xref: /petsc/src/tao/bound/impls/bnk/bnk.c (revision 5e9b73cb2546c7fbbdf5f3b5a906084e466c6a91) 
1 #include <petsctaolinesearch.h>
2 #include <../src/tao/bound/impls/bnk/bnk.h>
3 
4 #include <petscksp.h>
5 
6 /* Routine for BFGS preconditioner */
7 
8 PetscErrorCode MatLMVMSolveShell(PC pc, Vec b, Vec x)
9 {
10   PetscErrorCode ierr;
11   Mat            M;
12 
13   PetscFunctionBegin;
14   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
15   PetscValidHeaderSpecific(b,VEC_CLASSID,2);
16   PetscValidHeaderSpecific(x,VEC_CLASSID,3);
17   ierr = PCShellGetContext(pc,(void**)&M);CHKERRQ(ierr);
18   ierr = MatLMVMSolve(M, b, x);CHKERRQ(ierr);
19   PetscFunctionReturn(0);
20 }
21 
22 /*------------------------------------------------------------*/
23 
24 /* Routine for initializing the KSP solver, the BFGS preconditioner, and the initial trust radius estimation */
25 
26 PetscErrorCode TaoBNKInitialize(Tao tao, PetscInt initType)
27 {
28   PetscErrorCode               ierr;
29   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
30   PC                           pc;
31 
32   PetscReal                    f_min, ftrial, prered, actred, kappa, sigma;
33   PetscReal                    tau, tau_1, tau_2, tau_max, tau_min, max_radius;
34   PetscReal                    delta;
35 
36   PetscInt                     n,N,needH = 1;
37 
38   PetscInt                     i_max = 5;
39   PetscInt                     j_max = 1;
40   PetscInt                     i, j;
41 
42   PetscFunctionBegin;
43   /*   Project the current point onto the feasible set */
44   ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
45   ierr = TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);CHKERRQ(ierr);
46 
47   /* Project the initial point onto the feasible region */
48   ierr = VecMedian(tao->XL,tao->solution,tao->XU,tao->solution);CHKERRQ(ierr);
49 
50   /* Check convergence criteria */
51   ierr = TaoComputeObjectiveAndGradient(tao, tao->solution, &bnk->f, bnk->unprojected_gradient);CHKERRQ(ierr);
52   ierr = VecBoundGradientProjection(bnk->unprojected_gradient,tao->solution,tao->XL,tao->XU,tao->gradient);CHKERRQ(ierr);
53   ierr = TaoGradientNorm(tao, tao->gradient,NORM_2,&bnk->gnorm);CHKERRQ(ierr);
54   if (PetscIsInfOrNanReal(bnk->f) || PetscIsInfOrNanReal(bnk->gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
55 
56   /* Number of times ksp stopped because of these reasons */
57   bnk->ksp_atol = 0;
58   bnk->ksp_rtol = 0;
59   bnk->ksp_dtol = 0;
60   bnk->ksp_ctol = 0;
61   bnk->ksp_negc = 0;
62   bnk->ksp_iter = 0;
63   bnk->ksp_othr = 0;
64 
65   /* Initialize the Hessian perturbation */
66   bnk->pert = bnk->sval;
67 
68   /* Initialize trust-region radius when using nash, stcg, or gltr
69      Command automatically ignored for other methods
70      Will be reset during the first iteration
71   */
72   ierr = KSPCGSetRadius(tao->ksp,bnk->max_radius);CHKERRQ(ierr);
73   if (bnk->is_nash || bnk->is_stcg || bnk->is_gltr) {
74     if (tao->trust0 < 0.0) SETERRQ(PETSC_COMM_SELF,1,"Initial radius negative");
75     tao->trust = tao->trust0;
76     tao->trust = PetscMax(tao->trust, bnk->min_radius);
77     tao->trust = PetscMin(tao->trust, bnk->max_radius);
78   }
79 
80   ierr = TaoLogConvergenceHistory(tao,bnk->f,bnk->gnorm,0.0,tao->ksp_its);CHKERRQ(ierr);
81   ierr = TaoMonitor(tao,tao->niter,bnk->f,bnk->gnorm,0.0,1.0);CHKERRQ(ierr);
82   ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr);
83   if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
84 
85   /* Get vectors we will need */
86   if (BNK_PC_BFGS == bnk->pc_type && !bnk->M) {
87     ierr = VecGetLocalSize(tao->solution,&n);CHKERRQ(ierr);
88     ierr = VecGetSize(tao->solution,&N);CHKERRQ(ierr);
89     ierr = MatCreateLMVM(((PetscObject)tao)->comm,n,N,&bnk->M);CHKERRQ(ierr);
90     ierr = MatLMVMAllocateVectors(bnk->M,tao->solution);CHKERRQ(ierr);
91   }
92 
93   /* create vectors for the limited memory preconditioner */
94   if ((BNK_PC_BFGS == bnk->pc_type) && (BFGS_SCALE_BFGS != bnk->bfgs_scale_type)) {
95     if (!bnk->Diag) {ierr = VecDuplicate(tao->solution,&bnk->Diag);CHKERRQ(ierr);}
96   }
97   ierr = VecSet(bnk->Diag_min, bnk->dmin);CHKERRQ(ierr);
98   ierr = VecSet(bnk->Diag_max, bnk->dmax);CHKERRQ(ierr);
99 
100   /* Modify the preconditioner to use the bfgs approximation */
101   ierr = KSPGetPC(tao->ksp, &pc);CHKERRQ(ierr);
102   switch(bnk->pc_type) {
103   case BNK_PC_NONE:
104     ierr = PCSetType(pc, PCNONE);CHKERRQ(ierr);
105     ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
106     break;
107 
108   case BNK_PC_AHESS:
109     ierr = PCSetType(pc, PCJACOBI);CHKERRQ(ierr);
110     ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
111     ierr = PCJacobiSetUseAbs(pc,PETSC_TRUE);CHKERRQ(ierr);
112     break;
113 
114   case BNK_PC_BFGS:
115     ierr = PCSetType(pc, PCSHELL);CHKERRQ(ierr);
116     ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
117     ierr = PCShellSetName(pc, "bfgs");CHKERRQ(ierr);
118     ierr = PCShellSetContext(pc, bnk->M);CHKERRQ(ierr);
119     ierr = PCShellSetApply(pc, MatLMVMSolveShell);CHKERRQ(ierr);
120     break;
121 
122   default:
123     /* Use the pc method set by pc_type */
124     break;
125   }
126 
127   /* Initialize trust-region radius.  The initialization is only performed
128      when we are using Nash, Steihaug-Toint or the Generalized Lanczos method. */
129   if (bnk->is_nash || bnk->is_stcg || bnk->is_gltr) {
130     switch(initType) {
131     case BNK_INIT_CONSTANT:
132       /* Use the initial radius specified */
133       break;
134 
135     case BNK_INIT_INTERPOLATION:
136       /* Use the initial radius specified */
137       max_radius = 0.0;
138 
139       for (j = 0; j < j_max; ++j) {
140         f_min = bnk->f;
141         sigma = 0.0;
142 
143         if (needH) {
144           /* Compute the Hessian at the new step, and extract the inactive subsystem */
145           ierr = TaoComputeHessian(tao, tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
146           if (bnk->inactive_idx) {
147             ierr = ISDestroy(&bnk->inactive_idx);CHKERRQ(ierr);
148             ierr = VecWhichInactive(tao->XL,tao->solution,bnk->unprojected_gradient,tao->XU,PETSC_TRUE,&bnk->inactive_idx);CHKERRQ(ierr);
149             ierr = TaoMatGetSubMat(tao->hessian, bnk->inactive_idx, bnk->Xwork, TAO_SUBSET_MASK, &bnk->H_inactive);CHKERRQ(ierr);
150           } else {
151             ierr = MatDestroy(&bnk->H_inactive);
152             ierr = MatDuplicate(tao->hessian, MAT_COPY_VALUES, &bnk->H_inactive);
153           }
154           needH = 0;
155         }
156 
157         for (i = 0; i < i_max; ++i) {
158           /* Take a steepest descent step and snap it to bounds */
159           ierr = VecCopy(tao->solution, bnk->Xold);CHKERRQ(ierr);
160           ierr = VecAXPY(tao->solution, -tao->trust/bnk->gnorm, tao->gradient);CHKERRQ(ierr);
161           ierr = VecMedian(tao->XL, tao->solution, tao->XU, tao->solution);CHKERRQ(ierr);
162           /* Recompute the step after bound snapping so that it can be used in predicted decrease calculation later */
163           ierr = VecCopy(tao->solution, bnk->W);CHKERRQ(ierr);
164           ierr = VecAXPY(bnk->W, -1.0, bnk->Xold);CHKERRQ(ierr);
165           /* Compute the objective at the trial */
166           ierr = TaoComputeObjective(tao, tao->solution, &ftrial);CHKERRQ(ierr);
167           ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr);
168           if (PetscIsInfOrNanReal(ftrial)) {
169             tau = bnk->gamma1_i;
170           } else {
171             if (ftrial < f_min) {
172               f_min = ftrial;
173               sigma = -tao->trust / bnk->gnorm;
174             }
175             /* Compute the predicted and actual reduction */
176             ierr = MatMult(bnk->H_inactive, tao->gradient, bnk->W);CHKERRQ(ierr);
177             ierr = VecDot(tao->gradient, bnk->W, &prered);CHKERRQ(ierr);
178             prered = tao->trust * (bnk->gnorm - 0.5 * tao->trust * prered / (bnk->gnorm * bnk->gnorm));
179             actred = bnk->f - ftrial;
180             if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) {
181               kappa = 1.0;
182             } else {
183               kappa = actred / prered;
184             }
185 
186             tau_1 = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust + (1.0 - bnk->theta_i) * prered - actred);
187             tau_2 = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust - (1.0 + bnk->theta_i) * prered + actred);
188             tau_min = PetscMin(tau_1, tau_2);
189             tau_max = PetscMax(tau_1, tau_2);
190 
191             if (PetscAbsScalar(kappa - 1.0) <= bnk->mu1_i) {
192               /* Great agreement */
193               max_radius = PetscMax(max_radius, tao->trust);
194 
195               if (tau_max < 1.0) {
196                 tau = bnk->gamma3_i;
197               } else if (tau_max > bnk->gamma4_i) {
198                 tau = bnk->gamma4_i;
199               } else if (tau_1 >= 1.0 && tau_1 <= bnk->gamma4_i && tau_2 < 1.0) {
200                 tau = tau_1;
201               } else if (tau_2 >= 1.0 && tau_2 <= bnk->gamma4_i && tau_1 < 1.0) {
202                 tau = tau_2;
203               } else {
204                 tau = tau_max;
205               }
206             } else if (PetscAbsScalar(kappa - 1.0) <= bnk->mu2_i) {
207               /* Good agreement */
208               max_radius = PetscMax(max_radius, tao->trust);
209 
210               if (tau_max < bnk->gamma2_i) {
211                 tau = bnk->gamma2_i;
212               } else if (tau_max > bnk->gamma3_i) {
213                 tau = bnk->gamma3_i;
214               } else {
215                 tau = tau_max;
216               }
217             } else {
218               /* Not good agreement */
219               if (tau_min > 1.0) {
220                 tau = bnk->gamma2_i;
221               } else if (tau_max < bnk->gamma1_i) {
222                 tau = bnk->gamma1_i;
223               } else if ((tau_min < bnk->gamma1_i) && (tau_max >= 1.0)) {
224                 tau = bnk->gamma1_i;
225               } else if ((tau_1 >= bnk->gamma1_i) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
226                 tau = tau_1;
227               } else if ((tau_2 >= bnk->gamma1_i) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
228                 tau = tau_2;
229               } else {
230                 tau = tau_max;
231               }
232             }
233           }
234           tao->trust = tau * tao->trust;
235         }
236 
237         if (f_min < bnk->f) {
238           bnk->f = f_min;
239           ierr = VecAXPY(tao->solution,sigma,tao->gradient);CHKERRQ(ierr);
240           ierr = VecMedian(tao->XL, tao->solution, tao->XU, tao->solution);CHKERRQ(ierr);
241           ierr = TaoComputeGradient(tao,tao->solution,bnk->unprojected_gradient);CHKERRQ(ierr);
242           ierr = VecBoundGradientProjection(bnk->unprojected_gradient,tao->solution,tao->XL,tao->XU,tao->gradient);CHKERRQ(ierr);
243 
244           ierr = TaoGradientNorm(tao, tao->gradient,NORM_2,&bnk->gnorm);CHKERRQ(ierr);
245           if (PetscIsInfOrNanReal(bnk->gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute gradient generated Inf or NaN");
246           needH = 1;
247 
248           ierr = TaoLogConvergenceHistory(tao,bnk->f,bnk->gnorm,0.0,tao->ksp_its);CHKERRQ(ierr);
249           ierr = TaoMonitor(tao,tao->niter,bnk->f,bnk->gnorm,0.0,1.0);CHKERRQ(ierr);
250           ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr);
251           if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
252         }
253       }
254       tao->trust = PetscMax(tao->trust, max_radius);
255 
256       /* Modify the radius if it is too large or small */
257       tao->trust = PetscMax(tao->trust, bnk->min_radius);
258       tao->trust = PetscMin(tao->trust, bnk->max_radius);
259       break;
260 
261     default:
262       /* Norm of the first direction will initialize radius */
263       tao->trust = 0.0;
264       break;
265     }
266   }
267 
268   /* Set initial scaling for the BFGS preconditioner
269      This step is done after computing the initial trust-region radius
270      since the function value may have decreased */
271   if (BNK_PC_BFGS == bnk->pc_type) {
272     delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
273     ierr = MatLMVMSetDelta(bnk->M,delta);CHKERRQ(ierr);
274   }
275 
276   /* Set counter for gradient/reset steps*/
277   bnk->newt = 0;
278   bnk->bfgs = 0;
279   bnk->sgrad = 0;
280   bnk->grad = 0;
281   PetscFunctionReturn(0);
282 }
283 
284 /*------------------------------------------------------------*/
285 
286 /* Routine for computing the Hessian and preparing the preconditioner at the new iterate */
287 
288 PetscErrorCode TaoBNKComputeHessian(Tao tao)
289 {
290   PetscErrorCode               ierr;
291   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
292 
293   PetscFunctionBegin;
294   /* Compute the Hessian */
295   ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
296   /* Add a correction to the BFGS preconditioner */
297   if (BNK_PC_BFGS == bnk->pc_type) {
298     ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
299     /* Update the BFGS diagonal scaling */
300     if (BFGS_SCALE_AHESS == bnk->bfgs_scale_type) {
301       ierr = MatGetDiagonal(tao->hessian, bnk->Diag);CHKERRQ(ierr);
302       ierr = VecAbs(bnk->Diag);CHKERRQ(ierr);
303       ierr = VecMedian(bnk->Diag_min, bnk->Diag, bnk->Diag_max, bnk->Diag);CHKERRQ(ierr);
304       ierr = VecReciprocal(bnk->Diag);CHKERRQ(ierr);
305       ierr = MatLMVMSetScale(bnk->M,bnk->Diag);CHKERRQ(ierr);
306     }
307   }
308   PetscFunctionReturn(0);
309 }
310 
311 /*------------------------------------------------------------*/
312 
313 /* Routine for estimating the active set */
314 
315 PetscErrorCode TaoBNKEstimateActiveSet(Tao tao)
316 {
317   PetscErrorCode               ierr;
318   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
319 
320   PetscFunctionBegin;
321   switch (bnk->as_type) {
322   case BNK_AS_NONE:
323     ierr = ISDestroy(&bnk->inactive_idx);CHKERRQ(ierr);
324     ierr = VecWhichInactive(tao->XL, tao->solution, bnk->unprojected_gradient, tao->XU, PETSC_TRUE, &bnk->inactive_idx);CHKERRQ(ierr);
325     ierr = ISDestroy(&bnk->active_idx);CHKERRQ(ierr);
326     ierr = ISComplementVec(bnk->inactive_idx, tao->solution, &bnk->active_idx);CHKERRQ(ierr);
327     break;
328 
329   case BNK_AS_BERTSEKAS:
330     /* Compute the trial step vector with which we will estimate the active set at the next iteration */
331     if (BNK_PC_BFGS == bnk->pc_type) {
332       /* If the BFGS preconditioner matrix is available, we will construct a trial step with it */
333       ierr = MatLMVMSetInactive(bnk->M, NULL);CHKERRQ(ierr);
334       ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, bnk->W);CHKERRQ(ierr);
335     } else {
336       /* BFGS preconditioner doesn't exist so let's invert the absolute diagonal of the Hessian instead onto the gradient */
337       ierr = MatGetDiagonal(tao->hessian, bnk->Xwork);CHKERRQ(ierr);
338       ierr = VecAbs(bnk->Xwork);CHKERRQ(ierr);
339       ierr = VecMedian(bnk->Diag_min, bnk->Xwork, bnk->Diag_max, bnk->Xwork);CHKERRQ(ierr);
340       ierr = VecReciprocal(bnk->Xwork);CHKERRQ(ierr);CHKERRQ(ierr);
341       ierr = VecPointwiseMult(bnk->W, bnk->Xwork, bnk->unprojected_gradient);CHKERRQ(ierr);
342     }
343     ierr = VecScale(bnk->W, -1.0);CHKERRQ(ierr);
344     ierr = TaoEstimateActiveBounds(tao->solution, tao->XL, tao->XU, bnk->unprojected_gradient, bnk->W, bnk->as_step, &bnk->as_tol, &bnk->active_lower, &bnk->active_upper, &bnk->active_fixed, &bnk->active_idx, &bnk->inactive_idx);CHKERRQ(ierr);
345 
346   default:
347     break;
348   }
349   PetscFunctionReturn(0);
350 }
351 
352 /*------------------------------------------------------------*/
353 
354 /* Routine for bounding the step direction */
355 
356 PetscErrorCode TaoBNKBoundStep(Tao tao, Vec step)
357 {
358   PetscErrorCode               ierr;
359   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
360 
361   PetscFunctionBegin;
362   if (bnk->active_idx) {
363     switch (bnk->as_type) {
364     case BNK_AS_NONE:
365       if (bnk->active_idx) {
366         ierr = VecGetSubVector(step, bnk->active_idx, &bnk->active_work);CHKERRQ(ierr);
367         ierr = VecSet(bnk->active_work, 0.0);CHKERRQ(ierr);
368         ierr = VecRestoreSubVector(step, bnk->active_idx, &bnk->active_work);CHKERRQ(ierr);
369       }
370       break;
371 
372     case BNK_AS_BERTSEKAS:
373       ierr = TaoBoundStep(tao->solution, tao->XL, tao->XU, bnk->active_lower, bnk->active_upper, bnk->active_fixed, step);CHKERRQ(ierr);
374       break;
375 
376     default:
377       break;
378     }
379   }
380   PetscFunctionReturn(0);
381 }
382 
383 /*------------------------------------------------------------*/
384 
385 /* Routine for computing the Newton step.
386 
387   If the safeguard is enabled, the Newton step is verified to be a
388   descent direction, with fallbacks onto BFGS, scaled gradient, and unscaled
389   gradient steps if/when necessary.
390 
391   The function reports back on which type of step has ultimately been stored
392   under tao->stepdirection.
393 */
394 
395 PetscErrorCode TaoBNKComputeStep(Tao tao, PetscBool shift, KSPConvergedReason *ksp_reason)
396 {
397   PetscErrorCode               ierr;
398   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
399 
400   PetscReal                    delta;
401   PetscInt                     bfgsUpdates = 0;
402   PetscInt                     kspits;
403 
404   PetscFunctionBegin;
405   /* Determine the active and inactive sets */
406   ierr = TaoBNKEstimateActiveSet(tao);CHKERRQ(ierr);
407 
408   /* Prepare the reduced sub-matrices for the inactive set */
409   if (BNK_PC_BFGS == bnk->pc_type) { ierr = MatLMVMSetInactive(bnk->M, bnk->inactive_idx);CHKERRQ(ierr); }
410   if (bnk->inactive_idx) {
411     ierr = MatDestroy(&bnk->H_inactive);
412     ierr = MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive);CHKERRQ(ierr);
413     if (tao->hessian == tao->hessian_pre) {
414       bnk->Hpre_inactive = bnk->H_inactive;
415     } else {
416       ierr = MatDestroy(&bnk->Hpre_inactive);
417       ierr = MatCreateSubMatrix(tao->hessian_pre, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->Hpre_inactive);CHKERRQ(ierr);
418     }
419   } else {
420     ierr = MatDestroy(&bnk->H_inactive);
421     ierr = MatDuplicate(tao->hessian, MAT_COPY_VALUES, &bnk->H_inactive);
422     if (tao->hessian == tao->hessian_pre) {
423       bnk->Hpre_inactive = bnk->H_inactive;
424     } else {
425       ierr = MatDestroy(&bnk->Hpre_inactive);
426       ierr = MatDuplicate(tao->hessian_pre, MAT_COPY_VALUES, &bnk->Hpre_inactive);
427     }
428   }
429 
430   /* Shift the reduced Hessian matrix */
431   if ((shift) && (bnk->pert > 0)) {
432     ierr = MatShift(bnk->H_inactive, bnk->pert);CHKERRQ(ierr);
433     if (bnk->H_inactive != bnk->Hpre_inactive) {
434       ierr = MatShift(bnk->Hpre_inactive, bnk->pert);CHKERRQ(ierr);
435     }
436   }
437 
438   /* Update the diagonal scaling for the BFGS preconditioner, this time with the Hessian perturbation */
439   if ((BNK_PC_BFGS == bnk->pc_type) && (BFGS_SCALE_PHESS == bnk->bfgs_scale_type)) {
440     /* Obtain diagonal for the bfgs preconditioner  */
441     ierr = VecSet(bnk->Diag, 1.0);CHKERRQ(ierr);
442     if (bnk->inactive_idx) {
443       ierr = VecGetSubVector(bnk->Diag, bnk->inactive_idx, &bnk->Diag_red);CHKERRQ(ierr);
444     } else {
445       bnk->Diag_red = bnk->Diag;
446     }
447     ierr = MatGetDiagonal(bnk->H_inactive, bnk->Diag_red);CHKERRQ(ierr);
448     if (bnk->inactive_idx) {
449       ierr = VecRestoreSubVector(bnk->Diag, bnk->inactive_idx, &bnk->Diag_red);CHKERRQ(ierr);
450     }
451     ierr = VecAbs(bnk->Diag);CHKERRQ(ierr);
452     ierr = VecMedian(bnk->Diag_min, bnk->Diag, bnk->Diag_max, bnk->Diag);CHKERRQ(ierr);
453     ierr = VecReciprocal(bnk->Diag);CHKERRQ(ierr);
454     ierr = MatLMVMSetScale(bnk->M,bnk->Diag);CHKERRQ(ierr);
455   }
456 
457   /* Solve the Newton system of equations */
458   ierr = VecSet(tao->stepdirection, 0.0);CHKERRQ(ierr);
459   ierr = KSPReset(tao->ksp);CHKERRQ(ierr);
460   ierr = KSPSetOperators(tao->ksp,bnk->H_inactive,bnk->Hpre_inactive);CHKERRQ(ierr);
461   ierr = VecCopy(bnk->unprojected_gradient, bnk->Gwork);CHKERRQ(ierr);
462   if (bnk->inactive_idx) {
463     ierr = VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr);
464     ierr = VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr);
465   } else {
466     bnk->G_inactive = bnk->unprojected_gradient;
467     bnk->X_inactive = tao->stepdirection;
468   }
469   if (bnk->is_nash || bnk->is_stcg || bnk->is_gltr) {
470     ierr = KSPCGSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr);
471     ierr = KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);CHKERRQ(ierr);
472     ierr = KSPGetIterationNumber(tao->ksp,&kspits);CHKERRQ(ierr);
473     tao->ksp_its+=kspits;
474     tao->ksp_tot_its+=kspits;
475     ierr = KSPCGGetNormD(tao->ksp,&bnk->dnorm);CHKERRQ(ierr);
476 
477     if (0.0 == tao->trust) {
478       /* Radius was uninitialized; use the norm of the direction */
479       if (bnk->dnorm > 0.0) {
480         tao->trust = bnk->dnorm;
481 
482         /* Modify the radius if it is too large or small */
483         tao->trust = PetscMax(tao->trust, bnk->min_radius);
484         tao->trust = PetscMin(tao->trust, bnk->max_radius);
485       } else {
486         /* The direction was bad; set radius to default value and re-solve
487            the trust-region subproblem to get a direction */
488         tao->trust = tao->trust0;
489 
490         /* Modify the radius if it is too large or small */
491         tao->trust = PetscMax(tao->trust, bnk->min_radius);
492         tao->trust = PetscMin(tao->trust, bnk->max_radius);
493 
494         ierr = KSPCGSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr);
495         ierr = KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);CHKERRQ(ierr);
496         ierr = KSPGetIterationNumber(tao->ksp,&kspits);CHKERRQ(ierr);
497         tao->ksp_its+=kspits;
498         tao->ksp_tot_its+=kspits;
499         ierr = KSPCGGetNormD(tao->ksp,&bnk->dnorm);CHKERRQ(ierr);
500 
501         if (bnk->dnorm == 0.0) SETERRQ(PETSC_COMM_SELF,1, "Initial direction zero");
502       }
503     }
504   } else {
505     ierr = KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);CHKERRQ(ierr);
506     ierr = KSPGetIterationNumber(tao->ksp, &kspits);CHKERRQ(ierr);
507     tao->ksp_its += kspits;
508     tao->ksp_tot_its+=kspits;
509   }
510   /* Restore sub vectors back */
511   if (bnk->inactive_idx) {
512     ierr = VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr);
513     ierr = VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr);
514   }
515   /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
516   ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
517   ierr = TaoBNKBoundStep(tao, tao->stepdirection);CHKERRQ(ierr);
518 
519   /* Record convergence reasons */
520   ierr = KSPGetConvergedReason(tao->ksp, ksp_reason);CHKERRQ(ierr);
521   if (KSP_CONVERGED_ATOL == *ksp_reason) {
522     ++bnk->ksp_atol;
523   } else if (KSP_CONVERGED_RTOL == *ksp_reason) {
524     ++bnk->ksp_rtol;
525   } else if (KSP_CONVERGED_CG_CONSTRAINED == *ksp_reason) {
526     ++bnk->ksp_ctol;
527   } else if (KSP_CONVERGED_CG_NEG_CURVE == *ksp_reason) {
528     ++bnk->ksp_negc;
529   } else if (KSP_DIVERGED_DTOL == *ksp_reason) {
530     ++bnk->ksp_dtol;
531   } else if (KSP_DIVERGED_ITS == *ksp_reason) {
532     ++bnk->ksp_iter;
533   } else {
534     ++bnk->ksp_othr;
535   }
536 
537   /* Make sure the BFGS preconditioner is healthy */
538   if (bnk->pc_type == BNK_PC_BFGS) {
539     ierr = MatLMVMGetUpdates(bnk->M, &bfgsUpdates);CHKERRQ(ierr);
540     if ((KSP_DIVERGED_INDEFINITE_PC == *ksp_reason) && (bfgsUpdates > 1)) {
541       /* Preconditioner is numerically indefinite; reset the approximation. */
542       delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
543       ierr = MatLMVMSetDelta(bnk->M,delta);CHKERRQ(ierr);
544       ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
545       ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
546     }
547   }
548   PetscFunctionReturn(0);
549 }
550 
551 /*------------------------------------------------------------*/
552 
553 /* Routine for recomputing the predicted reduction for a given step vector */
554 
555 PetscErrorCode TaoBNKRecomputePred(Tao tao, Vec S, PetscReal *prered)
556 {
557   PetscErrorCode               ierr;
558   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
559 
560   PetscFunctionBegin;
561   /* Extract subvectors associated with the inactive set */
562   if (bnk->inactive_idx){
563     ierr = VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr);
564     ierr = VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);CHKERRQ(ierr);
565     ierr = VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr);
566   } else {
567     bnk->X_inactive = tao->stepdirection;
568     bnk->inactive_work = bnk->Xwork;
569     bnk->G_inactive = bnk->Gwork;
570   }
571   /* Recompute the predicted decrease based on the quadratic model */
572   ierr = MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work);CHKERRQ(ierr);
573   ierr = VecAYPX(bnk->inactive_work, -0.5, bnk->G_inactive);CHKERRQ(ierr);
574   ierr = VecDot(bnk->inactive_work, bnk->X_inactive, prered);
575   /* Restore the sub vectors */
576   if (bnk->inactive_idx){
577     ierr = VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr);
578     ierr = VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);CHKERRQ(ierr);
579     ierr = VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr);
580   }
581   PetscFunctionReturn(0);
582 }
583 
584 /*------------------------------------------------------------*/
585 
586 /* Routine for ensuring that the Newton step is a descent direction.
587 
588    The step direction falls back onto BFGS, scaled gradient and gradient steps
589    in the event that the Newton step fails the test.
590 */
591 
592 PetscErrorCode TaoBNKSafeguardStep(Tao tao, KSPConvergedReason ksp_reason, PetscInt *stepType)
593 {
594   PetscErrorCode               ierr;
595   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
596 
597   PetscReal                    gdx, delta, e_min;
598   PetscInt                     bfgsUpdates;
599 
600   PetscFunctionBegin;
601   ierr = VecDot(tao->stepdirection, tao->gradient, &gdx);CHKERRQ(ierr);
602   if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) {
603     /* Newton step is not descent or direction produced Inf or NaN
604        Update the perturbation for next time */
605     if (bnk->pert <= 0.0) {
606       /* Initialize the perturbation */
607       bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
608       if (bnk->is_gltr) {
609         ierr = KSPCGGLTRGetMinEig(tao->ksp,&e_min);CHKERRQ(ierr);
610         bnk->pert = PetscMax(bnk->pert, -e_min);
611       }
612     } else {
613       /* Increase the perturbation */
614       bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
615     }
616 
617     if (BNK_PC_BFGS != bnk->pc_type) {
618       /* We don't have the bfgs matrix around and updated
619          Must use gradient direction in this case */
620       ierr = VecCopy(tao->gradient, tao->stepdirection);CHKERRQ(ierr);
621       *stepType = BNK_GRADIENT;
622     } else {
623       /* Attempt to use the BFGS direction */
624       ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
625 
626       /* Check for success (descent direction)
627          NOTE: Negative gdx here means not a descent direction because
628          the fall-back step is missing a negative sign. */
629       ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr);
630       if ((gdx <= 0) || PetscIsInfOrNanReal(gdx)) {
631         /* BFGS direction is not descent or direction produced not a number
632            We can assert bfgsUpdates > 1 in this case because
633            the first solve produces the scaled gradient direction,
634            which is guaranteed to be descent */
635 
636         /* Use steepest descent direction (scaled) */
637         delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
638         ierr = MatLMVMSetDelta(bnk->M, delta);CHKERRQ(ierr);
639         ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
640         ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
641         ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
642 
643         *stepType = BNK_SCALED_GRADIENT;
644       } else {
645         ierr = MatLMVMGetUpdates(bnk->M, &bfgsUpdates);CHKERRQ(ierr);
646         if (1 == bfgsUpdates) {
647           /* The first BFGS direction is always the scaled gradient */
648           *stepType = BNK_SCALED_GRADIENT;
649         } else {
650           *stepType = BNK_BFGS;
651         }
652       }
653     }
654     /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
655     ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
656     ierr = TaoBNKBoundStep(tao, tao->stepdirection);CHKERRQ(ierr);
657   } else {
658     /* Computed Newton step is descent */
659     switch (ksp_reason) {
660     case KSP_DIVERGED_NANORINF:
661     case KSP_DIVERGED_BREAKDOWN:
662     case KSP_DIVERGED_INDEFINITE_MAT:
663     case KSP_DIVERGED_INDEFINITE_PC:
664     case KSP_CONVERGED_CG_NEG_CURVE:
665       /* Matrix or preconditioner is indefinite; increase perturbation */
666       if (bnk->pert <= 0.0) {
667         /* Initialize the perturbation */
668         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
669         if (bnk->is_gltr) {
670           ierr = KSPCGGLTRGetMinEig(tao->ksp, &e_min);CHKERRQ(ierr);
671           bnk->pert = PetscMax(bnk->pert, -e_min);
672         }
673       } else {
674         /* Increase the perturbation */
675         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
676       }
677       break;
678 
679     default:
680       /* Newton step computation is good; decrease perturbation */
681       bnk->pert = PetscMin(bnk->psfac * bnk->pert, bnk->pmsfac * bnk->gnorm);
682       if (bnk->pert < bnk->pmin) {
683         bnk->pert = 0.0;
684       }
685       break;
686     }
687     *stepType = BNK_NEWTON;
688   }
689   PetscFunctionReturn(0);
690 }
691 
692 /*------------------------------------------------------------*/
693 
694 /* Routine for performing a bound-projected More-Thuente line search.
695 
696   Includes fallbacks to BFGS, scaled gradient, and unscaled gradient steps if the
697   Newton step does not produce a valid step length.
698 */
699 
700 PetscErrorCode TaoBNKPerformLineSearch(Tao tao, PetscInt stepType, PetscReal *steplen, TaoLineSearchConvergedReason *reason)
701 {
702   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
703   PetscErrorCode ierr;
704   TaoLineSearchConvergedReason ls_reason;
705 
706   PetscReal      e_min, gdx, delta;
707   PetscInt       bfgsUpdates;
708 
709   PetscFunctionBegin;
710   /* Perform the linesearch */
711   ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason);CHKERRQ(ierr);
712   ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
713 
714   while (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER && (stepType != BNK_GRADIENT || stepType !=BNK_SCALED_GRADIENT)) {
715     /* Linesearch failed, revert solution */
716     bnk->f = bnk->fold;
717     ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr);
718     ierr = VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);CHKERRQ(ierr);
719 
720     switch(stepType) {
721     case BNK_NEWTON:
722       /* Failed to obtain acceptable iterate with Newton step
723          Update the perturbation for next time */
724       if (bnk->pert <= 0.0) {
725         /* Initialize the perturbation */
726         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
727         if (bnk->is_gltr) {
728           ierr = KSPCGGLTRGetMinEig(tao->ksp,&e_min);CHKERRQ(ierr);
729           bnk->pert = PetscMax(bnk->pert, -e_min);
730         }
731       } else {
732         /* Increase the perturbation */
733         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
734       }
735 
736       if (BNK_PC_BFGS != bnk->pc_type) {
737         /* We don't have the bfgs matrix around and being updated
738            Must use gradient direction in this case */
739         ierr = VecCopy(tao->gradient, tao->stepdirection);CHKERRQ(ierr);
740         stepType = BNK_GRADIENT;
741       } else {
742         /* Attempt to use the BFGS direction */
743         ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
744         /* Check for success (descent direction)
745            NOTE: Negative gdx means not a descent direction because the step here is missing a negative sign. */
746         ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr);
747         if ((gdx <= 0) || PetscIsInfOrNanReal(gdx)) {
748           /* BFGS direction is not descent or direction produced not a number
749              We can assert bfgsUpdates > 1 in this case
750              Use steepest descent direction (scaled) */
751           delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
752           ierr = MatLMVMSetDelta(bnk->M, delta);CHKERRQ(ierr);
753           ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
754           ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
755           ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
756 
757           bfgsUpdates = 1;
758           stepType = BNK_SCALED_GRADIENT;
759         } else {
760           ierr = MatLMVMGetUpdates(bnk->M, &bfgsUpdates);CHKERRQ(ierr);
761           if (1 == bfgsUpdates) {
762             /* The first BFGS direction is always the scaled gradient */
763             stepType = BNK_SCALED_GRADIENT;
764           } else {
765             stepType = BNK_BFGS;
766           }
767         }
768       }
769       break;
770 
771     case BNK_BFGS:
772       /* Can only enter if pc_type == BNK_PC_BFGS
773          Failed to obtain acceptable iterate with BFGS step
774          Attempt to use the scaled gradient direction */
775       delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
776       ierr = MatLMVMSetDelta(bnk->M, delta);CHKERRQ(ierr);
777       ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
778       ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
779       ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
780 
781       bfgsUpdates = 1;
782       stepType = BNK_SCALED_GRADIENT;
783       break;
784 
785     case BNK_SCALED_GRADIENT:
786       /* Can only enter if pc_type == BNK_PC_BFGS
787          The scaled gradient step did not produce a new iterate;
788          attemp to use the gradient direction.
789          Need to make sure we are not using a different diagonal scaling */
790       ierr = MatLMVMSetScale(bnk->M,0);CHKERRQ(ierr);
791       ierr = MatLMVMSetDelta(bnk->M,1.0);CHKERRQ(ierr);
792       ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
793       ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
794       ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
795 
796       bfgsUpdates = 1;
797       stepType = BNK_GRADIENT;
798       break;
799     }
800     /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
801     ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
802     ierr = TaoBNKBoundStep(tao, tao->stepdirection);CHKERRQ(ierr);
803 
804     /* Perform one last line search with the fall-back step */
805     ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason);CHKERRQ(ierr);
806     ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
807   }
808   *reason = ls_reason;
809   PetscFunctionReturn(0);
810 }
811 
812 /*------------------------------------------------------------*/
813 
814 /* Routine for updating the trust radius.
815 
816   Function features three different update methods:
817   1) Line-search step length based
818   2) Predicted decrease on the CG quadratic model
819   3) Interpolation
820 */
821 
822 PetscErrorCode TaoBNKUpdateTrustRadius(Tao tao, PetscReal prered, PetscReal actred, PetscInt updateType, PetscInt stepType, PetscBool *accept)
823 {
824   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
825   PetscErrorCode ierr;
826 
827   PetscReal      step, kappa;
828   PetscReal      gdx, tau_1, tau_2, tau_min, tau_max;
829 
830   PetscFunctionBegin;
831   /* Update trust region radius */
832   *accept = PETSC_FALSE;
833   switch(updateType) {
834   case BNK_UPDATE_STEP:
835     *accept = PETSC_TRUE; /* always accept here because line search succeeded */
836     if (stepType == BNK_NEWTON) {
837       ierr = TaoLineSearchGetStepLength(tao->linesearch, &step);CHKERRQ(ierr);
838       if (step < bnk->nu1) {
839         /* Very bad step taken; reduce radius */
840         tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
841       } else if (step < bnk->nu2) {
842         /* Reasonably bad step taken; reduce radius */
843         tao->trust = bnk->omega2 * PetscMin(bnk->dnorm, tao->trust);
844       } else if (step < bnk->nu3) {
845         /*  Reasonable step was taken; leave radius alone */
846         if (bnk->omega3 < 1.0) {
847           tao->trust = bnk->omega3 * PetscMin(bnk->dnorm, tao->trust);
848         } else if (bnk->omega3 > 1.0) {
849           tao->trust = PetscMax(bnk->omega3 * bnk->dnorm, tao->trust);
850         }
851       } else if (step < bnk->nu4) {
852         /*  Full step taken; increase the radius */
853         tao->trust = PetscMax(bnk->omega4 * bnk->dnorm, tao->trust);
854       } else {
855         /*  More than full step taken; increase the radius */
856         tao->trust = PetscMax(bnk->omega5 * bnk->dnorm, tao->trust);
857       }
858     } else {
859       /*  Newton step was not good; reduce the radius */
860       tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
861     }
862     break;
863 
864   case BNK_UPDATE_REDUCTION:
865     if (stepType == BNK_NEWTON) {
866       if (prered < 0.0) {
867         /* The predicted reduction has the wrong sign.  This cannot
868            happen in infinite precision arithmetic.  Step should
869            be rejected! */
870         tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
871       }
872       else {
873         if (PetscIsInfOrNanReal(actred)) {
874           tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
875         } else {
876           if ((PetscAbsScalar(actred) <= PetscMax(1.0, PetscAbsScalar(bnk->f))*bnk->epsilon) &&
877               (PetscAbsScalar(prered) <= PetscMax(1.0, PetscAbsScalar(bnk->f))*bnk->epsilon)) {
878             kappa = 1.0;
879           }
880           else {
881             kappa = actred / prered;
882           }
883 
884           /* Accept or reject the step and update radius */
885           if (kappa < bnk->eta1) {
886             /* Reject the step */
887             tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
888           }
889           else {
890             /* Accept the step */
891             *accept = PETSC_TRUE;
892             /* Update the trust region radius only if the computed step is at the trust radius boundary */
893             if (bnk->dnorm == tao->trust) {
894               if (kappa < bnk->eta2) {
895                 /* Marginal bad step */
896                 tao->trust = bnk->alpha2 * tao->trust;
897               }
898               else if (kappa < bnk->eta3) {
899                 /* Reasonable step */
900                 tao->trust = bnk->alpha3 * tao->trust;
901               }
902               else if (kappa < bnk->eta4) {
903                 /* Good step */
904                 tao->trust = bnk->alpha4 * tao->trust;
905               }
906               else {
907                 /* Very good step */
908                 tao->trust = bnk->alpha5 * tao->trust;
909               }
910             }
911           }
912         }
913       }
914     } else {
915       /*  Newton step was not good; reduce the radius */
916       tao->trust = bnk->alpha1 * PetscMin(bnk->dnorm, tao->trust);
917     }
918     break;
919 
920   default:
921     if (stepType == BNK_NEWTON) {
922       if (prered < 0.0) {
923         /*  The predicted reduction has the wrong sign.  This cannot */
924         /*  happen in infinite precision arithmetic.  Step should */
925         /*  be rejected! */
926         tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
927       } else {
928         if (PetscIsInfOrNanReal(actred)) {
929           tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
930         } else {
931           if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) {
932             kappa = 1.0;
933           } else {
934             kappa = actred / prered;
935           }
936 
937           ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr);
938           tau_1 = bnk->theta * gdx / (bnk->theta * gdx - (1.0 - bnk->theta) * prered + actred);
939           tau_2 = bnk->theta * gdx / (bnk->theta * gdx + (1.0 + bnk->theta) * prered - actred);
940           tau_min = PetscMin(tau_1, tau_2);
941           tau_max = PetscMax(tau_1, tau_2);
942 
943           if (kappa >= 1.0 - bnk->mu1) {
944             /*  Great agreement */
945             *accept = PETSC_TRUE;
946             if (tau_max < 1.0) {
947               tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
948             } else if (tau_max > bnk->gamma4) {
949               tao->trust = PetscMax(tao->trust, bnk->gamma4 * bnk->dnorm);
950             } else {
951               tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
952             }
953           } else if (kappa >= 1.0 - bnk->mu2) {
954             /*  Good agreement */
955             *accept = PETSC_TRUE;
956             if (tau_max < bnk->gamma2) {
957               tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
958             } else if (tau_max > bnk->gamma3) {
959               tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
960             } else if (tau_max < 1.0) {
961               tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
962             } else {
963               tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
964             }
965           } else {
966             /*  Not good agreement */
967             if (tau_min > 1.0) {
968               tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
969             } else if (tau_max < bnk->gamma1) {
970               tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
971             } else if ((tau_min < bnk->gamma1) && (tau_max >= 1.0)) {
972               tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
973             } else if ((tau_1 >= bnk->gamma1) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1) || (tau_2 >= 1.0))) {
974               tao->trust = tau_1 * PetscMin(tao->trust, bnk->dnorm);
975             } else if ((tau_2 >= bnk->gamma1) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1) || (tau_2 >= 1.0))) {
976               tao->trust = tau_2 * PetscMin(tao->trust, bnk->dnorm);
977             } else {
978               tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
979             }
980           }
981         }
982       }
983     } else {
984       /*  Newton step was not good; reduce the radius */
985       tao->trust = bnk->gamma1 * PetscMin(bnk->dnorm, tao->trust);
986     }
987     break;
988   }
989   /* Make sure the radius does not violate min and max settings */
990   tao->trust = PetscMin(tao->trust, bnk->max_radius);
991   tao->trust = PetscMax(tao->trust, bnk->min_radius);
992   PetscFunctionReturn(0);
993 }
994 
995 /* ---------------------------------------------------------- */
996 
997 PetscErrorCode TaoBNKAddStepCounts(Tao tao, PetscInt stepType)
998 {
999   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1000 
1001   PetscFunctionBegin;
1002   switch (stepType) {
1003   case BNK_NEWTON:
1004     ++bnk->newt;
1005     break;
1006   case BNK_BFGS:
1007     ++bnk->bfgs;
1008     break;
1009   case BNK_SCALED_GRADIENT:
1010     ++bnk->sgrad;
1011     break;
1012   case BNK_GRADIENT:
1013     ++bnk->grad;
1014     break;
1015   default:
1016     break;
1017   }
1018   PetscFunctionReturn(0);
1019 }
1020 
1021 /* ---------------------------------------------------------- */
1022 
1023 PetscErrorCode TaoSetUp_BNK(Tao tao)
1024 {
1025   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1026   PetscErrorCode ierr;
1027   KSPType        ksp_type;
1028 
1029   PetscFunctionBegin;
1030   if (!tao->gradient) {ierr = VecDuplicate(tao->solution,&tao->gradient);CHKERRQ(ierr);}
1031   if (!tao->stepdirection) {ierr = VecDuplicate(tao->solution,&tao->stepdirection);CHKERRQ(ierr);}
1032   if (!bnk->W) {ierr = VecDuplicate(tao->solution,&bnk->W);CHKERRQ(ierr);}
1033   if (!bnk->Xold) {ierr = VecDuplicate(tao->solution,&bnk->Xold);CHKERRQ(ierr);}
1034   if (!bnk->Gold) {ierr = VecDuplicate(tao->solution,&bnk->Gold);CHKERRQ(ierr);}
1035   if (!bnk->Xwork) {ierr = VecDuplicate(tao->solution,&bnk->Xwork);CHKERRQ(ierr);}
1036   if (!bnk->Gwork) {ierr = VecDuplicate(tao->solution,&bnk->Gwork);CHKERRQ(ierr);}
1037   if (!bnk->unprojected_gradient) {ierr = VecDuplicate(tao->solution,&bnk->unprojected_gradient);CHKERRQ(ierr);}
1038   if (!bnk->unprojected_gradient_old) {ierr = VecDuplicate(tao->solution,&bnk->unprojected_gradient_old);CHKERRQ(ierr);}
1039   if (!bnk->G_inactive) {ierr = VecDuplicate(tao->solution,&bnk->G_inactive);CHKERRQ(ierr);}
1040   if (!bnk->Diag_min) {ierr = VecDuplicate(tao->solution,&bnk->Diag_min);CHKERRQ(ierr);}
1041   if (!bnk->Diag_max) {ierr = VecDuplicate(tao->solution,&bnk->Diag_max);CHKERRQ(ierr);}
1042   bnk->Diag = 0;
1043   bnk->inactive_work = 0;
1044   bnk->active_work = 0;
1045   bnk->inactive_idx = 0;
1046   bnk->active_idx = 0;
1047   bnk->active_lower = 0;
1048   bnk->active_upper = 0;
1049   bnk->active_fixed = 0;
1050   bnk->M = 0;
1051   bnk->H_inactive = 0;
1052   bnk->Hpre_inactive = 0;
1053   ierr = KSPGetType(tao->ksp,&ksp_type);CHKERRQ(ierr);
1054   ierr = PetscStrcmp(ksp_type,KSPCGNASH,&bnk->is_nash);CHKERRQ(ierr);
1055   ierr = PetscStrcmp(ksp_type,KSPCGSTCG,&bnk->is_stcg);CHKERRQ(ierr);
1056   ierr = PetscStrcmp(ksp_type,KSPCGGLTR,&bnk->is_gltr);CHKERRQ(ierr);
1057   PetscFunctionReturn(0);
1058 }
1059 
1060 /*------------------------------------------------------------*/
1061 
1062 static PetscErrorCode TaoDestroy_BNK(Tao tao)
1063 {
1064   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1065   PetscErrorCode ierr;
1066 
1067   PetscFunctionBegin;
1068   if (tao->setupcalled) {
1069     ierr = VecDestroy(&bnk->W);CHKERRQ(ierr);
1070     ierr = VecDestroy(&bnk->Xold);CHKERRQ(ierr);
1071     ierr = VecDestroy(&bnk->Gold);CHKERRQ(ierr);
1072     ierr = VecDestroy(&bnk->Xwork);CHKERRQ(ierr);
1073     ierr = VecDestroy(&bnk->Gwork);CHKERRQ(ierr);
1074     ierr = VecDestroy(&bnk->unprojected_gradient);CHKERRQ(ierr);
1075     ierr = VecDestroy(&bnk->unprojected_gradient_old);CHKERRQ(ierr);
1076     ierr = VecDestroy(&bnk->G_inactive);CHKERRQ(ierr);
1077     ierr = VecDestroy(&bnk->Diag_min);CHKERRQ(ierr);
1078     ierr = VecDestroy(&bnk->Diag_max);CHKERRQ(ierr);
1079   }
1080   ierr = VecDestroy(&bnk->Diag);CHKERRQ(ierr);
1081   ierr = MatDestroy(&bnk->M);CHKERRQ(ierr);
1082   if (bnk->Hpre_inactive != bnk->H_inactive) {ierr = MatDestroy(&bnk->Hpre_inactive);CHKERRQ(ierr);}
1083   ierr = MatDestroy(&bnk->H_inactive);CHKERRQ(ierr);
1084   ierr = PetscFree(tao->data);CHKERRQ(ierr);
1085   PetscFunctionReturn(0);
1086 }
1087 
1088 /*------------------------------------------------------------*/
1089 
1090 static PetscErrorCode TaoSetFromOptions_BNK(PetscOptionItems *PetscOptionsObject,Tao tao)
1091 {
1092   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1093   PetscErrorCode ierr;
1094 
1095   PetscFunctionBegin;
1096   ierr = PetscOptionsHead(PetscOptionsObject,"Newton line search method for unconstrained optimization");CHKERRQ(ierr);
1097   ierr = PetscOptionsEList("-tao_bnk_pc_type", "pc type", "", BNK_PC, BNK_PC_TYPES, BNK_PC[bnk->pc_type], &bnk->pc_type, 0);CHKERRQ(ierr);
1098   ierr = PetscOptionsEList("-tao_bnk_bfgs_scale_type", "bfgs scale type", "", BFGS_SCALE, BFGS_SCALE_TYPES, BFGS_SCALE[bnk->bfgs_scale_type], &bnk->bfgs_scale_type, 0);CHKERRQ(ierr);
1099   ierr = PetscOptionsEList("-tao_bnk_init_type", "radius initialization type", "", BNK_INIT, BNK_INIT_TYPES, BNK_INIT[bnk->init_type], &bnk->init_type, 0);CHKERRQ(ierr);
1100   ierr = PetscOptionsEList("-tao_bnk_update_type", "radius update type", "", BNK_UPDATE, BNK_UPDATE_TYPES, BNK_UPDATE[bnk->update_type], &bnk->update_type, 0);CHKERRQ(ierr);
1101   ierr = PetscOptionsEList("-tao_bnk_as_type", "active set estimation method", "", BNK_AS, BNK_AS_TYPES, BNK_AS[bnk->as_type], &bnk->as_type, 0);CHKERRQ(ierr);
1102   ierr = PetscOptionsReal("-tao_bnk_sval", "perturbation starting value", "", bnk->sval, &bnk->sval,NULL);CHKERRQ(ierr);
1103   ierr = PetscOptionsReal("-tao_bnk_imin", "minimum initial perturbation", "", bnk->imin, &bnk->imin,NULL);CHKERRQ(ierr);
1104   ierr = PetscOptionsReal("-tao_bnk_imax", "maximum initial perturbation", "", bnk->imax, &bnk->imax,NULL);CHKERRQ(ierr);
1105   ierr = PetscOptionsReal("-tao_bnk_imfac", "initial merit factor", "", bnk->imfac, &bnk->imfac,NULL);CHKERRQ(ierr);
1106   ierr = PetscOptionsReal("-tao_bnk_pmin", "minimum perturbation", "", bnk->pmin, &bnk->pmin,NULL);CHKERRQ(ierr);
1107   ierr = PetscOptionsReal("-tao_bnk_pmax", "maximum perturbation", "", bnk->pmax, &bnk->pmax,NULL);CHKERRQ(ierr);
1108   ierr = PetscOptionsReal("-tao_bnk_pgfac", "growth factor", "", bnk->pgfac, &bnk->pgfac,NULL);CHKERRQ(ierr);
1109   ierr = PetscOptionsReal("-tao_bnk_psfac", "shrink factor", "", bnk->psfac, &bnk->psfac,NULL);CHKERRQ(ierr);
1110   ierr = PetscOptionsReal("-tao_bnk_pmgfac", "merit growth factor", "", bnk->pmgfac, &bnk->pmgfac,NULL);CHKERRQ(ierr);
1111   ierr = PetscOptionsReal("-tao_bnk_pmsfac", "merit shrink factor", "", bnk->pmsfac, &bnk->pmsfac,NULL);CHKERRQ(ierr);
1112   ierr = PetscOptionsReal("-tao_bnk_eta1", "poor steplength; reduce radius", "", bnk->eta1, &bnk->eta1,NULL);CHKERRQ(ierr);
1113   ierr = PetscOptionsReal("-tao_bnk_eta2", "reasonable steplength; leave radius alone", "", bnk->eta2, &bnk->eta2,NULL);CHKERRQ(ierr);
1114   ierr = PetscOptionsReal("-tao_bnk_eta3", "good steplength; increase radius", "", bnk->eta3, &bnk->eta3,NULL);CHKERRQ(ierr);
1115   ierr = PetscOptionsReal("-tao_bnk_eta4", "excellent steplength; greatly increase radius", "", bnk->eta4, &bnk->eta4,NULL);CHKERRQ(ierr);
1116   ierr = PetscOptionsReal("-tao_bnk_alpha1", "", "", bnk->alpha1, &bnk->alpha1,NULL);CHKERRQ(ierr);
1117   ierr = PetscOptionsReal("-tao_bnk_alpha2", "", "", bnk->alpha2, &bnk->alpha2,NULL);CHKERRQ(ierr);
1118   ierr = PetscOptionsReal("-tao_bnk_alpha3", "", "", bnk->alpha3, &bnk->alpha3,NULL);CHKERRQ(ierr);
1119   ierr = PetscOptionsReal("-tao_bnk_alpha4", "", "", bnk->alpha4, &bnk->alpha4,NULL);CHKERRQ(ierr);
1120   ierr = PetscOptionsReal("-tao_bnk_alpha5", "", "", bnk->alpha5, &bnk->alpha5,NULL);CHKERRQ(ierr);
1121   ierr = PetscOptionsReal("-tao_bnk_nu1", "poor steplength; reduce radius", "", bnk->nu1, &bnk->nu1,NULL);CHKERRQ(ierr);
1122   ierr = PetscOptionsReal("-tao_bnk_nu2", "reasonable steplength; leave radius alone", "", bnk->nu2, &bnk->nu2,NULL);CHKERRQ(ierr);
1123   ierr = PetscOptionsReal("-tao_bnk_nu3", "good steplength; increase radius", "", bnk->nu3, &bnk->nu3,NULL);CHKERRQ(ierr);
1124   ierr = PetscOptionsReal("-tao_bnk_nu4", "excellent steplength; greatly increase radius", "", bnk->nu4, &bnk->nu4,NULL);CHKERRQ(ierr);
1125   ierr = PetscOptionsReal("-tao_bnk_omega1", "", "", bnk->omega1, &bnk->omega1,NULL);CHKERRQ(ierr);
1126   ierr = PetscOptionsReal("-tao_bnk_omega2", "", "", bnk->omega2, &bnk->omega2,NULL);CHKERRQ(ierr);
1127   ierr = PetscOptionsReal("-tao_bnk_omega3", "", "", bnk->omega3, &bnk->omega3,NULL);CHKERRQ(ierr);
1128   ierr = PetscOptionsReal("-tao_bnk_omega4", "", "", bnk->omega4, &bnk->omega4,NULL);CHKERRQ(ierr);
1129   ierr = PetscOptionsReal("-tao_bnk_omega5", "", "", bnk->omega5, &bnk->omega5,NULL);CHKERRQ(ierr);
1130   ierr = PetscOptionsReal("-tao_bnk_mu1_i", "", "", bnk->mu1_i, &bnk->mu1_i,NULL);CHKERRQ(ierr);
1131   ierr = PetscOptionsReal("-tao_bnk_mu2_i", "", "", bnk->mu2_i, &bnk->mu2_i,NULL);CHKERRQ(ierr);
1132   ierr = PetscOptionsReal("-tao_bnk_gamma1_i", "", "", bnk->gamma1_i, &bnk->gamma1_i,NULL);CHKERRQ(ierr);
1133   ierr = PetscOptionsReal("-tao_bnk_gamma2_i", "", "", bnk->gamma2_i, &bnk->gamma2_i,NULL);CHKERRQ(ierr);
1134   ierr = PetscOptionsReal("-tao_bnk_gamma3_i", "", "", bnk->gamma3_i, &bnk->gamma3_i,NULL);CHKERRQ(ierr);
1135   ierr = PetscOptionsReal("-tao_bnk_gamma4_i", "", "", bnk->gamma4_i, &bnk->gamma4_i,NULL);CHKERRQ(ierr);
1136   ierr = PetscOptionsReal("-tao_bnk_theta_i", "", "", bnk->theta_i, &bnk->theta_i,NULL);CHKERRQ(ierr);
1137   ierr = PetscOptionsReal("-tao_bnk_mu1", "", "", bnk->mu1, &bnk->mu1,NULL);CHKERRQ(ierr);
1138   ierr = PetscOptionsReal("-tao_bnk_mu2", "", "", bnk->mu2, &bnk->mu2,NULL);CHKERRQ(ierr);
1139   ierr = PetscOptionsReal("-tao_bnk_gamma1", "", "", bnk->gamma1, &bnk->gamma1,NULL);CHKERRQ(ierr);
1140   ierr = PetscOptionsReal("-tao_bnk_gamma2", "", "", bnk->gamma2, &bnk->gamma2,NULL);CHKERRQ(ierr);
1141   ierr = PetscOptionsReal("-tao_bnk_gamma3", "", "", bnk->gamma3, &bnk->gamma3,NULL);CHKERRQ(ierr);
1142   ierr = PetscOptionsReal("-tao_bnk_gamma4", "", "", bnk->gamma4, &bnk->gamma4,NULL);CHKERRQ(ierr);
1143   ierr = PetscOptionsReal("-tao_bnk_theta", "", "", bnk->theta, &bnk->theta,NULL);CHKERRQ(ierr);
1144   ierr = PetscOptionsReal("-tao_bnk_min_radius", "lower bound on initial radius", "", bnk->min_radius, &bnk->min_radius,NULL);CHKERRQ(ierr);
1145   ierr = PetscOptionsReal("-tao_bnk_max_radius", "upper bound on radius", "", bnk->max_radius, &bnk->max_radius,NULL);CHKERRQ(ierr);
1146   ierr = PetscOptionsReal("-tao_bnk_epsilon", "tolerance used when computing actual and predicted reduction", "", bnk->epsilon, &bnk->epsilon,NULL);CHKERRQ(ierr);
1147   ierr = PetscOptionsReal("-tao_bnk_as_tol", "initial tolerance used when estimating actively bounded variables", "", bnk->as_tol, &bnk->as_tol,NULL);CHKERRQ(ierr);
1148   ierr = PetscOptionsReal("-tao_bnk_as_step", "step length used when estimating actively bounded variables", "", bnk->as_step, &bnk->as_step,NULL);CHKERRQ(ierr);
1149   ierr = PetscOptionsTail();CHKERRQ(ierr);
1150   ierr = TaoLineSearchSetFromOptions(tao->linesearch);CHKERRQ(ierr);
1151   ierr = KSPSetFromOptions(tao->ksp);CHKERRQ(ierr);
1152   PetscFunctionReturn(0);
1153 }
1154 
1155 /*------------------------------------------------------------*/
1156 
1157 static PetscErrorCode TaoView_BNK(Tao tao, PetscViewer viewer)
1158 {
1159   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1160   PetscInt       nrejects;
1161   PetscBool      isascii;
1162   PetscErrorCode ierr;
1163 
1164   PetscFunctionBegin;
1165   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
1166   if (isascii) {
1167     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1168     if (BNK_PC_BFGS == bnk->pc_type && bnk->M) {
1169       ierr = MatLMVMGetRejects(bnk->M,&nrejects);CHKERRQ(ierr);
1170       ierr = PetscViewerASCIIPrintf(viewer, "Rejected matrix updates: %D\n",nrejects);CHKERRQ(ierr);
1171     }
1172     ierr = PetscViewerASCIIPrintf(viewer, "Newton steps: %D\n", bnk->newt);CHKERRQ(ierr);
1173     ierr = PetscViewerASCIIPrintf(viewer, "BFGS steps: %D\n", bnk->bfgs);CHKERRQ(ierr);
1174     ierr = PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %D\n", bnk->sgrad);CHKERRQ(ierr);
1175     ierr = PetscViewerASCIIPrintf(viewer, "Gradient steps: %D\n", bnk->grad);CHKERRQ(ierr);
1176     ierr = PetscViewerASCIIPrintf(viewer, "KSP termination reasons:\n");CHKERRQ(ierr);
1177     ierr = PetscViewerASCIIPrintf(viewer, "  atol: %D\n", bnk->ksp_atol);CHKERRQ(ierr);
1178     ierr = PetscViewerASCIIPrintf(viewer, "  rtol: %D\n", bnk->ksp_rtol);CHKERRQ(ierr);
1179     ierr = PetscViewerASCIIPrintf(viewer, "  ctol: %D\n", bnk->ksp_ctol);CHKERRQ(ierr);
1180     ierr = PetscViewerASCIIPrintf(viewer, "  negc: %D\n", bnk->ksp_negc);CHKERRQ(ierr);
1181     ierr = PetscViewerASCIIPrintf(viewer, "  dtol: %D\n", bnk->ksp_dtol);CHKERRQ(ierr);
1182     ierr = PetscViewerASCIIPrintf(viewer, "  iter: %D\n", bnk->ksp_iter);CHKERRQ(ierr);
1183     ierr = PetscViewerASCIIPrintf(viewer, "  othr: %D\n", bnk->ksp_othr);CHKERRQ(ierr);
1184     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1185   }
1186   PetscFunctionReturn(0);
1187 }
1188 
1189 /* ---------------------------------------------------------- */
1190 
1191 /*MC
1192   TAOBNK - Shared base-type for Bounded Newton-Krylov type algorithms.
1193   At each iteration, the BNK methods solve the symmetric
1194   system of equations to obtain the step diretion dk:
1195               Hk dk = -gk
1196   for free variables only. The step can be globalized either through
1197   trust-region methods, or a line search, or a heuristic mixture of both.
1198 
1199     Options Database Keys:
1200 + -tao_bnk_pc_type - "none","ahess","bfgs","petsc"
1201 . -tao_bnk_bfgs_scale_type - "ahess","phess","bfgs"
1202 . -tao_bnk_init_type - "constant","direction","interpolation"
1203 . -tao_bnk_update_type - "step","direction","interpolation"
1204 . -tao_bnk_as_type - "none","bertsekas"
1205 . -tao_bnk_sval - perturbation starting value
1206 . -tao_bnk_imin - minimum initial perturbation
1207 . -tao_bnk_imax - maximum initial perturbation
1208 . -tao_bnk_pmin - minimum perturbation
1209 . -tao_bnk_pmax - maximum perturbation
1210 . -tao_bnk_pgfac - growth factor
1211 . -tao_bnk_psfac - shrink factor
1212 . -tao_bnk_imfac - initial merit factor
1213 . -tao_bnk_pmgfac - merit growth factor
1214 . -tao_bnk_pmsfac - merit shrink factor
1215 . -tao_bnk_eta1 - poor steplength; reduce radius
1216 . -tao_bnk_eta2 - reasonable steplength; leave radius
1217 . -tao_bnk_eta3 - good steplength; increase readius
1218 . -tao_bnk_eta4 - excellent steplength; greatly increase radius
1219 . -tao_bnk_alpha1 - alpha1 reduction
1220 . -tao_bnk_alpha2 - alpha2 reduction
1221 . -tao_bnk_alpha3 - alpha3 reduction
1222 . -tao_bnk_alpha4 - alpha4 reduction
1223 . -tao_bnk_alpha - alpha5 reduction
1224 . -tao_bnk_mu1 - mu1 interpolation update
1225 . -tao_bnk_mu2 - mu2 interpolation update
1226 . -tao_bnk_gamma1 - gamma1 interpolation update
1227 . -tao_bnk_gamma2 - gamma2 interpolation update
1228 . -tao_bnk_gamma3 - gamma3 interpolation update
1229 . -tao_bnk_gamma4 - gamma4 interpolation update
1230 . -tao_bnk_theta - theta interpolation update
1231 . -tao_bnk_omega1 - omega1 step update
1232 . -tao_bnk_omega2 - omega2 step update
1233 . -tao_bnk_omega3 - omega3 step update
1234 . -tao_bnk_omega4 - omega4 step update
1235 . -tao_bnk_omega5 - omega5 step update
1236 . -tao_bnk_mu1_i -  mu1 interpolation init factor
1237 . -tao_bnk_mu2_i -  mu2 interpolation init factor
1238 . -tao_bnk_gamma1_i -  gamma1 interpolation init factor
1239 . -tao_bnk_gamma2_i -  gamma2 interpolation init factor
1240 . -tao_bnk_gamma3_i -  gamma3 interpolation init factor
1241 . -tao_bnk_gamma4_i -  gamma4 interpolation init factor
1242 . -tao_bnk_theta_i -  theta interpolation init factor
1243 - -tao_bnk_bound_tol -  initial tolerance used in estimating bounded active variables
1244 
1245   Level: beginner
1246 M*/
1247 
1248 PetscErrorCode TaoCreate_BNK(Tao tao)
1249 {
1250   TAO_BNK        *bnk;
1251   const char     *morethuente_type = TAOLINESEARCHMT;
1252   PetscErrorCode ierr;
1253 
1254   PetscFunctionBegin;
1255   ierr = PetscNewLog(tao,&bnk);CHKERRQ(ierr);
1256 
1257   tao->ops->setup = TaoSetUp_BNK;
1258   tao->ops->view = TaoView_BNK;
1259   tao->ops->setfromoptions = TaoSetFromOptions_BNK;
1260   tao->ops->destroy = TaoDestroy_BNK;
1261 
1262   /*  Override default settings (unless already changed) */
1263   if (!tao->max_it_changed) tao->max_it = 50;
1264   if (!tao->trust0_changed) tao->trust0 = 100.0;
1265 
1266   tao->data = (void*)bnk;
1267 
1268   /*  Hessian shifting parameters */
1269   bnk->sval   = 0.0;
1270   bnk->imin   = 1.0e-4;
1271   bnk->imax   = 1.0e+2;
1272   bnk->imfac  = 1.0e-1;
1273 
1274   bnk->pmin   = 1.0e-12;
1275   bnk->pmax   = 1.0e+2;
1276   bnk->pgfac  = 1.0e+1;
1277   bnk->psfac  = 4.0e-1;
1278   bnk->pmgfac = 1.0e-1;
1279   bnk->pmsfac = 1.0e-1;
1280 
1281   /*  Default values for trust-region radius update based on steplength */
1282   bnk->nu1 = 0.25;
1283   bnk->nu2 = 0.50;
1284   bnk->nu3 = 1.00;
1285   bnk->nu4 = 1.25;
1286 
1287   bnk->omega1 = 0.25;
1288   bnk->omega2 = 0.50;
1289   bnk->omega3 = 1.00;
1290   bnk->omega4 = 2.00;
1291   bnk->omega5 = 4.00;
1292 
1293   /*  Default values for trust-region radius update based on reduction */
1294   bnk->eta1 = 1.0e-4;
1295   bnk->eta2 = 0.25;
1296   bnk->eta3 = 0.50;
1297   bnk->eta4 = 0.90;
1298 
1299   bnk->alpha1 = 0.25;
1300   bnk->alpha2 = 0.50;
1301   bnk->alpha3 = 1.00;
1302   bnk->alpha4 = 2.00;
1303   bnk->alpha5 = 4.00;
1304 
1305   /*  Default values for trust-region radius update based on interpolation */
1306   bnk->mu1 = 0.10;
1307   bnk->mu2 = 0.50;
1308 
1309   bnk->gamma1 = 0.25;
1310   bnk->gamma2 = 0.50;
1311   bnk->gamma3 = 2.00;
1312   bnk->gamma4 = 4.00;
1313 
1314   bnk->theta = 0.05;
1315 
1316   /*  Default values for trust region initialization based on interpolation */
1317   bnk->mu1_i = 0.35;
1318   bnk->mu2_i = 0.50;
1319 
1320   bnk->gamma1_i = 0.0625;
1321   bnk->gamma2_i = 0.5;
1322   bnk->gamma3_i = 2.0;
1323   bnk->gamma4_i = 5.0;
1324 
1325   bnk->theta_i = 0.25;
1326 
1327   /*  Remaining parameters */
1328   bnk->min_radius = 1.0e-10;
1329   bnk->max_radius = 1.0e10;
1330   bnk->epsilon = PetscPowReal(PETSC_MACHINE_EPSILON, 2.0/3.0);
1331   bnk->as_tol = 1.0e-3;
1332   bnk->as_step = 1.0e-3;
1333   bnk->dmin = 1.0e-6;
1334   bnk->dmax = 1.0e6;
1335 
1336   bnk->pc_type         = BNK_PC_BFGS;
1337   bnk->bfgs_scale_type = BFGS_SCALE_PHESS;
1338   bnk->init_type       = BNK_INIT_INTERPOLATION;
1339   bnk->update_type     = BNK_UPDATE_INTERPOLATION;
1340   bnk->as_type         = BNK_AS_BERTSEKAS;
1341 
1342   ierr = TaoLineSearchCreate(((PetscObject)tao)->comm,&tao->linesearch);CHKERRQ(ierr);
1343   ierr = PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);CHKERRQ(ierr);
1344   ierr = TaoLineSearchSetType(tao->linesearch,morethuente_type);CHKERRQ(ierr);
1345   ierr = TaoLineSearchUseTaoRoutines(tao->linesearch,tao);CHKERRQ(ierr);
1346   ierr = TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);CHKERRQ(ierr);
1347 
1348   /*  Set linear solver to default for symmetric matrices */
1349   ierr = KSPCreate(((PetscObject)tao)->comm,&tao->ksp);CHKERRQ(ierr);
1350   ierr = PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1);CHKERRQ(ierr);
1351   ierr = KSPSetOptionsPrefix(tao->ksp,tao->hdr.prefix);CHKERRQ(ierr);
1352   ierr = KSPSetType(tao->ksp,KSPCGSTCG);CHKERRQ(ierr);
1353   PetscFunctionReturn(0);
1354 }
1355