xref: /petsc/src/tao/bound/impls/bnk/bnk.c (revision 61be54a68cd238714af883d2215bb04911cc1c21)
1 #include <petsctaolinesearch.h>
2 #include <../src/tao/bound/impls/bnk/bnk.h>
3 
4 #include <petscksp.h>
5 
6 static const char *BNK_PC[64] = {"none", "ahess", "bfgs", "petsc"};
7 static const char *BFGS_SCALE[64] = {"ahess", "phess", "bfgs"};
8 static const char *BNK_INIT[64] = {"constant", "direction", "interpolation"};
9 static const char *BNK_UPDATE[64] = {"step", "reduction", "interpolation"};
10 static const char *BNK_AS[64] = {"none", "bertsekas"};
11 
12 /*------------------------------------------------------------*/
13 
14 /* Routine for BFGS preconditioner */
15 
16 PetscErrorCode MatLMVMSolveShell(PC pc, Vec b, Vec x)
17 {
18   PetscErrorCode ierr;
19   Mat            M;
20 
21   PetscFunctionBegin;
22   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
23   PetscValidHeaderSpecific(b,VEC_CLASSID,2);
24   PetscValidHeaderSpecific(x,VEC_CLASSID,3);
25   ierr = PCShellGetContext(pc,(void**)&M);CHKERRQ(ierr);
26   ierr = MatLMVMSolve(M, b, x);CHKERRQ(ierr);
27   PetscFunctionReturn(0);
28 }
29 
30 /*------------------------------------------------------------*/
31 
32 /* Routine for initializing the KSP solver, the BFGS preconditioner, and the initial trust radius estimation */
33 
34 PetscErrorCode TaoBNKInitialize(Tao tao, PetscInt initType, PetscBool *needH)
35 {
36   PetscErrorCode               ierr;
37   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
38   PC                           pc;
39 
40   PetscReal                    f_min, ftrial, prered, actred, kappa, sigma;
41   PetscReal                    tau, tau_1, tau_2, tau_max, tau_min, max_radius;
42   PetscReal                    resnorm, delta;
43 
44   PetscInt                     n,N;
45 
46   PetscInt                     i_max = 5;
47   PetscInt                     j_max = 1;
48   PetscInt                     i, j;
49 
50   PetscFunctionBegin;
51   /* Project the current point onto the feasible set */
52   ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
53   ierr = TaoSetVariableBounds(bnk->bncg, tao->XL, tao->XU);CHKERRQ(ierr);
54   ierr = TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);CHKERRQ(ierr);
55 
56   /* Project the initial point onto the feasible region */
57   ierr = VecMedian(tao->XL,tao->solution,tao->XU,tao->solution);CHKERRQ(ierr);
58 
59   /* Check convergence criteria */
60   ierr = TaoComputeObjectiveAndGradient(tao, tao->solution, &bnk->f, bnk->unprojected_gradient);CHKERRQ(ierr);
61   ierr = TaoBNKEstimateActiveSet(tao, bnk->as_type);CHKERRQ(ierr);
62   ierr = VecCopy(bnk->unprojected_gradient, tao->gradient);CHKERRQ(ierr);
63   ierr = VecISSet(tao->gradient, bnk->active_idx, 0.0);CHKERRQ(ierr);
64   ierr = VecNorm(tao->gradient,NORM_2,&bnk->gnorm);CHKERRQ(ierr);
65   if (PetscIsInfOrNanReal(bnk->f) || PetscIsInfOrNanReal(bnk->gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
66 
67   /* Test the initial point for convergence */
68   ierr = VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->Gwork);CHKERRQ(ierr);
69   ierr = VecNorm(bnk->Gwork, NORM_2, &resnorm);CHKERRQ(ierr);
70   ierr = TaoLogConvergenceHistory(tao,bnk->f,resnorm,0.0,tao->ksp_its);CHKERRQ(ierr);
71   ierr = TaoMonitor(tao,tao->niter,bnk->f,resnorm,0.0,1.0);CHKERRQ(ierr);
72   ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr);
73   if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
74 
75   /* Reset KSP stopping reason counters */
76   bnk->ksp_atol = 0;
77   bnk->ksp_rtol = 0;
78   bnk->ksp_dtol = 0;
79   bnk->ksp_ctol = 0;
80   bnk->ksp_negc = 0;
81   bnk->ksp_iter = 0;
82   bnk->ksp_othr = 0;
83 
84   /* Reset accepted step type counters */
85   bnk->tot_cg_its = 0;
86   bnk->newt = 0;
87   bnk->bfgs = 0;
88   bnk->sgrad = 0;
89   bnk->grad = 0;
90 
91   /* Initialize the Hessian perturbation */
92   bnk->pert = bnk->sval;
93 
94   /* Reset initial steplength to zero (this helps BNCG reset its direction internally) */
95   ierr = VecSet(tao->stepdirection, 0.0);CHKERRQ(ierr);
96 
97   /* Allocate the vectors needed for the BFGS approximation */
98   if (BNK_PC_BFGS == bnk->pc_type) {
99     if (!bnk->M) {
100       ierr = VecGetLocalSize(tao->solution,&n);CHKERRQ(ierr);
101       ierr = VecGetSize(tao->solution,&N);CHKERRQ(ierr);
102       ierr = MatCreateLMVM(((PetscObject)tao)->comm,n,N,&bnk->M);CHKERRQ(ierr);
103       ierr = MatLMVMAllocateVectors(bnk->M,tao->solution);CHKERRQ(ierr);
104     }
105     if (bnk->bfgs_scale_type != BFGS_SCALE_BFGS && !bnk->Diag) {
106       ierr = VecDuplicate(tao->solution,&bnk->Diag);CHKERRQ(ierr);
107     }
108   }
109 
110   /* Prepare the min/max vectors for safeguarding diagonal scales */
111   ierr = VecSet(bnk->Diag_min, bnk->dmin);CHKERRQ(ierr);
112   ierr = VecSet(bnk->Diag_max, bnk->dmax);CHKERRQ(ierr);
113 
114   /* Modify the preconditioner to use the bfgs approximation */
115   ierr = KSPGetPC(tao->ksp, &pc);CHKERRQ(ierr);
116   switch(bnk->pc_type) {
117   case BNK_PC_NONE:
118     ierr = PCSetType(pc, PCNONE);CHKERRQ(ierr);
119     ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
120     break;
121 
122   case BNK_PC_AHESS:
123     ierr = PCSetType(pc, PCJACOBI);CHKERRQ(ierr);
124     ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
125     ierr = PCJacobiSetUseAbs(pc,PETSC_TRUE);CHKERRQ(ierr);
126     break;
127 
128   case BNK_PC_BFGS:
129     ierr = PCSetType(pc, PCSHELL);CHKERRQ(ierr);
130     ierr = PCSetFromOptions(pc);CHKERRQ(ierr);
131     ierr = PCShellSetName(pc, "bfgs");CHKERRQ(ierr);
132     ierr = PCShellSetContext(pc, bnk->M);CHKERRQ(ierr);
133     ierr = PCShellSetApply(pc, MatLMVMSolveShell);CHKERRQ(ierr);
134     break;
135 
136   default:
137     /* Use the pc method set by pc_type */
138     break;
139   }
140 
141   /* Initialize trust-region radius.  The initialization is only performed
142      when we are using Nash, Steihaug-Toint or the Generalized Lanczos method. */
143   *needH = PETSC_TRUE;
144   if (bnk->is_nash || bnk->is_stcg || bnk->is_gltr) {
145     switch(initType) {
146     case BNK_INIT_CONSTANT:
147       /* Use the initial radius specified */
148       tao->trust = tao->trust0;
149       break;
150 
151     case BNK_INIT_INTERPOLATION:
152       /* Use interpolation based on the initial Hessian */
153       max_radius = 0.0;
154       tao->trust = tao->trust0;
155       for (j = 0; j < j_max; ++j) {
156         f_min = bnk->f;
157         sigma = 0.0;
158 
159         if (*needH) {
160           /* Compute the Hessian at the new step, and extract the inactive subsystem */
161           ierr = TaoBNKComputeHessian(tao);CHKERRQ(ierr);
162           ierr = TaoBNKEstimateActiveSet(tao, BNK_AS_NONE);CHKERRQ(ierr);
163           if (bnk->inactive_idx) {
164             ierr = MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive);CHKERRQ(ierr);
165           } else {
166             ierr = MatDuplicate(tao->hessian, MAT_COPY_VALUES, &bnk->H_inactive);CHKERRQ(ierr);
167           }
168           *needH = PETSC_FALSE;
169         }
170 
171         for (i = 0; i < i_max; ++i) {
172           /* Take a steepest descent step and snap it to bounds */
173           ierr = VecCopy(tao->solution, bnk->Xold);CHKERRQ(ierr);
174           ierr = VecAXPY(tao->solution, -tao->trust/bnk->gnorm, tao->gradient);CHKERRQ(ierr);
175           ierr = VecMedian(tao->XL, tao->solution, tao->XU, tao->solution);CHKERRQ(ierr);
176           /* Recompute the step after bound snapping so that it can be used in predicted decrease calculation later */
177           ierr = VecCopy(tao->solution, bnk->W);CHKERRQ(ierr);
178           ierr = VecAXPY(bnk->W, -1.0, bnk->Xold);CHKERRQ(ierr);
179           /* Compute the objective at the trial */
180           ierr = TaoComputeObjective(tao, tao->solution, &ftrial);CHKERRQ(ierr);
181           ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr);
182           if (PetscIsInfOrNanReal(ftrial)) {
183             tau = bnk->gamma1_i;
184           } else {
185             if (ftrial < f_min) {
186               f_min = ftrial;
187               sigma = -tao->trust / bnk->gnorm;
188             }
189 
190             /* Compute the predicted and actual reduction */
191             if (bnk->inactive_idx) {
192               ierr = VecGetSubVector(bnk->W, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr);
193               ierr = VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);CHKERRQ(ierr);
194             } else {
195               bnk->X_inactive = bnk->W;
196               bnk->inactive_work = bnk->Xwork;
197             }
198             ierr = MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work);CHKERRQ(ierr);
199             ierr = VecDot(bnk->X_inactive, bnk->inactive_work, &prered);CHKERRQ(ierr);
200             if (bnk->inactive_idx) {
201               ierr = VecRestoreSubVector(bnk->W, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr);
202               ierr = VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);CHKERRQ(ierr);
203             }
204             prered = tao->trust * (bnk->gnorm - 0.5 * tao->trust * prered / (bnk->gnorm * bnk->gnorm));
205             actred = bnk->f - ftrial;
206             if ((PetscAbsScalar(actred) <= bnk->epsilon) &&
207                 (PetscAbsScalar(prered) <= bnk->epsilon)) {
208               kappa = 1.0;
209             }
210             else {
211               kappa = actred / prered;
212             }
213 
214             tau_1 = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust + (1.0 - bnk->theta_i) * prered - actred);
215             tau_2 = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust - (1.0 + bnk->theta_i) * prered + actred);
216             tau_min = PetscMin(tau_1, tau_2);
217             tau_max = PetscMax(tau_1, tau_2);
218 
219             if (PetscAbsScalar(kappa - 1.0) <= bnk->mu1_i) {
220               /*  Great agreement */
221               max_radius = PetscMax(max_radius, tao->trust);
222 
223               if (tau_max < 1.0) {
224                 tau = bnk->gamma3_i;
225               }
226               else if (tau_max > bnk->gamma4_i) {
227                 tau = bnk->gamma4_i;
228               }
229               else {
230                 tau = tau_max;
231               }
232             }
233             else if (PetscAbsScalar(kappa - 1.0) <= bnk->mu2_i) {
234               /*  Good agreement */
235               max_radius = PetscMax(max_radius, tao->trust);
236 
237               if (tau_max < bnk->gamma2_i) {
238                 tau = bnk->gamma2_i;
239               } else if (tau_max > bnk->gamma3_i) {
240                 tau = bnk->gamma3_i;
241               } else {
242                 tau = tau_max;
243               }
244             }
245             else {
246               /*  Not good agreement */
247               if (tau_min > 1.0) {
248                 tau = bnk->gamma2_i;
249               } else if (tau_max < bnk->gamma1_i) {
250                 tau = bnk->gamma1_i;
251               } else if ((tau_min < bnk->gamma1_i) && (tau_max >= 1.0)) {
252                 tau = bnk->gamma1_i;
253               } else if ((tau_1 >= bnk->gamma1_i) && (tau_1 < 1.0) &&
254                         ((tau_2 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
255                 tau = tau_1;
256               } else if ((tau_2 >= bnk->gamma1_i) && (tau_2 < 1.0) &&
257                         ((tau_1 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
258                 tau = tau_2;
259               } else {
260                 tau = tau_max;
261               }
262             }
263           }
264           tao->trust = tau * tao->trust;
265         }
266 
267         if (f_min < bnk->f) {
268           /* We accidentally found a solution better than the initial, so accept it */
269           bnk->f = f_min;
270           ierr = VecCopy(tao->solution, bnk->Xold);CHKERRQ(ierr);
271           ierr = VecAXPY(tao->solution,sigma,tao->gradient);CHKERRQ(ierr);
272           ierr = VecMedian(tao->XL, tao->solution, tao->XU, tao->solution);CHKERRQ(ierr);
273           ierr = VecCopy(tao->solution, tao->stepdirection);CHKERRQ(ierr);
274           ierr = VecAXPY(tao->stepdirection, -1.0, bnk->Xold);CHKERRQ(ierr);
275           ierr = TaoComputeGradient(tao,tao->solution,bnk->unprojected_gradient);CHKERRQ(ierr);
276           ierr = TaoBNKEstimateActiveSet(tao, bnk->as_type);CHKERRQ(ierr);
277           ierr = VecCopy(bnk->unprojected_gradient, tao->gradient);CHKERRQ(ierr);
278           ierr = VecISSet(tao->gradient, bnk->active_idx, 0.0);CHKERRQ(ierr);
279           /* Compute gradient at the new iterate and flip switch to compute the Hessian later */
280           ierr = TaoGradientNorm(tao, tao->gradient,NORM_2,&bnk->gnorm);CHKERRQ(ierr);
281           if (PetscIsInfOrNanReal(bnk->gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute gradient generated Inf or NaN");
282           *needH = PETSC_TRUE;
283           /* Test the new step for convergence */
284           ierr = VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->Gwork);CHKERRQ(ierr);
285           ierr = VecNorm(bnk->Gwork, NORM_2, &resnorm);CHKERRQ(ierr);
286           ierr = TaoLogConvergenceHistory(tao,bnk->f,resnorm,0.0,tao->ksp_its);CHKERRQ(ierr);
287           ierr = TaoMonitor(tao,tao->niter,bnk->f,resnorm,0.0,1.0);CHKERRQ(ierr);
288           ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr);
289           if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
290           /* active BNCG recycling early because we have a stepdirection computed */
291           ierr = TaoBNCGSetRecycleFlag(bnk->bncg, PETSC_TRUE);CHKERRQ(ierr);
292         }
293       }
294       tao->trust = PetscMax(tao->trust, max_radius);
295 
296       /* Ensure that the trust radius is within the limits */
297       tao->trust = PetscMax(tao->trust, bnk->min_radius);
298       tao->trust = PetscMin(tao->trust, bnk->max_radius);
299       break;
300 
301     default:
302       /* Norm of the first direction will initialize radius */
303       tao->trust = 0.0;
304       break;
305     }
306   }
307 
308   /* Set initial scaling for the BFGS preconditioner
309      This step is done after computing the initial trust-region radius
310      since the function value may have decreased */
311   if (BNK_PC_BFGS == bnk->pc_type) {
312     delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
313     ierr = MatLMVMSetDelta(bnk->M,delta);CHKERRQ(ierr);
314   }
315   PetscFunctionReturn(0);
316 }
317 
318 /*------------------------------------------------------------*/
319 
320 /* Routine for computing the Hessian and preparing the preconditioner at the new iterate */
321 
322 PetscErrorCode TaoBNKComputeHessian(Tao tao)
323 {
324   PetscErrorCode               ierr;
325   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
326 
327   PetscFunctionBegin;
328   /* Compute the Hessian */
329   ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
330   /* Add a correction to the BFGS preconditioner */
331   if (BNK_PC_BFGS == bnk->pc_type) {
332     ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
333     /* Update the BFGS diagonal scaling */
334     if (BFGS_SCALE_AHESS == bnk->bfgs_scale_type) {
335       ierr = MatGetDiagonal(tao->hessian, bnk->Diag);CHKERRQ(ierr);
336       ierr = VecAbs(bnk->Diag);CHKERRQ(ierr);
337       ierr = VecMedian(bnk->Diag_min, bnk->Diag, bnk->Diag_max, bnk->Diag);CHKERRQ(ierr);
338       ierr = VecReciprocal(bnk->Diag);CHKERRQ(ierr);
339       ierr = MatLMVMSetScale(bnk->M,bnk->Diag);CHKERRQ(ierr);
340     }
341   }
342   PetscFunctionReturn(0);
343 }
344 
345 /*------------------------------------------------------------*/
346 
347 /* Routine for estimating the active set */
348 
349 PetscErrorCode TaoBNKEstimateActiveSet(Tao tao, PetscInt asType)
350 {
351   PetscErrorCode               ierr;
352   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
353   PetscBool                    hessComputed;
354 
355   PetscFunctionBegin;
356   switch (asType) {
357   case BNK_AS_NONE:
358     ierr = ISDestroy(&bnk->inactive_idx);CHKERRQ(ierr);
359     ierr = VecWhichInactive(tao->XL, tao->solution, bnk->unprojected_gradient, tao->XU, PETSC_TRUE, &bnk->inactive_idx);CHKERRQ(ierr);
360     ierr = ISDestroy(&bnk->active_idx);CHKERRQ(ierr);
361     ierr = ISComplementVec(bnk->inactive_idx, tao->solution, &bnk->active_idx);CHKERRQ(ierr);
362     break;
363 
364   case BNK_AS_BERTSEKAS:
365     /* Compute the trial step vector with which we will estimate the active set at the next iteration */
366     if (BNK_PC_BFGS == bnk->pc_type) {
367       /* If the BFGS preconditioner matrix is available, we will construct a trial step with it */
368       ierr = MatLMVMSetInactive(bnk->M, NULL);CHKERRQ(ierr);
369       ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, bnk->W);CHKERRQ(ierr);
370     } else {
371       ierr = MatAssembled(tao->hessian, &hessComputed);CHKERRQ(ierr);
372       if (hessComputed) {
373         /* BFGS preconditioner doesn't exist so let's invert the absolute diagonal of the Hessian instead onto the gradient */
374         ierr = MatGetDiagonal(tao->hessian, bnk->Xwork);CHKERRQ(ierr);
375         ierr = VecAbs(bnk->Xwork);CHKERRQ(ierr);
376         ierr = VecMedian(bnk->Diag_min, bnk->Xwork, bnk->Diag_max, bnk->Xwork);CHKERRQ(ierr);
377         ierr = VecReciprocal(bnk->Xwork);CHKERRQ(ierr);CHKERRQ(ierr);
378         ierr = VecPointwiseMult(bnk->W, bnk->Xwork, bnk->unprojected_gradient);CHKERRQ(ierr);
379       } else {
380         /* If the Hessian does not exist yet, we will simply use gradient step */
381         ierr = VecCopy(bnk->unprojected_gradient, bnk->W);CHKERRQ(ierr);
382       }
383     }
384     ierr = VecScale(bnk->W, -1.0);CHKERRQ(ierr);
385     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);
386 
387   default:
388     break;
389   }
390   PetscFunctionReturn(0);
391 }
392 
393 /*------------------------------------------------------------*/
394 
395 /* Routine for bounding the step direction */
396 
397 PetscErrorCode TaoBNKBoundStep(Tao tao, Vec step)
398 {
399   PetscErrorCode               ierr;
400   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
401 
402   PetscFunctionBegin;
403   switch (bnk->as_type) {
404   case BNK_AS_NONE:
405     if (bnk->active_idx) {ierr = VecISSet(step, bnk->active_idx, 0.0);CHKERRQ(ierr);}
406     break;
407 
408   case BNK_AS_BERTSEKAS:
409     ierr = TaoBoundStep(tao->solution, tao->XL, tao->XU, bnk->active_lower, bnk->active_upper, bnk->active_fixed, step);CHKERRQ(ierr);
410     break;
411 
412   default:
413     break;
414   }
415   PetscFunctionReturn(0);
416 }
417 
418 /*------------------------------------------------------------*/
419 
420 /* Routine for taking a finite number of BNCG iterations to
421    accelerate Newton convergence.
422 
423    In practice, this approach simply trades off Hessian evaluations
424    for more gradient evaluations.
425 */
426 
427 PetscErrorCode TaoBNKTakeCGSteps(Tao tao, PetscBool *terminate)
428 {
429   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
430   PetscErrorCode               ierr;
431 
432   PetscFunctionBegin;
433   *terminate = PETSC_FALSE;
434   if (bnk->max_cg_its > 0) {
435     /* Copy the current solution, unprojected gradient and step info into BNCG */
436     bnk->bncg_ctx->f = bnk->f;
437     ierr = VecCopy(tao->solution, bnk->bncg->solution);CHKERRQ(ierr);
438     ierr = VecCopy(bnk->unprojected_gradient, bnk->bncg_ctx->unprojected_gradient);CHKERRQ(ierr);
439     ierr = VecCopy(tao->stepdirection, bnk->bncg->stepdirection);CHKERRQ(ierr);
440     /* Take some small finite number of BNCG iterations */
441     ierr = TaoSolve(bnk->bncg);CHKERRQ(ierr);
442     /* Add the number of gradient and function evaluations to the total */
443     tao->nfuncs += bnk->bncg->nfuncs;
444     tao->nfuncgrads += bnk->bncg->nfuncgrads;
445     tao->ngrads += bnk->bncg->ngrads;
446     tao->nhess += bnk->bncg->nhess;
447     bnk->tot_cg_its += bnk->bncg->niter;
448     /* Extract the BNCG solution out and save it into BNK */
449     bnk->f = bnk->bncg_ctx->f;
450     ierr = VecCopy(bnk->bncg->solution, tao->solution);
451     ierr = VecCopy(bnk->bncg_ctx->unprojected_gradient, bnk->unprojected_gradient);
452     ierr = VecCopy(bnk->bncg->gradient, tao->gradient);CHKERRQ(ierr);
453     if (bnk->bncg->reason == TAO_CONVERGED_GATOL || bnk->bncg->reason == TAO_CONVERGED_GRTOL || bnk->bncg->reason == TAO_CONVERGED_GTTOL || bnk->bncg->reason == TAO_CONVERGED_MINF) {
454       *terminate = PETSC_TRUE;
455     } else {
456       ierr = TaoBNKEstimateActiveSet(tao, bnk->as_type);
457     }
458   }
459   PetscFunctionReturn(0);
460 }
461 
462 /*------------------------------------------------------------*/
463 
464 /* Routine for computing the Newton step. */
465 
466 PetscErrorCode TaoBNKComputeStep(Tao tao, PetscBool shift, KSPConvergedReason *ksp_reason)
467 {
468   PetscErrorCode               ierr;
469   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
470 
471   PetscReal                    delta;
472   PetscInt                     bfgsUpdates = 0;
473   PetscInt                     kspits;
474 
475   PetscFunctionBegin;
476   /* Prepare the reduced sub-matrices for the inactive set */
477   if (BNK_PC_BFGS == bnk->pc_type) { ierr = MatLMVMSetInactive(bnk->M, bnk->inactive_idx);CHKERRQ(ierr); }
478   if (bnk->inactive_idx) {
479     ierr = MatDestroy(&bnk->H_inactive);
480     ierr = MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive);CHKERRQ(ierr);
481     if (tao->hessian == tao->hessian_pre) {
482       bnk->Hpre_inactive = bnk->H_inactive;
483     } else {
484       ierr = MatDestroy(&bnk->Hpre_inactive);
485       ierr = MatCreateSubMatrix(tao->hessian_pre, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->Hpre_inactive);CHKERRQ(ierr);
486     }
487   } else {
488     ierr = MatDestroy(&bnk->H_inactive);
489     ierr = MatDuplicate(tao->hessian, MAT_COPY_VALUES, &bnk->H_inactive);
490     if (tao->hessian == tao->hessian_pre) {
491       bnk->Hpre_inactive = bnk->H_inactive;
492     } else {
493       ierr = MatDestroy(&bnk->Hpre_inactive);
494       ierr = MatDuplicate(tao->hessian_pre, MAT_COPY_VALUES, &bnk->Hpre_inactive);
495     }
496   }
497 
498   /* Shift the reduced Hessian matrix */
499   if ((shift) && (bnk->pert > 0)) {
500     ierr = MatShift(bnk->H_inactive, bnk->pert);CHKERRQ(ierr);
501     if (bnk->H_inactive != bnk->Hpre_inactive) {
502       ierr = MatShift(bnk->Hpre_inactive, bnk->pert);CHKERRQ(ierr);
503     }
504   }
505 
506   /* Update the diagonal scaling for the BFGS preconditioner, this time with the Hessian perturbation */
507   if ((BNK_PC_BFGS == bnk->pc_type) && (BFGS_SCALE_PHESS == bnk->bfgs_scale_type)) {
508     /* Obtain diagonal for the bfgs preconditioner  */
509     ierr = VecSet(bnk->Diag, 1.0);CHKERRQ(ierr);
510     if (bnk->inactive_idx) {
511       ierr = VecGetSubVector(bnk->Diag, bnk->inactive_idx, &bnk->Diag_red);CHKERRQ(ierr);
512     } else {
513       bnk->Diag_red = bnk->Diag;
514     }
515     ierr = MatGetDiagonal(bnk->H_inactive, bnk->Diag_red);CHKERRQ(ierr);
516     if (bnk->inactive_idx) {
517       ierr = VecRestoreSubVector(bnk->Diag, bnk->inactive_idx, &bnk->Diag_red);CHKERRQ(ierr);
518     }
519     ierr = VecAbs(bnk->Diag);CHKERRQ(ierr);
520     ierr = VecMedian(bnk->Diag_min, bnk->Diag, bnk->Diag_max, bnk->Diag);CHKERRQ(ierr);
521     ierr = VecReciprocal(bnk->Diag);CHKERRQ(ierr);
522     ierr = MatLMVMSetScale(bnk->M,bnk->Diag);CHKERRQ(ierr);
523   }
524 
525   /* Solve the Newton system of equations */
526   tao->ksp_its = 0;
527   ierr = VecSet(tao->stepdirection, 0.0);CHKERRQ(ierr);
528   ierr = KSPReset(tao->ksp);CHKERRQ(ierr);
529   ierr = KSPSetOperators(tao->ksp,bnk->H_inactive,bnk->Hpre_inactive);CHKERRQ(ierr);
530   ierr = VecCopy(bnk->unprojected_gradient, bnk->Gwork);CHKERRQ(ierr);
531   if (bnk->inactive_idx) {
532     ierr = VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr);
533     ierr = VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr);
534   } else {
535     bnk->G_inactive = bnk->unprojected_gradient;
536     bnk->X_inactive = tao->stepdirection;
537   }
538   if (bnk->is_nash || bnk->is_stcg || bnk->is_gltr) {
539     ierr = KSPCGSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr);
540     ierr = KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);CHKERRQ(ierr);
541     ierr = KSPGetIterationNumber(tao->ksp,&kspits);CHKERRQ(ierr);
542     tao->ksp_its+=kspits;
543     tao->ksp_tot_its+=kspits;
544     ierr = KSPCGGetNormD(tao->ksp,&bnk->dnorm);CHKERRQ(ierr);
545 
546     if (0.0 == tao->trust) {
547       /* Radius was uninitialized; use the norm of the direction */
548       if (bnk->dnorm > 0.0) {
549         tao->trust = bnk->dnorm;
550 
551         /* Modify the radius if it is too large or small */
552         tao->trust = PetscMax(tao->trust, bnk->min_radius);
553         tao->trust = PetscMin(tao->trust, bnk->max_radius);
554       } else {
555         /* The direction was bad; set radius to default value and re-solve
556            the trust-region subproblem to get a direction */
557         tao->trust = tao->trust0;
558 
559         /* Modify the radius if it is too large or small */
560         tao->trust = PetscMax(tao->trust, bnk->min_radius);
561         tao->trust = PetscMin(tao->trust, bnk->max_radius);
562 
563         ierr = KSPCGSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr);
564         ierr = KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);CHKERRQ(ierr);
565         ierr = KSPGetIterationNumber(tao->ksp,&kspits);CHKERRQ(ierr);
566         tao->ksp_its+=kspits;
567         tao->ksp_tot_its+=kspits;
568         ierr = KSPCGGetNormD(tao->ksp,&bnk->dnorm);CHKERRQ(ierr);
569 
570         if (bnk->dnorm == 0.0) SETERRQ(PETSC_COMM_SELF,1, "Initial direction zero");
571       }
572     }
573   } else {
574     ierr = KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);CHKERRQ(ierr);
575     ierr = KSPGetIterationNumber(tao->ksp, &kspits);CHKERRQ(ierr);
576     tao->ksp_its += kspits;
577     tao->ksp_tot_its+=kspits;
578   }
579   /* Restore sub vectors back */
580   if (bnk->inactive_idx) {
581     ierr = VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr);
582     ierr = VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr);
583   }
584   /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
585   ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
586   ierr = TaoBNKBoundStep(tao, tao->stepdirection);CHKERRQ(ierr);
587 
588   /* Record convergence reasons */
589   ierr = KSPGetConvergedReason(tao->ksp, ksp_reason);CHKERRQ(ierr);
590   if (KSP_CONVERGED_ATOL == *ksp_reason) {
591     ++bnk->ksp_atol;
592   } else if (KSP_CONVERGED_RTOL == *ksp_reason) {
593     ++bnk->ksp_rtol;
594   } else if (KSP_CONVERGED_CG_CONSTRAINED == *ksp_reason) {
595     ++bnk->ksp_ctol;
596   } else if (KSP_CONVERGED_CG_NEG_CURVE == *ksp_reason) {
597     ++bnk->ksp_negc;
598   } else if (KSP_DIVERGED_DTOL == *ksp_reason) {
599     ++bnk->ksp_dtol;
600   } else if (KSP_DIVERGED_ITS == *ksp_reason) {
601     ++bnk->ksp_iter;
602   } else {
603     ++bnk->ksp_othr;
604   }
605 
606   /* Make sure the BFGS preconditioner is healthy */
607   if (bnk->pc_type == BNK_PC_BFGS) {
608     ierr = MatLMVMGetUpdates(bnk->M, &bfgsUpdates);CHKERRQ(ierr);
609     if ((KSP_DIVERGED_INDEFINITE_PC == *ksp_reason) && (bfgsUpdates > 1)) {
610       /* Preconditioner is numerically indefinite; reset the approximation. */
611       delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
612       ierr = MatLMVMSetDelta(bnk->M,delta);CHKERRQ(ierr);
613       ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
614       ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
615     }
616   }
617   PetscFunctionReturn(0);
618 }
619 
620 /*------------------------------------------------------------*/
621 
622 /* Routine for recomputing the predicted reduction for a given step vector */
623 
624 PetscErrorCode TaoBNKRecomputePred(Tao tao, Vec S, PetscReal *prered)
625 {
626   PetscErrorCode               ierr;
627   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
628 
629   PetscFunctionBegin;
630   /* Extract subvectors associated with the inactive set */
631   if (bnk->inactive_idx){
632     ierr = VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr);
633     ierr = VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);CHKERRQ(ierr);
634     ierr = VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr);
635   } else {
636     bnk->X_inactive = tao->stepdirection;
637     bnk->inactive_work = bnk->Xwork;
638     bnk->G_inactive = bnk->Gwork;
639   }
640   /* Recompute the predicted decrease based on the quadratic model */
641   ierr = MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work);CHKERRQ(ierr);
642   ierr = VecAYPX(bnk->inactive_work, -0.5, bnk->G_inactive);CHKERRQ(ierr);
643   ierr = VecDot(bnk->inactive_work, bnk->X_inactive, prered);
644   /* Restore the sub vectors */
645   if (bnk->inactive_idx){
646     ierr = VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr);
647     ierr = VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);CHKERRQ(ierr);
648     ierr = VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr);
649   }
650   PetscFunctionReturn(0);
651 }
652 
653 /*------------------------------------------------------------*/
654 
655 /* Routine for ensuring that the Newton step is a descent direction.
656 
657    The step direction falls back onto BFGS, scaled gradient and gradient steps
658    in the event that the Newton step fails the test.
659 */
660 
661 PetscErrorCode TaoBNKSafeguardStep(Tao tao, KSPConvergedReason ksp_reason, PetscInt *stepType)
662 {
663   PetscErrorCode               ierr;
664   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
665 
666   PetscReal                    gdx, delta, e_min;
667   PetscInt                     bfgsUpdates;
668 
669   PetscFunctionBegin;
670   ierr = VecDot(tao->stepdirection, tao->gradient, &gdx);CHKERRQ(ierr);
671   if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) {
672     /* Newton step is not descent or direction produced Inf or NaN
673        Update the perturbation for next time */
674     if (bnk->pert <= 0.0) {
675       /* Initialize the perturbation */
676       bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
677       if (bnk->is_gltr) {
678         ierr = KSPCGGLTRGetMinEig(tao->ksp,&e_min);CHKERRQ(ierr);
679         bnk->pert = PetscMax(bnk->pert, -e_min);
680       }
681     } else {
682       /* Increase the perturbation */
683       bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
684     }
685 
686     if (BNK_PC_BFGS != bnk->pc_type) {
687       /* We don't have the bfgs matrix around and updated
688          Must use gradient direction in this case */
689       ierr = VecCopy(tao->gradient, tao->stepdirection);CHKERRQ(ierr);
690       *stepType = BNK_GRADIENT;
691     } else {
692       /* Attempt to use the BFGS direction */
693       ierr = MatLMVMSetInactive(bnk->M, NULL);CHKERRQ(ierr);
694       ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
695 
696       /* Check for success (descent direction)
697          NOTE: Negative gdx here means not a descent direction because
698          the fall-back step is missing a negative sign. */
699       ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr);
700       if ((gdx <= 0) || PetscIsInfOrNanReal(gdx)) {
701         /* BFGS direction is not descent or direction produced not a number
702            We can assert bfgsUpdates > 1 in this case because
703            the first solve produces the scaled gradient direction,
704            which is guaranteed to be descent */
705 
706         /* Use steepest descent direction (scaled) */
707         delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
708         ierr = MatLMVMSetDelta(bnk->M, delta);CHKERRQ(ierr);
709         ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
710         ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
711         ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
712 
713         *stepType = BNK_SCALED_GRADIENT;
714       } else {
715         ierr = MatLMVMGetUpdates(bnk->M, &bfgsUpdates);CHKERRQ(ierr);
716         if (1 == bfgsUpdates) {
717           /* The first BFGS direction is always the scaled gradient */
718           *stepType = BNK_SCALED_GRADIENT;
719         } else {
720           *stepType = BNK_BFGS;
721         }
722       }
723     }
724     /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
725     ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
726     ierr = TaoBNKBoundStep(tao, tao->stepdirection);CHKERRQ(ierr);
727   } else {
728     /* Computed Newton step is descent */
729     switch (ksp_reason) {
730     case KSP_DIVERGED_NANORINF:
731     case KSP_DIVERGED_BREAKDOWN:
732     case KSP_DIVERGED_INDEFINITE_MAT:
733     case KSP_DIVERGED_INDEFINITE_PC:
734     case KSP_CONVERGED_CG_NEG_CURVE:
735       /* Matrix or preconditioner is indefinite; increase perturbation */
736       if (bnk->pert <= 0.0) {
737         /* Initialize the perturbation */
738         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
739         if (bnk->is_gltr) {
740           ierr = KSPCGGLTRGetMinEig(tao->ksp, &e_min);CHKERRQ(ierr);
741           bnk->pert = PetscMax(bnk->pert, -e_min);
742         }
743       } else {
744         /* Increase the perturbation */
745         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
746       }
747       break;
748 
749     default:
750       /* Newton step computation is good; decrease perturbation */
751       bnk->pert = PetscMin(bnk->psfac * bnk->pert, bnk->pmsfac * bnk->gnorm);
752       if (bnk->pert < bnk->pmin) {
753         bnk->pert = 0.0;
754       }
755       break;
756     }
757     *stepType = BNK_NEWTON;
758   }
759   PetscFunctionReturn(0);
760 }
761 
762 /*------------------------------------------------------------*/
763 
764 /* Routine for performing a bound-projected More-Thuente line search.
765 
766   Includes fallbacks to BFGS, scaled gradient, and unscaled gradient steps if the
767   Newton step does not produce a valid step length.
768 */
769 
770 PetscErrorCode TaoBNKPerformLineSearch(Tao tao, PetscInt *stepType, PetscReal *steplen, TaoLineSearchConvergedReason *reason)
771 {
772   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
773   PetscErrorCode ierr;
774   TaoLineSearchConvergedReason ls_reason;
775 
776   PetscReal      e_min, gdx, delta;
777   PetscInt       bfgsUpdates;
778 
779   PetscFunctionBegin;
780   /* Perform the linesearch */
781   ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason);CHKERRQ(ierr);
782   ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
783 
784   while (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER && *stepType != BNK_GRADIENT) {
785     /* Linesearch failed, revert solution */
786     bnk->f = bnk->fold;
787     ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr);
788     ierr = VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);CHKERRQ(ierr);
789 
790     switch(*stepType) {
791     case BNK_NEWTON:
792       /* Failed to obtain acceptable iterate with Newton step
793          Update the perturbation for next time */
794       if (bnk->pert <= 0.0) {
795         /* Initialize the perturbation */
796         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
797         if (bnk->is_gltr) {
798           ierr = KSPCGGLTRGetMinEig(tao->ksp,&e_min);CHKERRQ(ierr);
799           bnk->pert = PetscMax(bnk->pert, -e_min);
800         }
801       } else {
802         /* Increase the perturbation */
803         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
804       }
805 
806       if (BNK_PC_BFGS != bnk->pc_type) {
807         /* We don't have the bfgs matrix around and being updated
808            Must use gradient direction in this case */
809         ierr = VecCopy(bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
810         *stepType = BNK_GRADIENT;
811       } else {
812         /* Attempt to use the BFGS direction */
813         ierr = MatLMVMSetInactive(bnk->M, NULL);CHKERRQ(ierr);
814         ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
815         /* Check for success (descent direction)
816            NOTE: Negative gdx means not a descent direction because the step here is missing a negative sign. */
817         ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr);
818         if ((gdx <= 0) || PetscIsInfOrNanReal(gdx)) {
819           /* BFGS direction is not descent or direction produced not a number
820              We can assert bfgsUpdates > 1 in this case
821              Use steepest descent direction (scaled) */
822           delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
823           ierr = MatLMVMSetDelta(bnk->M, delta);CHKERRQ(ierr);
824           ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
825           ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
826           ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
827 
828           bfgsUpdates = 1;
829           *stepType = BNK_SCALED_GRADIENT;
830         } else {
831           ierr = MatLMVMGetUpdates(bnk->M, &bfgsUpdates);CHKERRQ(ierr);
832           if (1 == bfgsUpdates) {
833             /* The first BFGS direction is always the scaled gradient */
834             *stepType = BNK_SCALED_GRADIENT;
835           } else {
836             *stepType = BNK_BFGS;
837           }
838         }
839       }
840       break;
841 
842     case BNK_BFGS:
843       /* Can only enter if pc_type == BNK_PC_BFGS
844          Failed to obtain acceptable iterate with BFGS step
845          Attempt to use the scaled gradient direction */
846       delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
847       ierr = MatLMVMSetDelta(bnk->M, delta);CHKERRQ(ierr);
848       ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
849       ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
850       ierr = MatLMVMSetInactive(bnk->M, NULL);CHKERRQ(ierr);
851       ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
852 
853       bfgsUpdates = 1;
854       *stepType = BNK_SCALED_GRADIENT;
855       break;
856 
857     case BNK_SCALED_GRADIENT:
858       /* Can only enter if pc_type == BNK_PC_BFGS
859          The scaled gradient step did not produce a new iterate;
860          reset the BFGS matrix and attemp to use the gradient direction. */
861       ierr = MatLMVMSetScale(bnk->M,0);CHKERRQ(ierr);
862       ierr = MatLMVMSetDelta(bnk->M,1.0);CHKERRQ(ierr);
863       ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
864       ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
865       ierr = VecCopy(bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
866 
867       bfgsUpdates = 1;
868       *stepType = BNK_GRADIENT;
869       break;
870     }
871     /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
872     ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
873     ierr = TaoBNKBoundStep(tao, tao->stepdirection);CHKERRQ(ierr);
874 
875     /* Perform one last line search with the fall-back step */
876     ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason);CHKERRQ(ierr);
877     ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
878   }
879   *reason = ls_reason;
880   PetscFunctionReturn(0);
881 }
882 
883 /*------------------------------------------------------------*/
884 
885 /* Routine for updating the trust radius.
886 
887   Function features three different update methods:
888   1) Line-search step length based
889   2) Predicted decrease on the CG quadratic model
890   3) Interpolation
891 */
892 
893 PetscErrorCode TaoBNKUpdateTrustRadius(Tao tao, PetscReal prered, PetscReal actred, PetscInt updateType, PetscInt stepType, PetscBool *accept)
894 {
895   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
896   PetscErrorCode ierr;
897 
898   PetscReal      step, kappa;
899   PetscReal      gdx, tau_1, tau_2, tau_min, tau_max;
900 
901   PetscFunctionBegin;
902   /* Update trust region radius */
903   *accept = PETSC_FALSE;
904   switch(updateType) {
905   case BNK_UPDATE_STEP:
906     *accept = PETSC_TRUE; /* always accept here because line search succeeded */
907     if (stepType == BNK_NEWTON) {
908       ierr = TaoLineSearchGetStepLength(tao->linesearch, &step);CHKERRQ(ierr);
909       if (step < bnk->nu1) {
910         /* Very bad step taken; reduce radius */
911         tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
912       } else if (step < bnk->nu2) {
913         /* Reasonably bad step taken; reduce radius */
914         tao->trust = bnk->omega2 * PetscMin(bnk->dnorm, tao->trust);
915       } else if (step < bnk->nu3) {
916         /*  Reasonable step was taken; leave radius alone */
917         if (bnk->omega3 < 1.0) {
918           tao->trust = bnk->omega3 * PetscMin(bnk->dnorm, tao->trust);
919         } else if (bnk->omega3 > 1.0) {
920           tao->trust = PetscMax(bnk->omega3 * bnk->dnorm, tao->trust);
921         }
922       } else if (step < bnk->nu4) {
923         /*  Full step taken; increase the radius */
924         tao->trust = PetscMax(bnk->omega4 * bnk->dnorm, tao->trust);
925       } else {
926         /*  More than full step taken; increase the radius */
927         tao->trust = PetscMax(bnk->omega5 * bnk->dnorm, tao->trust);
928       }
929     } else {
930       /*  Newton step was not good; reduce the radius */
931       tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
932     }
933     break;
934 
935   case BNK_UPDATE_REDUCTION:
936     if (stepType == BNK_NEWTON) {
937       if (prered < 0.0) {
938         /* The predicted reduction has the wrong sign.  This cannot
939            happen in infinite precision arithmetic.  Step should
940            be rejected! */
941         tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
942       }
943       else {
944         if (PetscIsInfOrNanReal(actred)) {
945           tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
946         } else {
947           if ((PetscAbsScalar(actred) <= PetscMax(1.0, PetscAbsScalar(bnk->f))*bnk->epsilon) &&
948               (PetscAbsScalar(prered) <= PetscMax(1.0, PetscAbsScalar(bnk->f))*bnk->epsilon)) {
949             kappa = 1.0;
950           }
951           else {
952             kappa = actred / prered;
953           }
954 
955           /* Accept or reject the step and update radius */
956           if (kappa < bnk->eta1) {
957             /* Reject the step */
958             tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
959           }
960           else {
961             /* Accept the step */
962             *accept = PETSC_TRUE;
963             /* Update the trust region radius only if the computed step is at the trust radius boundary */
964             if (bnk->dnorm == tao->trust) {
965               if (kappa < bnk->eta2) {
966                 /* Marginal bad step */
967                 tao->trust = bnk->alpha2 * tao->trust;
968               }
969               else if (kappa < bnk->eta3) {
970                 /* Reasonable step */
971                 tao->trust = bnk->alpha3 * tao->trust;
972               }
973               else if (kappa < bnk->eta4) {
974                 /* Good step */
975                 tao->trust = bnk->alpha4 * tao->trust;
976               }
977               else {
978                 /* Very good step */
979                 tao->trust = bnk->alpha5 * tao->trust;
980               }
981             }
982           }
983         }
984       }
985     } else {
986       /*  Newton step was not good; reduce the radius */
987       tao->trust = bnk->alpha1 * PetscMin(bnk->dnorm, tao->trust);
988     }
989     break;
990 
991   default:
992     if (stepType == BNK_NEWTON) {
993       if (prered < 0.0) {
994         /*  The predicted reduction has the wrong sign.  This cannot */
995         /*  happen in infinite precision arithmetic.  Step should */
996         /*  be rejected! */
997         tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
998       } else {
999         if (PetscIsInfOrNanReal(actred)) {
1000           tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
1001         } else {
1002           if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) {
1003             kappa = 1.0;
1004           } else {
1005             kappa = actred / prered;
1006           }
1007 
1008           ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr);
1009           tau_1 = bnk->theta * gdx / (bnk->theta * gdx - (1.0 - bnk->theta) * prered + actred);
1010           tau_2 = bnk->theta * gdx / (bnk->theta * gdx + (1.0 + bnk->theta) * prered - actred);
1011           tau_min = PetscMin(tau_1, tau_2);
1012           tau_max = PetscMax(tau_1, tau_2);
1013 
1014           if (kappa >= 1.0 - bnk->mu1) {
1015             /*  Great agreement */
1016             *accept = PETSC_TRUE;
1017             if (tau_max < 1.0) {
1018               tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
1019             } else if (tau_max > bnk->gamma4) {
1020               tao->trust = PetscMax(tao->trust, bnk->gamma4 * bnk->dnorm);
1021             } else {
1022               tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
1023             }
1024           } else if (kappa >= 1.0 - bnk->mu2) {
1025             /*  Good agreement */
1026             *accept = PETSC_TRUE;
1027             if (tau_max < bnk->gamma2) {
1028               tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
1029             } else if (tau_max > bnk->gamma3) {
1030               tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
1031             } else if (tau_max < 1.0) {
1032               tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
1033             } else {
1034               tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
1035             }
1036           } else {
1037             /*  Not good agreement */
1038             if (tau_min > 1.0) {
1039               tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
1040             } else if (tau_max < bnk->gamma1) {
1041               tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
1042             } else if ((tau_min < bnk->gamma1) && (tau_max >= 1.0)) {
1043               tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
1044             } else if ((tau_1 >= bnk->gamma1) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1) || (tau_2 >= 1.0))) {
1045               tao->trust = tau_1 * PetscMin(tao->trust, bnk->dnorm);
1046             } else if ((tau_2 >= bnk->gamma1) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1) || (tau_2 >= 1.0))) {
1047               tao->trust = tau_2 * PetscMin(tao->trust, bnk->dnorm);
1048             } else {
1049               tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
1050             }
1051           }
1052         }
1053       }
1054     } else {
1055       /*  Newton step was not good; reduce the radius */
1056       tao->trust = bnk->gamma1 * PetscMin(bnk->dnorm, tao->trust);
1057     }
1058     break;
1059   }
1060   /* Make sure the radius does not violate min and max settings */
1061   tao->trust = PetscMin(tao->trust, bnk->max_radius);
1062   tao->trust = PetscMax(tao->trust, bnk->min_radius);
1063   PetscFunctionReturn(0);
1064 }
1065 
1066 /* ---------------------------------------------------------- */
1067 
1068 PetscErrorCode TaoBNKAddStepCounts(Tao tao, PetscInt stepType)
1069 {
1070   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1071 
1072   PetscFunctionBegin;
1073   switch (stepType) {
1074   case BNK_NEWTON:
1075     ++bnk->newt;
1076     break;
1077   case BNK_BFGS:
1078     ++bnk->bfgs;
1079     break;
1080   case BNK_SCALED_GRADIENT:
1081     ++bnk->sgrad;
1082     break;
1083   case BNK_GRADIENT:
1084     ++bnk->grad;
1085     break;
1086   default:
1087     break;
1088   }
1089   PetscFunctionReturn(0);
1090 }
1091 
1092 /* ---------------------------------------------------------- */
1093 
1094 PetscErrorCode TaoSetUp_BNK(Tao tao)
1095 {
1096   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1097   PetscErrorCode ierr;
1098   KSPType        ksp_type;
1099   PetscInt       i;
1100 
1101   PetscFunctionBegin;
1102   if (!tao->gradient) {ierr = VecDuplicate(tao->solution,&tao->gradient);CHKERRQ(ierr);}
1103   if (!tao->stepdirection) {ierr = VecDuplicate(tao->solution,&tao->stepdirection);CHKERRQ(ierr);}
1104   if (!bnk->W) {ierr = VecDuplicate(tao->solution,&bnk->W);CHKERRQ(ierr);}
1105   if (!bnk->Xold) {ierr = VecDuplicate(tao->solution,&bnk->Xold);CHKERRQ(ierr);}
1106   if (!bnk->Gold) {ierr = VecDuplicate(tao->solution,&bnk->Gold);CHKERRQ(ierr);}
1107   if (!bnk->Xwork) {ierr = VecDuplicate(tao->solution,&bnk->Xwork);CHKERRQ(ierr);}
1108   if (!bnk->Gwork) {ierr = VecDuplicate(tao->solution,&bnk->Gwork);CHKERRQ(ierr);}
1109   if (!bnk->unprojected_gradient) {ierr = VecDuplicate(tao->solution,&bnk->unprojected_gradient);CHKERRQ(ierr);}
1110   if (!bnk->unprojected_gradient_old) {ierr = VecDuplicate(tao->solution,&bnk->unprojected_gradient_old);CHKERRQ(ierr);}
1111   if (!bnk->Diag_min) {ierr = VecDuplicate(tao->solution,&bnk->Diag_min);CHKERRQ(ierr);}
1112   if (!bnk->Diag_max) {ierr = VecDuplicate(tao->solution,&bnk->Diag_max);CHKERRQ(ierr);}
1113   if (bnk->max_cg_its > 0) {
1114     if (!bnk->bncg_sol) {ierr = VecDuplicate(tao->solution,&bnk->bncg_sol);CHKERRQ(ierr);}
1115     ierr = TaoSetInitialVector(bnk->bncg, bnk->bncg_sol);CHKERRQ(ierr);
1116     ierr = TaoSetMaximumIterations(bnk->bncg, bnk->max_cg_its);CHKERRQ(ierr);
1117     ierr = TaoSetTolerances(bnk->bncg, tao->gatol, tao->grtol, tao->gttol);CHKERRQ(ierr);
1118     ierr = TaoSetFunctionLowerBound(bnk->bncg, tao->fmin);CHKERRQ(ierr);
1119 
1120     ierr = TaoSetConvergenceTest(bnk->bncg, tao->ops->convergencetest, tao->cnvP);CHKERRQ(ierr);
1121     ierr = TaoSetObjectiveRoutine(bnk->bncg, tao->ops->computeobjective, tao->user_objP);CHKERRQ(ierr);
1122     ierr = TaoSetGradientRoutine(bnk->bncg, tao->ops->computegradient, tao->user_gradP);CHKERRQ(ierr);
1123     ierr = TaoSetObjectiveAndGradientRoutine(bnk->bncg, tao->ops->computeobjectiveandgradient, tao->user_objgradP);CHKERRQ(ierr);
1124     ierr = PetscObjectCopyFortranFunctionPointers((PetscObject)tao, (PetscObject)(bnk->bncg));CHKERRQ(ierr);
1125     for (i=0; i<tao->numbermonitors; i++) {
1126       ierr = TaoSetMonitor(bnk->bncg, tao->monitor[i], tao->monitorcontext[i], tao->monitordestroy[i]);CHKERRQ(ierr);
1127       ierr = PetscObjectReference((PetscObject)(tao->monitorcontext[i]));CHKERRQ(ierr);
1128     }
1129     ierr = TaoSetUp(bnk->bncg);CHKERRQ(ierr);
1130     bnk->bncg_ctx = (TAO_BNCG *)bnk->bncg->data;
1131   }
1132   bnk->Diag = 0;
1133   bnk->Diag_red = 0;
1134   bnk->X_inactive = 0;
1135   bnk->G_inactive = 0;
1136   bnk->inactive_work = 0;
1137   bnk->active_work = 0;
1138   bnk->inactive_idx = 0;
1139   bnk->active_idx = 0;
1140   bnk->active_lower = 0;
1141   bnk->active_upper = 0;
1142   bnk->active_fixed = 0;
1143   bnk->M = 0;
1144   bnk->H_inactive = 0;
1145   bnk->Hpre_inactive = 0;
1146   ierr = KSPGetType(tao->ksp,&ksp_type);CHKERRQ(ierr);
1147   ierr = PetscStrcmp(ksp_type,KSPCGNASH,&bnk->is_nash);CHKERRQ(ierr);
1148   ierr = PetscStrcmp(ksp_type,KSPCGSTCG,&bnk->is_stcg);CHKERRQ(ierr);
1149   ierr = PetscStrcmp(ksp_type,KSPCGGLTR,&bnk->is_gltr);CHKERRQ(ierr);
1150   PetscFunctionReturn(0);
1151 }
1152 
1153 /*------------------------------------------------------------*/
1154 
1155 static PetscErrorCode TaoDestroy_BNK(Tao tao)
1156 {
1157   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1158   PetscErrorCode ierr;
1159 
1160   PetscFunctionBegin;
1161   if (tao->setupcalled) {
1162     ierr = VecDestroy(&bnk->W);CHKERRQ(ierr);
1163     ierr = VecDestroy(&bnk->Xold);CHKERRQ(ierr);
1164     ierr = VecDestroy(&bnk->Gold);CHKERRQ(ierr);
1165     ierr = VecDestroy(&bnk->Xwork);CHKERRQ(ierr);
1166     ierr = VecDestroy(&bnk->Gwork);CHKERRQ(ierr);
1167     ierr = VecDestroy(&bnk->unprojected_gradient);CHKERRQ(ierr);
1168     ierr = VecDestroy(&bnk->unprojected_gradient_old);CHKERRQ(ierr);
1169     ierr = VecDestroy(&bnk->Diag_min);CHKERRQ(ierr);
1170     ierr = VecDestroy(&bnk->Diag_max);CHKERRQ(ierr);
1171     if (bnk->max_cg_its > 0) {
1172       ierr = TaoDestroy(&bnk->bncg);CHKERRQ(ierr);
1173       ierr = VecDestroy(&bnk->bncg_sol);CHKERRQ(ierr);
1174     }
1175   }
1176   ierr = VecDestroy(&bnk->Diag);CHKERRQ(ierr);
1177   ierr = MatDestroy(&bnk->M);CHKERRQ(ierr);
1178   if (bnk->Hpre_inactive != tao->hessian_pre && bnk->Hpre_inactive != bnk->H_inactive) {ierr = MatDestroy(&bnk->Hpre_inactive);CHKERRQ(ierr);}
1179   if (bnk->H_inactive != tao->hessian) {ierr = MatDestroy(&bnk->H_inactive);CHKERRQ(ierr);}
1180   ierr = PetscFree(tao->data);CHKERRQ(ierr);
1181   PetscFunctionReturn(0);
1182 }
1183 
1184 /*------------------------------------------------------------*/
1185 
1186 static PetscErrorCode TaoSetFromOptions_BNK(PetscOptionItems *PetscOptionsObject,Tao tao)
1187 {
1188   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1189   PetscErrorCode ierr;
1190 
1191   PetscFunctionBegin;
1192   ierr = PetscOptionsHead(PetscOptionsObject,"Newton line search method for unconstrained optimization");CHKERRQ(ierr);
1193   ierr = PetscOptionsEList("-tao_bnk_pc_type", "pc type", "", BNK_PC, BNK_PC_TYPES, BNK_PC[bnk->pc_type], &bnk->pc_type, 0);CHKERRQ(ierr);
1194   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);
1195   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);
1196   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);
1197   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);
1198   ierr = PetscOptionsReal("-tao_bnk_sval", "perturbation starting value", "", bnk->sval, &bnk->sval,NULL);CHKERRQ(ierr);
1199   ierr = PetscOptionsReal("-tao_bnk_imin", "minimum initial perturbation", "", bnk->imin, &bnk->imin,NULL);CHKERRQ(ierr);
1200   ierr = PetscOptionsReal("-tao_bnk_imax", "maximum initial perturbation", "", bnk->imax, &bnk->imax,NULL);CHKERRQ(ierr);
1201   ierr = PetscOptionsReal("-tao_bnk_imfac", "initial merit factor", "", bnk->imfac, &bnk->imfac,NULL);CHKERRQ(ierr);
1202   ierr = PetscOptionsReal("-tao_bnk_pmin", "minimum perturbation", "", bnk->pmin, &bnk->pmin,NULL);CHKERRQ(ierr);
1203   ierr = PetscOptionsReal("-tao_bnk_pmax", "maximum perturbation", "", bnk->pmax, &bnk->pmax,NULL);CHKERRQ(ierr);
1204   ierr = PetscOptionsReal("-tao_bnk_pgfac", "growth factor", "", bnk->pgfac, &bnk->pgfac,NULL);CHKERRQ(ierr);
1205   ierr = PetscOptionsReal("-tao_bnk_psfac", "shrink factor", "", bnk->psfac, &bnk->psfac,NULL);CHKERRQ(ierr);
1206   ierr = PetscOptionsReal("-tao_bnk_pmgfac", "merit growth factor", "", bnk->pmgfac, &bnk->pmgfac,NULL);CHKERRQ(ierr);
1207   ierr = PetscOptionsReal("-tao_bnk_pmsfac", "merit shrink factor", "", bnk->pmsfac, &bnk->pmsfac,NULL);CHKERRQ(ierr);
1208   ierr = PetscOptionsReal("-tao_bnk_eta1", "poor steplength; reduce radius", "", bnk->eta1, &bnk->eta1,NULL);CHKERRQ(ierr);
1209   ierr = PetscOptionsReal("-tao_bnk_eta2", "reasonable steplength; leave radius alone", "", bnk->eta2, &bnk->eta2,NULL);CHKERRQ(ierr);
1210   ierr = PetscOptionsReal("-tao_bnk_eta3", "good steplength; increase radius", "", bnk->eta3, &bnk->eta3,NULL);CHKERRQ(ierr);
1211   ierr = PetscOptionsReal("-tao_bnk_eta4", "excellent steplength; greatly increase radius", "", bnk->eta4, &bnk->eta4,NULL);CHKERRQ(ierr);
1212   ierr = PetscOptionsReal("-tao_bnk_alpha1", "", "", bnk->alpha1, &bnk->alpha1,NULL);CHKERRQ(ierr);
1213   ierr = PetscOptionsReal("-tao_bnk_alpha2", "", "", bnk->alpha2, &bnk->alpha2,NULL);CHKERRQ(ierr);
1214   ierr = PetscOptionsReal("-tao_bnk_alpha3", "", "", bnk->alpha3, &bnk->alpha3,NULL);CHKERRQ(ierr);
1215   ierr = PetscOptionsReal("-tao_bnk_alpha4", "", "", bnk->alpha4, &bnk->alpha4,NULL);CHKERRQ(ierr);
1216   ierr = PetscOptionsReal("-tao_bnk_alpha5", "", "", bnk->alpha5, &bnk->alpha5,NULL);CHKERRQ(ierr);
1217   ierr = PetscOptionsReal("-tao_bnk_nu1", "poor steplength; reduce radius", "", bnk->nu1, &bnk->nu1,NULL);CHKERRQ(ierr);
1218   ierr = PetscOptionsReal("-tao_bnk_nu2", "reasonable steplength; leave radius alone", "", bnk->nu2, &bnk->nu2,NULL);CHKERRQ(ierr);
1219   ierr = PetscOptionsReal("-tao_bnk_nu3", "good steplength; increase radius", "", bnk->nu3, &bnk->nu3,NULL);CHKERRQ(ierr);
1220   ierr = PetscOptionsReal("-tao_bnk_nu4", "excellent steplength; greatly increase radius", "", bnk->nu4, &bnk->nu4,NULL);CHKERRQ(ierr);
1221   ierr = PetscOptionsReal("-tao_bnk_omega1", "", "", bnk->omega1, &bnk->omega1,NULL);CHKERRQ(ierr);
1222   ierr = PetscOptionsReal("-tao_bnk_omega2", "", "", bnk->omega2, &bnk->omega2,NULL);CHKERRQ(ierr);
1223   ierr = PetscOptionsReal("-tao_bnk_omega3", "", "", bnk->omega3, &bnk->omega3,NULL);CHKERRQ(ierr);
1224   ierr = PetscOptionsReal("-tao_bnk_omega4", "", "", bnk->omega4, &bnk->omega4,NULL);CHKERRQ(ierr);
1225   ierr = PetscOptionsReal("-tao_bnk_omega5", "", "", bnk->omega5, &bnk->omega5,NULL);CHKERRQ(ierr);
1226   ierr = PetscOptionsReal("-tao_bnk_mu1_i", "", "", bnk->mu1_i, &bnk->mu1_i,NULL);CHKERRQ(ierr);
1227   ierr = PetscOptionsReal("-tao_bnk_mu2_i", "", "", bnk->mu2_i, &bnk->mu2_i,NULL);CHKERRQ(ierr);
1228   ierr = PetscOptionsReal("-tao_bnk_gamma1_i", "", "", bnk->gamma1_i, &bnk->gamma1_i,NULL);CHKERRQ(ierr);
1229   ierr = PetscOptionsReal("-tao_bnk_gamma2_i", "", "", bnk->gamma2_i, &bnk->gamma2_i,NULL);CHKERRQ(ierr);
1230   ierr = PetscOptionsReal("-tao_bnk_gamma3_i", "", "", bnk->gamma3_i, &bnk->gamma3_i,NULL);CHKERRQ(ierr);
1231   ierr = PetscOptionsReal("-tao_bnk_gamma4_i", "", "", bnk->gamma4_i, &bnk->gamma4_i,NULL);CHKERRQ(ierr);
1232   ierr = PetscOptionsReal("-tao_bnk_theta_i", "", "", bnk->theta_i, &bnk->theta_i,NULL);CHKERRQ(ierr);
1233   ierr = PetscOptionsReal("-tao_bnk_mu1", "", "", bnk->mu1, &bnk->mu1,NULL);CHKERRQ(ierr);
1234   ierr = PetscOptionsReal("-tao_bnk_mu2", "", "", bnk->mu2, &bnk->mu2,NULL);CHKERRQ(ierr);
1235   ierr = PetscOptionsReal("-tao_bnk_gamma1", "", "", bnk->gamma1, &bnk->gamma1,NULL);CHKERRQ(ierr);
1236   ierr = PetscOptionsReal("-tao_bnk_gamma2", "", "", bnk->gamma2, &bnk->gamma2,NULL);CHKERRQ(ierr);
1237   ierr = PetscOptionsReal("-tao_bnk_gamma3", "", "", bnk->gamma3, &bnk->gamma3,NULL);CHKERRQ(ierr);
1238   ierr = PetscOptionsReal("-tao_bnk_gamma4", "", "", bnk->gamma4, &bnk->gamma4,NULL);CHKERRQ(ierr);
1239   ierr = PetscOptionsReal("-tao_bnk_theta", "", "", bnk->theta, &bnk->theta,NULL);CHKERRQ(ierr);
1240   ierr = PetscOptionsReal("-tao_bnk_min_radius", "lower bound on initial radius", "", bnk->min_radius, &bnk->min_radius,NULL);CHKERRQ(ierr);
1241   ierr = PetscOptionsReal("-tao_bnk_max_radius", "upper bound on radius", "", bnk->max_radius, &bnk->max_radius,NULL);CHKERRQ(ierr);
1242   ierr = PetscOptionsReal("-tao_bnk_epsilon", "tolerance used when computing actual and predicted reduction", "", bnk->epsilon, &bnk->epsilon,NULL);CHKERRQ(ierr);
1243   ierr = PetscOptionsReal("-tao_bnk_as_tol", "initial tolerance used when estimating actively bounded variables", "", bnk->as_tol, &bnk->as_tol,NULL);CHKERRQ(ierr);
1244   ierr = PetscOptionsReal("-tao_bnk_as_step", "step length used when estimating actively bounded variables", "", bnk->as_step, &bnk->as_step,NULL);CHKERRQ(ierr);
1245   ierr = PetscOptionsInt("-tao_bnk_max_cg_its", "number of BNCG iterations to take for each Newton step", "", bnk->max_cg_its, &bnk->max_cg_its,NULL);CHKERRQ(ierr);
1246   ierr = PetscOptionsTail();CHKERRQ(ierr);
1247   ierr = TaoSetFromOptions(bnk->bncg);
1248   ierr = TaoLineSearchSetFromOptions(tao->linesearch);CHKERRQ(ierr);
1249   ierr = KSPSetFromOptions(tao->ksp);CHKERRQ(ierr);
1250   PetscFunctionReturn(0);
1251 }
1252 
1253 /*------------------------------------------------------------*/
1254 
1255 static PetscErrorCode TaoView_BNK(Tao tao, PetscViewer viewer)
1256 {
1257   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1258   PetscInt       nrejects;
1259   PetscBool      isascii;
1260   PetscErrorCode ierr;
1261 
1262   PetscFunctionBegin;
1263   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
1264   if (isascii) {
1265     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1266     if (BNK_PC_BFGS == bnk->pc_type && bnk->M) {
1267       ierr = MatLMVMGetRejects(bnk->M,&nrejects);CHKERRQ(ierr);
1268       ierr = PetscViewerASCIIPrintf(viewer, "Rejected matrix updates: %D\n",nrejects);CHKERRQ(ierr);
1269     }
1270     ierr = PetscViewerASCIIPrintf(viewer, "CG steps: %D\n", bnk->tot_cg_its);CHKERRQ(ierr);
1271     ierr = PetscViewerASCIIPrintf(viewer, "Newton steps: %D\n", bnk->newt);CHKERRQ(ierr);
1272     ierr = PetscViewerASCIIPrintf(viewer, "BFGS steps: %D\n", bnk->bfgs);CHKERRQ(ierr);
1273     ierr = PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %D\n", bnk->sgrad);CHKERRQ(ierr);
1274     ierr = PetscViewerASCIIPrintf(viewer, "Gradient steps: %D\n", bnk->grad);CHKERRQ(ierr);
1275     ierr = PetscViewerASCIIPrintf(viewer, "KSP termination reasons:\n");CHKERRQ(ierr);
1276     ierr = PetscViewerASCIIPrintf(viewer, "  atol: %D\n", bnk->ksp_atol);CHKERRQ(ierr);
1277     ierr = PetscViewerASCIIPrintf(viewer, "  rtol: %D\n", bnk->ksp_rtol);CHKERRQ(ierr);
1278     ierr = PetscViewerASCIIPrintf(viewer, "  ctol: %D\n", bnk->ksp_ctol);CHKERRQ(ierr);
1279     ierr = PetscViewerASCIIPrintf(viewer, "  negc: %D\n", bnk->ksp_negc);CHKERRQ(ierr);
1280     ierr = PetscViewerASCIIPrintf(viewer, "  dtol: %D\n", bnk->ksp_dtol);CHKERRQ(ierr);
1281     ierr = PetscViewerASCIIPrintf(viewer, "  iter: %D\n", bnk->ksp_iter);CHKERRQ(ierr);
1282     ierr = PetscViewerASCIIPrintf(viewer, "  othr: %D\n", bnk->ksp_othr);CHKERRQ(ierr);
1283     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1284   }
1285   PetscFunctionReturn(0);
1286 }
1287 
1288 /* ---------------------------------------------------------- */
1289 
1290 /*MC
1291   TAOBNK - Shared base-type for Bounded Newton-Krylov type algorithms.
1292   At each iteration, the BNK methods solve the symmetric
1293   system of equations to obtain the step diretion dk:
1294               Hk dk = -gk
1295   for free variables only. The step can be globalized either through
1296   trust-region methods, or a line search, or a heuristic mixture of both.
1297 
1298     Options Database Keys:
1299 + -tao_bnk_pc_type - "none","ahess","bfgs","petsc"
1300 . -tao_bnk_bfgs_scale_type - "ahess","phess","bfgs"
1301 . -tao_bnk_init_type - "constant","direction","interpolation"
1302 . -tao_bnk_update_type - "step","direction","interpolation"
1303 . -tao_bnk_as_type - "none","bertsekas"
1304 . -tao_bnk_sval - perturbation starting value
1305 . -tao_bnk_imin - minimum initial perturbation
1306 . -tao_bnk_imax - maximum initial perturbation
1307 . -tao_bnk_pmin - minimum perturbation
1308 . -tao_bnk_pmax - maximum perturbation
1309 . -tao_bnk_pgfac - growth factor
1310 . -tao_bnk_psfac - shrink factor
1311 . -tao_bnk_imfac - initial merit factor
1312 . -tao_bnk_pmgfac - merit growth factor
1313 . -tao_bnk_pmsfac - merit shrink factor
1314 . -tao_bnk_eta1 - poor steplength; reduce radius
1315 . -tao_bnk_eta2 - reasonable steplength; leave radius
1316 . -tao_bnk_eta3 - good steplength; increase readius
1317 . -tao_bnk_eta4 - excellent steplength; greatly increase radius
1318 . -tao_bnk_alpha1 - alpha1 reduction
1319 . -tao_bnk_alpha2 - alpha2 reduction
1320 . -tao_bnk_alpha3 - alpha3 reduction
1321 . -tao_bnk_alpha4 - alpha4 reduction
1322 . -tao_bnk_alpha - alpha5 reduction
1323 . -tao_bnk_mu1 - mu1 interpolation update
1324 . -tao_bnk_mu2 - mu2 interpolation update
1325 . -tao_bnk_gamma1 - gamma1 interpolation update
1326 . -tao_bnk_gamma2 - gamma2 interpolation update
1327 . -tao_bnk_gamma3 - gamma3 interpolation update
1328 . -tao_bnk_gamma4 - gamma4 interpolation update
1329 . -tao_bnk_theta - theta interpolation update
1330 . -tao_bnk_omega1 - omega1 step update
1331 . -tao_bnk_omega2 - omega2 step update
1332 . -tao_bnk_omega3 - omega3 step update
1333 . -tao_bnk_omega4 - omega4 step update
1334 . -tao_bnk_omega5 - omega5 step update
1335 . -tao_bnk_mu1_i -  mu1 interpolation init factor
1336 . -tao_bnk_mu2_i -  mu2 interpolation init factor
1337 . -tao_bnk_gamma1_i -  gamma1 interpolation init factor
1338 . -tao_bnk_gamma2_i -  gamma2 interpolation init factor
1339 . -tao_bnk_gamma3_i -  gamma3 interpolation init factor
1340 . -tao_bnk_gamma4_i -  gamma4 interpolation init factor
1341 . -tao_bnk_theta_i -  theta interpolation init factor
1342 - -tao_bnk_bound_tol -  initial tolerance used in estimating bounded active variables
1343 
1344   Level: beginner
1345 M*/
1346 
1347 PetscErrorCode TaoCreate_BNK(Tao tao)
1348 {
1349   TAO_BNK        *bnk;
1350   const char     *morethuente_type = TAOLINESEARCHMT;
1351   PetscErrorCode ierr;
1352 
1353   PetscFunctionBegin;
1354   ierr = PetscNewLog(tao,&bnk);CHKERRQ(ierr);
1355 
1356   tao->ops->setup = TaoSetUp_BNK;
1357   tao->ops->view = TaoView_BNK;
1358   tao->ops->setfromoptions = TaoSetFromOptions_BNK;
1359   tao->ops->destroy = TaoDestroy_BNK;
1360 
1361   /*  Override default settings (unless already changed) */
1362   if (!tao->max_it_changed) tao->max_it = 50;
1363   if (!tao->trust0_changed) tao->trust0 = 100.0;
1364 
1365   tao->data = (void*)bnk;
1366 
1367   /*  Hessian shifting parameters */
1368   bnk->sval   = 0.0;
1369   bnk->imin   = 1.0e-4;
1370   bnk->imax   = 1.0e+2;
1371   bnk->imfac  = 1.0e-1;
1372 
1373   bnk->pmin   = 1.0e-12;
1374   bnk->pmax   = 1.0e+2;
1375   bnk->pgfac  = 1.0e+1;
1376   bnk->psfac  = 4.0e-1;
1377   bnk->pmgfac = 1.0e-1;
1378   bnk->pmsfac = 1.0e-1;
1379 
1380   /*  Default values for trust-region radius update based on steplength */
1381   bnk->nu1 = 0.25;
1382   bnk->nu2 = 0.50;
1383   bnk->nu3 = 1.00;
1384   bnk->nu4 = 1.25;
1385 
1386   bnk->omega1 = 0.25;
1387   bnk->omega2 = 0.50;
1388   bnk->omega3 = 1.00;
1389   bnk->omega4 = 2.00;
1390   bnk->omega5 = 4.00;
1391 
1392   /*  Default values for trust-region radius update based on reduction */
1393   bnk->eta1 = 1.0e-4;
1394   bnk->eta2 = 0.25;
1395   bnk->eta3 = 0.50;
1396   bnk->eta4 = 0.90;
1397 
1398   bnk->alpha1 = 0.25;
1399   bnk->alpha2 = 0.50;
1400   bnk->alpha3 = 1.00;
1401   bnk->alpha4 = 2.00;
1402   bnk->alpha5 = 4.00;
1403 
1404   /*  Default values for trust-region radius update based on interpolation */
1405   bnk->mu1 = 0.10;
1406   bnk->mu2 = 0.50;
1407 
1408   bnk->gamma1 = 0.25;
1409   bnk->gamma2 = 0.50;
1410   bnk->gamma3 = 2.00;
1411   bnk->gamma4 = 4.00;
1412 
1413   bnk->theta = 0.05;
1414 
1415   /*  Default values for trust region initialization based on interpolation */
1416   bnk->mu1_i = 0.35;
1417   bnk->mu2_i = 0.50;
1418 
1419   bnk->gamma1_i = 0.0625;
1420   bnk->gamma2_i = 0.5;
1421   bnk->gamma3_i = 2.0;
1422   bnk->gamma4_i = 5.0;
1423 
1424   bnk->theta_i = 0.25;
1425 
1426   /*  Remaining parameters */
1427   bnk->max_cg_its = 0;
1428   bnk->min_radius = 1.0e-10;
1429   bnk->max_radius = 1.0e10;
1430   bnk->epsilon = PetscPowReal(PETSC_MACHINE_EPSILON, 2.0/3.0);
1431   bnk->as_tol = 1.0e-3;
1432   bnk->as_step = 1.0e-3;
1433   bnk->dmin = 1.0e-6;
1434   bnk->dmax = 1.0e6;
1435 
1436   bnk->pc_type         = BNK_PC_AHESS;
1437   bnk->bfgs_scale_type = BFGS_SCALE_PHESS;
1438   bnk->init_type       = BNK_INIT_INTERPOLATION;
1439   bnk->update_type     = BNK_UPDATE_INTERPOLATION;
1440   bnk->as_type         = BNK_AS_BERTSEKAS;
1441 
1442   /* Create the embedded BNCG solver */
1443   ierr = TaoCreate(PetscObjectComm((PetscObject)tao), &bnk->bncg);CHKERRQ(ierr);
1444   ierr = PetscObjectIncrementTabLevel((PetscObject)bnk->bncg, (PetscObject)tao, 1);CHKERRQ(ierr);
1445   ierr = TaoSetOptionsPrefix(bnk->bncg, "tao_bnk_");CHKERRQ(ierr);
1446   ierr = TaoSetType(bnk->bncg, TAOBNCG);CHKERRQ(ierr);
1447 
1448   /* Create the line search */
1449   ierr = TaoLineSearchCreate(((PetscObject)tao)->comm,&tao->linesearch);CHKERRQ(ierr);
1450   ierr = PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);CHKERRQ(ierr);
1451   ierr = TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);CHKERRQ(ierr);
1452   ierr = TaoLineSearchSetType(tao->linesearch,morethuente_type);CHKERRQ(ierr);
1453   ierr = TaoLineSearchUseTaoRoutines(tao->linesearch,tao);CHKERRQ(ierr);
1454 
1455   /*  Set linear solver to default for symmetric matrices */
1456   ierr = KSPCreate(((PetscObject)tao)->comm,&tao->ksp);CHKERRQ(ierr);
1457   ierr = PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1);CHKERRQ(ierr);
1458   ierr = KSPSetOptionsPrefix(tao->ksp,tao->hdr.prefix);CHKERRQ(ierr);
1459   ierr = KSPSetType(tao->ksp,KSPCGSTCG);CHKERRQ(ierr);
1460   PetscFunctionReturn(0);
1461 }
1462