->nu1,NULL);
666:   PetscOptionsReal("-tao_ntl_nu2", "reasonable steplength; leave radius alone", "", tl->nu2, &tl->nu2,NULL);
667:   PetscOptionsReal("-tao_ntl_nu3", "good steplength; increase radius", "", tl->nu3, &tl->nu3,NULL);
668:   PetscOptionsReal("-tao_ntl_nu4", "excellent steplength; greatly increase radius", "", tl->nu4, &tl->nu4,NULL);
669:   PetscOptionsReal("-tao_ntl_omega1", "", "", tl->omega1, &tl->omega1,NULL);
670:   PetscOptionsReal("-tao_ntl_omega2", "", "", tl->omega2, &tl->omega2,NULL);
671:   PetscOptionsReal("-tao_ntl_omega3", "", "", tl->omega3, &tl->omega3,NULL);
672:   PetscOptionsReal("-tao_ntl_omega4", "", "", tl->omega4, &tl->omega4,NULL);
673:   PetscOptionsReal("-tao_ntl_omega5", "", "", tl->omega5, &tl->omega5,NULL);
674:   PetscOptionsReal("-tao_ntl_mu1_i", "", "", tl->mu1_i, &tl->mu1_i,NULL);
675:   PetscOptionsReal("-tao_ntl_mu2_i", "", "", tl->mu2_i, &tl->mu2_i,NULL);
676:   PetscOptionsReal("-tao_ntl_gamma1_i", "", "", tl->gamma1_i, &tl->gamma1_i,NULL);
677:   PetscOptionsReal("-tao_ntl_gamma2_i", "", "", tl->gamma2_i, &tl->gamma2_i,NULL);
678:   PetscOptionsReal("-tao_ntl_gamma3_i", "", "", tl->gamma3_i, &tl->gamma3_i,NULL);
679:   PetscOptionsReal("-tao_ntl_gamma4_i", "", "", tl->gamma4_i, &tl->gamma4_i,NULL);
680:   PetscOptionsReal("-tao_ntl_theta_i", "", "", tl->theta_i, &tl->theta_i,NULL);
681:   PetscOptionsReal("-tao_ntl_mu1", "", "", tl->mu1, &tl->mu1,NULL);
682:   PetscOptionsReal("-tao_ntl_mu2", "", "", tl->mu2, &tl->mu2,NULL);
683:   PetscOptionsReal("-tao_ntl_gamma1", "", "", tl->gamma1, &tl->gamma1,NULL);
684:   PetscOptionsReal("-tao_ntl_gamma2", "", "", tl->gamma2, &tl->gamma2,NULL);
685:   PetscOptionsReal("-tao_ntl_gamma3", "", "", tl->gamma3, &tl->gamma3,NULL);
686:   PetscOptionsReal("-tao_ntl_gamma4", "", "", tl->gamma4, &tl->gamma4,NULL);
687:   PetscOptionsReal("-tao_ntl_theta", "", "", tl->theta, &tl->theta,NULL);
688:   PetscOptionsReal("-tao_ntl_min_radius", "lower bound on initial radius", "", tl->min_radius, &tl->min_radius,NULL);
689:   PetscOptionsReal("-tao_ntl_max_radius", "upper bound on radius", "", tl->max_radius, &tl->max_radius,NULL);
690:   PetscOptionsReal("-tao_ntl_epsilon", "tolerance used when computing actual and predicted reduction", "", tl->epsilon, &tl->epsilon,NULL);
691:   PetscOptionsTail();
692:   TaoLineSearchSetFromOptions(tao->linesearch);
693:   KSPSetFromOptions(tao->ksp);
694:   return(0);
695: }

697: /*------------------------------------------------------------*/
698: static PetscErrorCode TaoView_NTL(Tao tao, PetscViewer viewer)
699: {
700:   TAO_NTL        *tl = (TAO_NTL *)tao->data;
701:   PetscBool      isascii;

705:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
706:   if (isascii) {
707:     PetscViewerASCIIPushTab(viewer);
708:     PetscViewerASCIIPrintf(viewer, "Trust-region steps: %D\n", tl->ntrust);
709:     PetscViewerASCIIPrintf(viewer, "Newton search steps: %D\n", tl->newt);
710:     PetscViewerASCIIPrintf(viewer, "BFGS search steps: %D\n", tl->bfgs);
711:     PetscViewerASCIIPrintf(viewer, "Gradient search steps: %D\n", tl->grad);
712:     PetscViewerASCIIPopTab(viewer);
713:   }
714:   return(0);
715: }

717: /* ---------------------------------------------------------- */
718: /*MC
719:   TAONTL - Newton's method with trust region globalization and line search fallback.
720:   At each iteration, the Newton trust region method solves the system for d
721:   and performs a line search in the d direction:

723:             min_d  .5 dT Hk d + gkT d,  s.t.   ||d|| < Delta_k

725:   Options Database Keys:
726: + -tao_ntl_init_type - "constant","direction","interpolation"
727: . -tao_ntl_update_type - "reduction","interpolation"
728: . -tao_ntl_min_radius - lower bound on trust region radius
729: . -tao_ntl_max_radius - upper bound on trust region radius
730: . -tao_ntl_epsilon - tolerance for accepting actual / predicted reduction
731: . -tao_ntl_mu1_i - mu1 interpolation init factor
732: . -tao_ntl_mu2_i - mu2 interpolation init factor
733: . -tao_ntl_gamma1_i - gamma1 interpolation init factor
734: . -tao_ntl_gamma2_i - gamma2 interpolation init factor
735: . -tao_ntl_gamma3_i - gamma3 interpolation init factor
736: . -tao_ntl_gamma4_i - gamma4 interpolation init factor
737: . -tao_ntl_theta_i - theta1 interpolation init factor
738: . -tao_ntl_eta1 - eta1 reduction update factor
739: . -tao_ntl_eta2 - eta2 reduction update factor
740: . -tao_ntl_eta3 - eta3 reduction update factor
741: . -tao_ntl_eta4 - eta4 reduction update factor
742: . -tao_ntl_alpha1 - alpha1 reduction update factor
743: . -tao_ntl_alpha2 - alpha2 reduction update factor
744: . -tao_ntl_alpha3 - alpha3 reduction update factor
745: . -tao_ntl_alpha4 - alpha4 reduction update factor
746: . -tao_ntl_alpha4 - alpha4 reduction update factor
747: . -tao_ntl_mu1 - mu1 interpolation update
748: . -tao_ntl_mu2 - mu2 interpolation update
749: . -tao_ntl_gamma1 - gamma1 interpolcation update
750: . -tao_ntl_gamma2 - gamma2 interpolcation update
751: . -tao_ntl_gamma3 - gamma3 interpolcation update
752: . -tao_ntl_gamma4 - gamma4 interpolation update
753: - -tao_ntl_theta - theta1 interpolation update

755:   Level: beginner
756: M*/
757: PETSC_EXTERN PetscErrorCode TaoCreate_NTL(Tao tao)
758: {
759:   TAO_NTL        *tl;
761:   const char     *morethuente_type = TAOLINESEARCHMT;

764:   PetscNewLog(tao,&tl);
765:   tao->ops->setup = TaoSetUp_NTL;
766:   tao->ops->solve = TaoSolve_NTL;
767:   tao->ops->view = TaoView_NTL;
768:   tao->ops->setfromoptions = TaoSetFromOptions_NTL;
769:   tao->ops->destroy = TaoDestroy_NTL;

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

775:   tao->data = (void*)tl;

777:   /* Default values for trust-region radius update based on steplength */
778:   tl->nu1 = 0.25;
779:   tl->nu2 = 0.50;
780:   tl->nu3 = 1.00;
781:   tl->nu4 = 1.25;

783:   tl->omega1 = 0.25;
784:   tl->omega2 = 0.50;
785:   tl->omega3 = 1.00;
786:   tl->omega4 = 2.00;
787:   tl->omega5 = 4.00;

789:   /* Default values for trust-region radius update based on reduction */
790:   tl->eta1 = 1.0e-4;
791:   tl->eta2 = 0.25;
792:   tl->eta3 = 0.50;
793:   tl->eta4 = 0.90;

795:   tl->alpha1 = 0.25;
796:   tl->alpha2 = 0.50;
797:   tl->alpha3 = 1.00;
798:   tl->alpha4 = 2.00;
799:   tl->alpha5 = 4.00;

801:   /* Default values for trust-region radius update based on interpolation */
802:   tl->mu1 = 0.10;
803:   tl->mu2 = 0.50;

805:   tl->gamma1 = 0.25;
806:   tl->gamma2 = 0.50;
807:   tl->gamma3 = 2.00;
808:   tl->gamma4 = 4.00;

810:   tl->theta = 0.05;

812:   /* Default values for trust region initialization based on interpolation */
813:   tl->mu1_i = 0.35;
814:   tl->mu2_i = 0.50;

816:   tl->gamma1_i = 0.0625;
817:   tl->gamma2_i = 0.5;
818:   tl->gamma3_i = 2.0;
819:   tl->gamma4_i = 5.0;

821:   tl->theta_i = 0.25;

823:   /* Remaining parameters */
824:   tl->min_radius = 1.0e-10;
825:   tl->max_radius = 1.0e10;
826:   tl->epsilon = 1.0e-6;

828:   tl->init_type       = NTL_INIT_INTERPOLATION;
829:   tl->update_type     = NTL_UPDATE_REDUCTION;

831:   TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch);
832:   PetscObjectIncrementTabLevel((PetscObject)tao->linesearch,(PetscObject)tao,1);
833:   TaoLineSearchSetType(tao->linesearch, morethuente_type);
834:   TaoLineSearchUseTaoRoutines(tao->linesearch, tao);
835:   TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);
836:   KSPCreate(((PetscObject)tao)->comm,&tao->ksp);
837:   PetscObjectIncrementTabLevel((PetscObject)tao->ksp,(PetscObject)tao,1);
838:   KSPSetOptionsPrefix(tao->ksp,tao->hdr.prefix);
839:   KSPAppendOptionsPrefix(tao->ksp,"tao_ntl_");
840:   KSPSetType(tao->ksp,KSPSTCG);
841:   return(0);
842: }