xref: /petsc/src/tao/bound/impls/bnk/bnk.c (revision c0f10754485ee18591b934b1c07ed0e16c2beadd)
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, PetscBool *needH)
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;
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   /* Test the initial point for convergence */
57   ierr = TaoLogConvergenceHistory(tao,bnk->f,bnk->gnorm,0.0,tao->ksp_its);CHKERRQ(ierr);
58   ierr = TaoMonitor(tao,tao->niter,bnk->f,bnk->gnorm,0.0,1.0);CHKERRQ(ierr);
59   ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr);
60   if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
61 
62   /* Prep the embedded BNCG algorithm */
63   if (bnk->max_cg_its > 0) {
64     ierr = VecCopy(tao->solution, bnk->bncg_sol);CHKERRQ(ierr);
65     ierr = TaoCreate(PetscObjectComm((PetscObject)tao), &bnk->bncg);CHKERRQ(ierr);
66     ierr = PetscObjectIncrementTabLevel((PetscObject)bnk->bncg, (PetscObject)tao, 1);CHKERRQ(ierr);
67     ierr = TaoSetType(bnk->bncg, TAOBNCG);CHKERRQ(ierr);
68 
69     ierr = TaoSetInitialVector(bnk->bncg, bnk->bncg_sol);CHKERRQ(ierr);
70     ierr = TaoSetObjectiveRoutine(bnk->bncg, tao->ops->computeobjective, tao->user_objP);CHKERRQ(ierr);
71     ierr = TaoSetGradientRoutine(bnk->bncg, tao->ops->computegradient, tao->user_gradP);CHKERRQ(ierr);
72     ierr = TaoSetObjectiveAndGradientRoutine(bnk->bncg, tao->ops->computeobjectiveandgradient, tao->user_objgradP);CHKERRQ(ierr);
73 
74     ierr = TaoSetOptionsPrefix(bnk->bncg, "tao_bnk_bncg_");CHKERRQ(ierr);
75     ierr = TaoSetVariableBounds(bnk->bncg, tao->XL, tao->XU);CHKERRQ(ierr);
76     ierr = TaoSetMaximumIterations(bnk->bncg, bnk->max_cg_its);CHKERRQ(ierr);
77     ierr = TaoSetTolerances(bnk->bncg, tao->gatol, tao->grtol, tao->gttol);CHKERRQ(ierr);
78     ierr = TaoSetFunctionLowerBound(bnk->bncg, tao->fmin);CHKERRQ(ierr);
79     for (i=0; i<tao->numbermonitors; i++) {
80       ierr = TaoSetMonitor(bnk->bncg, tao->monitor[i], tao->monitorcontext[i], tao->monitordestroy[i]);CHKERRQ(ierr);
81       ierr = PetscObjectReference((PetscObject)(tao->monitorcontext[i]));CHKERRQ(ierr);
82     }
83     ierr = TaoSetFromOptions(bnk->bncg);
84     bnk->bncg_ctx = (TAO_BNCG *)bnk->bncg->data;
85   }
86 
87   /* Number of times ksp stopped because of these reasons */
88   bnk->ksp_atol = 0;
89   bnk->ksp_rtol = 0;
90   bnk->ksp_dtol = 0;
91   bnk->ksp_ctol = 0;
92   bnk->ksp_negc = 0;
93   bnk->ksp_iter = 0;
94   bnk->ksp_othr = 0;
95 
96   /* Initialize the Hessian perturbation */
97   bnk->pert = bnk->sval;
98 
99   /* Get vectors we will need */
100   if (BNK_PC_BFGS == bnk->pc_type && !bnk->M) {
101     ierr = VecGetLocalSize(tao->solution,&n);CHKERRQ(ierr);
102     ierr = VecGetSize(tao->solution,&N);CHKERRQ(ierr);
103     ierr = MatCreateLMVM(((PetscObject)tao)->comm,n,N,&bnk->M);CHKERRQ(ierr);
104     ierr = MatLMVMAllocateVectors(bnk->M,tao->solution);CHKERRQ(ierr);
105   }
106 
107   /* create vectors for the limited memory preconditioner */
108   if ((BNK_PC_BFGS == bnk->pc_type) && (BFGS_SCALE_BFGS != bnk->bfgs_scale_type)) {
109     if (!bnk->Diag) {ierr = VecDuplicate(tao->solution,&bnk->Diag);CHKERRQ(ierr);}
110   }
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       for (j = 0; j < j_max; ++j) {
155         f_min = bnk->f;
156         sigma = 0.0;
157 
158         if (*needH) {
159           /* Compute the Hessian at the new step, and extract the inactive subsystem */
160           ierr = TaoComputeHessian(tao, tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
161           ierr = MatDestroy(&bnk->H_inactive);
162           if (bnk->inactive_idx) {
163             ierr = ISDestroy(&bnk->inactive_idx);CHKERRQ(ierr);
164             ierr = VecWhichInactive(tao->XL,tao->solution,bnk->unprojected_gradient,tao->XU,PETSC_TRUE,&bnk->inactive_idx);CHKERRQ(ierr);
165             ierr = MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive);CHKERRQ(ierr);
166           } else {
167             ierr = MatDuplicate(tao->hessian, MAT_COPY_VALUES, &bnk->H_inactive);
168           }
169           *needH = PETSC_FALSE;
170         }
171 
172         for (i = 0; i < i_max; ++i) {
173           /* Take a steepest descent step and snap it to bounds */
174           ierr = VecCopy(tao->solution, bnk->Xold);CHKERRQ(ierr);
175           ierr = VecAXPY(tao->solution, -tao->trust/bnk->gnorm, tao->gradient);CHKERRQ(ierr);
176           ierr = VecMedian(tao->XL, tao->solution, tao->XU, tao->solution);CHKERRQ(ierr);
177           /* Recompute the step after bound snapping so that it can be used in predicted decrease calculation later */
178           ierr = VecCopy(tao->solution, bnk->W);CHKERRQ(ierr);
179           ierr = VecAXPY(bnk->W, -1.0, bnk->Xold);CHKERRQ(ierr);
180           /* Compute the objective at the trial */
181           ierr = TaoComputeObjective(tao, tao->solution, &ftrial);CHKERRQ(ierr);
182           ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr);
183           if (PetscIsInfOrNanReal(ftrial)) {
184             tau = bnk->gamma1_i;
185           } else {
186             if (ftrial < f_min) {
187               f_min = ftrial;
188               sigma = -tao->trust / bnk->gnorm;
189             }
190             /* Compute the predicted and actual reduction */
191             if (bnk->inactive_idx) {
192               ierr = VecGetSubVector(bnk->unprojected_gradient, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr);
193               ierr = VecGetSubVector(bnk->W, bnk->inactive_idx, &bnk->inactive_work);CHKERRQ(ierr);
194             } else {
195               bnk->G_inactive = bnk->unprojected_gradient;
196               bnk->inactive_work = bnk->W;
197             }
198             ierr = MatMult(bnk->H_inactive, bnk->G_inactive, bnk->inactive_work);CHKERRQ(ierr);
199             ierr = VecDot(bnk->G_inactive, bnk->inactive_work, &prered);CHKERRQ(ierr);
200             if (bnk->inactive_idx) {
201               ierr = VecRestoreSubVector(bnk->unprojected_gradient, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr);
202               ierr = VecRestoreSubVector(bnk->W, 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) && (PetscAbsScalar(prered) <= bnk->epsilon)) {
207               kappa = 1.0;
208             } else {
209               kappa = actred / prered;
210             }
211 
212             tau_1 = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust + (1.0 - bnk->theta_i) * prered - actred);
213             tau_2 = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust - (1.0 + bnk->theta_i) * prered + actred);
214             tau_min = PetscMin(tau_1, tau_2);
215             tau_max = PetscMax(tau_1, tau_2);
216 
217             if (PetscAbsScalar(kappa - 1.0) <= bnk->mu1_i) {
218               /* Great agreement */
219               max_radius = PetscMax(max_radius, tao->trust);
220 
221               if (tau_max < 1.0) {
222                 tau = bnk->gamma3_i;
223               } else if (tau_max > bnk->gamma4_i) {
224                 tau = bnk->gamma4_i;
225               } else if (tau_1 >= 1.0 && tau_1 <= bnk->gamma4_i && tau_2 < 1.0) {
226                 tau = tau_1;
227               } else if (tau_2 >= 1.0 && tau_2 <= bnk->gamma4_i && tau_1 < 1.0) {
228                 tau = tau_2;
229               } else {
230                 tau = tau_max;
231               }
232             } else if (PetscAbsScalar(kappa - 1.0) <= bnk->mu2_i) {
233               /* Good agreement */
234               max_radius = PetscMax(max_radius, tao->trust);
235 
236               if (tau_max < bnk->gamma2_i) {
237                 tau = bnk->gamma2_i;
238               } else if (tau_max > bnk->gamma3_i) {
239                 tau = bnk->gamma3_i;
240               } else {
241                 tau = tau_max;
242               }
243             } else {
244               /* Not good agreement */
245               if (tau_min > 1.0) {
246                 tau = bnk->gamma2_i;
247               } else if (tau_max < bnk->gamma1_i) {
248                 tau = bnk->gamma1_i;
249               } else if ((tau_min < bnk->gamma1_i) && (tau_max >= 1.0)) {
250                 tau = bnk->gamma1_i;
251               } else if ((tau_1 >= bnk->gamma1_i) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
252                 tau = tau_1;
253               } else if ((tau_2 >= bnk->gamma1_i) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
254                 tau = tau_2;
255               } else {
256                 tau = tau_max;
257               }
258             }
259           }
260           tao->trust = tau * tao->trust;
261 
262           /* Ensure that the trust radius is within the limits */
263           tao->trust = PetscMax(tao->trust, bnk->min_radius);
264           tao->trust = PetscMin(tao->trust, bnk->max_radius);
265         }
266 
267         if (f_min < bnk->f) {
268           bnk->f = f_min;
269           ierr = VecAXPY(tao->solution,sigma,tao->gradient);CHKERRQ(ierr);
270           ierr = VecMedian(tao->XL, tao->solution, tao->XU, tao->solution);CHKERRQ(ierr);
271           ierr = TaoComputeGradient(tao,tao->solution,bnk->unprojected_gradient);CHKERRQ(ierr);
272           ierr = VecBoundGradientProjection(bnk->unprojected_gradient,tao->solution,tao->XL,tao->XU,tao->gradient);CHKERRQ(ierr);
273 
274           ierr = TaoGradientNorm(tao, tao->gradient,NORM_2,&bnk->gnorm);CHKERRQ(ierr);
275           if (PetscIsInfOrNanReal(bnk->gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute gradient generated Inf or NaN");
276           *needH = PETSC_TRUE;
277 
278           ierr = TaoLogConvergenceHistory(tao,bnk->f,bnk->gnorm,0.0,tao->ksp_its);CHKERRQ(ierr);
279           ierr = TaoMonitor(tao,tao->niter,bnk->f,bnk->gnorm,0.0,1.0);CHKERRQ(ierr);
280           ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr);
281           if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
282         }
283       }
284       tao->trust = PetscMax(tao->trust, max_radius);
285       break;
286 
287     default:
288       /* Norm of the first direction will initialize radius */
289       tao->trust = 0.0;
290       break;
291     }
292   }
293   /* Set initial scaling for the BFGS preconditioner
294      This step is done after computing the initial trust-region radius
295      since the function value may have decreased */
296   if (BNK_PC_BFGS == bnk->pc_type) {
297     delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
298     ierr = MatLMVMSetDelta(bnk->M,delta);CHKERRQ(ierr);
299   }
300 
301   /* Set counter for gradient/reset steps*/
302   bnk->newt = 0;
303   bnk->bfgs = 0;
304   bnk->sgrad = 0;
305   bnk->grad = 0;
306   PetscFunctionReturn(0);
307 }
308 
309 /*------------------------------------------------------------*/
310 
311 /* Routine for computing the Hessian and preparing the preconditioner at the new iterate */
312 
313 PetscErrorCode TaoBNKComputeHessian(Tao tao)
314 {
315   PetscErrorCode               ierr;
316   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
317 
318   PetscFunctionBegin;
319   /* Compute the Hessian */
320   ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
321   /* Add a correction to the BFGS preconditioner */
322   if (BNK_PC_BFGS == bnk->pc_type) {
323     ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
324     /* Update the BFGS diagonal scaling */
325     if (BFGS_SCALE_AHESS == bnk->bfgs_scale_type) {
326       ierr = MatGetDiagonal(tao->hessian, bnk->Diag);CHKERRQ(ierr);
327       ierr = VecAbs(bnk->Diag);CHKERRQ(ierr);
328       ierr = VecMedian(bnk->Diag_min, bnk->Diag, bnk->Diag_max, bnk->Diag);CHKERRQ(ierr);
329       ierr = VecReciprocal(bnk->Diag);CHKERRQ(ierr);
330       ierr = MatLMVMSetScale(bnk->M,bnk->Diag);CHKERRQ(ierr);
331     }
332   }
333   PetscFunctionReturn(0);
334 }
335 
336 /*------------------------------------------------------------*/
337 
338 /* Routine for estimating the active set */
339 
340 PetscErrorCode TaoBNKEstimateActiveSet(Tao tao)
341 {
342   PetscErrorCode               ierr;
343   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
344 
345   PetscFunctionBegin;
346   switch (bnk->as_type) {
347   case BNK_AS_NONE:
348     ierr = ISDestroy(&bnk->inactive_idx);CHKERRQ(ierr);
349     ierr = VecWhichInactive(tao->XL, tao->solution, bnk->unprojected_gradient, tao->XU, PETSC_TRUE, &bnk->inactive_idx);CHKERRQ(ierr);
350     ierr = ISDestroy(&bnk->active_idx);CHKERRQ(ierr);
351     ierr = ISComplementVec(bnk->inactive_idx, tao->solution, &bnk->active_idx);CHKERRQ(ierr);
352     break;
353 
354   case BNK_AS_BERTSEKAS:
355     /* Compute the trial step vector with which we will estimate the active set at the next iteration */
356     if (BNK_PC_BFGS == bnk->pc_type) {
357       /* If the BFGS preconditioner matrix is available, we will construct a trial step with it */
358       ierr = MatLMVMSetInactive(bnk->M, NULL);CHKERRQ(ierr);
359       ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, bnk->W);CHKERRQ(ierr);
360     } else {
361       /* BFGS preconditioner doesn't exist so let's invert the absolute diagonal of the Hessian instead onto the gradient */
362       ierr = MatGetDiagonal(tao->hessian, bnk->Xwork);CHKERRQ(ierr);
363       ierr = VecAbs(bnk->Xwork);CHKERRQ(ierr);
364       ierr = VecMedian(bnk->Diag_min, bnk->Xwork, bnk->Diag_max, bnk->Xwork);CHKERRQ(ierr);
365       ierr = VecReciprocal(bnk->Xwork);CHKERRQ(ierr);CHKERRQ(ierr);
366       ierr = VecPointwiseMult(bnk->W, bnk->Xwork, bnk->unprojected_gradient);CHKERRQ(ierr);
367     }
368     ierr = VecScale(bnk->W, -1.0);CHKERRQ(ierr);
369     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);
370 
371   default:
372     break;
373   }
374   PetscFunctionReturn(0);
375 }
376 
377 /*------------------------------------------------------------*/
378 
379 /* Routine for bounding the step direction */
380 
381 PetscErrorCode TaoBNKBoundStep(Tao tao, Vec step)
382 {
383   PetscErrorCode               ierr;
384   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
385 
386   PetscFunctionBegin;
387   if (bnk->active_idx) {
388     switch (bnk->as_type) {
389     case BNK_AS_NONE:
390       if (bnk->active_idx) {
391         ierr = VecGetSubVector(step, bnk->active_idx, &bnk->active_work);CHKERRQ(ierr);
392         ierr = VecSet(bnk->active_work, 0.0);CHKERRQ(ierr);
393         ierr = VecRestoreSubVector(step, bnk->active_idx, &bnk->active_work);CHKERRQ(ierr);
394       }
395       break;
396 
397     case BNK_AS_BERTSEKAS:
398       ierr = TaoBoundStep(tao->solution, tao->XL, tao->XU, bnk->active_lower, bnk->active_upper, bnk->active_fixed, step);CHKERRQ(ierr);
399       break;
400 
401     default:
402       break;
403     }
404   }
405   PetscFunctionReturn(0);
406 }
407 
408 PetscErrorCode TaoBNKTakeCGSteps(Tao tao, PetscBool *terminate)
409 {
410   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
411   PetscErrorCode               ierr;
412 
413   PetscFunctionBegin;
414   *terminate = PETSC_FALSE;
415   if (bnk->max_cg_its > 0) {
416     /* Copy the current solution, unprojected gradient and step info into BNCG */
417     ierr = VecCopy(tao->solution, bnk->bncg->solution);CHKERRQ(ierr);
418     if (tao->niter > 1) {
419       bnk->bncg_ctx->f = bnk->f;
420       ierr = VecCopy(bnk->unprojected_gradient, bnk->bncg_ctx->unprojected_gradient);CHKERRQ(ierr);
421       ierr = VecCopy(tao->stepdirection, bnk->bncg->stepdirection);CHKERRQ(ierr);
422       ierr = TaoBNCGSetRecycleFlag(bnk->bncg, PETSC_TRUE);CHKERRQ(ierr);
423     }
424     /* Take some small finite number of BNCG iterations */
425     ierr = TaoSolve(bnk->bncg);CHKERRQ(ierr);
426     /* Add the number of gradient and function evaluations to the total */
427     tao->nfuncs += bnk->bncg->nfuncs;
428     tao->nfuncgrads += bnk->bncg->nfuncgrads;
429     tao->ngrads += bnk->bncg->ngrads;
430     tao->nhess += bnk->bncg->nhess;
431     /* Extract the BNCG solution out and save it into BNK */
432     bnk->f = bnk->bncg_ctx->f;
433     ierr = VecCopy(bnk->bncg->solution, tao->solution);
434     ierr = VecCopy(bnk->bncg_ctx->unprojected_gradient, bnk->unprojected_gradient);
435     ierr = VecCopy(bnk->bncg->gradient, tao->gradient);
436     /* Check to see if BNCG converged the problem */
437     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) {
438       *terminate = PETSC_TRUE;
439     }
440   }
441   PetscFunctionReturn(0);
442 }
443 
444 /*------------------------------------------------------------*/
445 
446 /* Routine for computing the Newton step. */
447 
448 PetscErrorCode TaoBNKComputeStep(Tao tao, PetscBool shift, KSPConvergedReason *ksp_reason)
449 {
450   PetscErrorCode               ierr;
451   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
452 
453   PetscReal                    delta;
454   PetscInt                     bfgsUpdates = 0;
455   PetscInt                     kspits;
456 
457   PetscFunctionBegin;
458   /* Determine the active and inactive sets */
459   ierr = TaoBNKEstimateActiveSet(tao);CHKERRQ(ierr);
460 
461   /* Prepare the reduced sub-matrices for the inactive set */
462   if (BNK_PC_BFGS == bnk->pc_type) { ierr = MatLMVMSetInactive(bnk->M, bnk->inactive_idx);CHKERRQ(ierr); }
463   if (bnk->inactive_idx) {
464     ierr = MatDestroy(&bnk->H_inactive);
465     ierr = MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive);CHKERRQ(ierr);
466     if (tao->hessian == tao->hessian_pre) {
467       bnk->Hpre_inactive = bnk->H_inactive;
468     } else {
469       ierr = MatDestroy(&bnk->Hpre_inactive);
470       ierr = MatCreateSubMatrix(tao->hessian_pre, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->Hpre_inactive);CHKERRQ(ierr);
471     }
472   } else {
473     ierr = MatDestroy(&bnk->H_inactive);
474     ierr = MatDuplicate(tao->hessian, MAT_COPY_VALUES, &bnk->H_inactive);
475     if (tao->hessian == tao->hessian_pre) {
476       bnk->Hpre_inactive = bnk->H_inactive;
477     } else {
478       ierr = MatDestroy(&bnk->Hpre_inactive);
479       ierr = MatDuplicate(tao->hessian_pre, MAT_COPY_VALUES, &bnk->Hpre_inactive);
480     }
481   }
482 
483   /* Shift the reduced Hessian matrix */
484   if ((shift) && (bnk->pert > 0)) {
485     ierr = MatShift(bnk->H_inactive, bnk->pert);CHKERRQ(ierr);
486     if (bnk->H_inactive != bnk->Hpre_inactive) {
487       ierr = MatShift(bnk->Hpre_inactive, bnk->pert);CHKERRQ(ierr);
488     }
489   }
490 
491   /* Update the diagonal scaling for the BFGS preconditioner, this time with the Hessian perturbation */
492   if ((BNK_PC_BFGS == bnk->pc_type) && (BFGS_SCALE_PHESS == bnk->bfgs_scale_type)) {
493     /* Obtain diagonal for the bfgs preconditioner  */
494     ierr = VecSet(bnk->Diag, 1.0);CHKERRQ(ierr);
495     if (bnk->inactive_idx) {
496       ierr = VecGetSubVector(bnk->Diag, bnk->inactive_idx, &bnk->Diag_red);CHKERRQ(ierr);
497     } else {
498       bnk->Diag_red = bnk->Diag;
499     }
500     ierr = MatGetDiagonal(bnk->H_inactive, bnk->Diag_red);CHKERRQ(ierr);
501     if (bnk->inactive_idx) {
502       ierr = VecRestoreSubVector(bnk->Diag, bnk->inactive_idx, &bnk->Diag_red);CHKERRQ(ierr);
503     }
504     ierr = VecAbs(bnk->Diag);CHKERRQ(ierr);
505     ierr = VecMedian(bnk->Diag_min, bnk->Diag, bnk->Diag_max, bnk->Diag);CHKERRQ(ierr);
506     ierr = VecReciprocal(bnk->Diag);CHKERRQ(ierr);
507     ierr = MatLMVMSetScale(bnk->M,bnk->Diag);CHKERRQ(ierr);
508   }
509 
510   /* Solve the Newton system of equations */
511   ierr = VecSet(tao->stepdirection, 0.0);CHKERRQ(ierr);
512   ierr = KSPReset(tao->ksp);CHKERRQ(ierr);
513   ierr = KSPSetOperators(tao->ksp,bnk->H_inactive,bnk->Hpre_inactive);CHKERRQ(ierr);
514   ierr = VecCopy(bnk->unprojected_gradient, bnk->Gwork);CHKERRQ(ierr);
515   if (bnk->inactive_idx) {
516     ierr = VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr);
517     ierr = VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr);
518   } else {
519     bnk->G_inactive = bnk->unprojected_gradient;
520     bnk->X_inactive = tao->stepdirection;
521   }
522   if (bnk->is_nash || bnk->is_stcg || bnk->is_gltr) {
523     ierr = KSPCGSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr);
524     ierr = KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);CHKERRQ(ierr);
525     ierr = KSPGetIterationNumber(tao->ksp,&kspits);CHKERRQ(ierr);
526     tao->ksp_its+=kspits;
527     tao->ksp_tot_its+=kspits;
528     ierr = KSPCGGetNormD(tao->ksp,&bnk->dnorm);CHKERRQ(ierr);
529 
530     if (0.0 == tao->trust) {
531       /* Radius was uninitialized; use the norm of the direction */
532       if (bnk->dnorm > 0.0) {
533         tao->trust = bnk->dnorm;
534 
535         /* Modify the radius if it is too large or small */
536         tao->trust = PetscMax(tao->trust, bnk->min_radius);
537         tao->trust = PetscMin(tao->trust, bnk->max_radius);
538       } else {
539         /* The direction was bad; set radius to default value and re-solve
540            the trust-region subproblem to get a direction */
541         tao->trust = tao->trust0;
542 
543         /* Modify the radius if it is too large or small */
544         tao->trust = PetscMax(tao->trust, bnk->min_radius);
545         tao->trust = PetscMin(tao->trust, bnk->max_radius);
546 
547         ierr = KSPCGSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr);
548         ierr = KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);CHKERRQ(ierr);
549         ierr = KSPGetIterationNumber(tao->ksp,&kspits);CHKERRQ(ierr);
550         tao->ksp_its+=kspits;
551         tao->ksp_tot_its+=kspits;
552         ierr = KSPCGGetNormD(tao->ksp,&bnk->dnorm);CHKERRQ(ierr);
553 
554         if (bnk->dnorm == 0.0) SETERRQ(PETSC_COMM_SELF,1, "Initial direction zero");
555       }
556     }
557   } else {
558     ierr = KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive);CHKERRQ(ierr);
559     ierr = KSPGetIterationNumber(tao->ksp, &kspits);CHKERRQ(ierr);
560     tao->ksp_its += kspits;
561     tao->ksp_tot_its+=kspits;
562   }
563   /* Restore sub vectors back */
564   if (bnk->inactive_idx) {
565     ierr = VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr);
566     ierr = VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr);
567   }
568   /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
569   ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
570   ierr = TaoBNKBoundStep(tao, tao->stepdirection);CHKERRQ(ierr);
571 
572   /* Record convergence reasons */
573   ierr = KSPGetConvergedReason(tao->ksp, ksp_reason);CHKERRQ(ierr);
574   if (KSP_CONVERGED_ATOL == *ksp_reason) {
575     ++bnk->ksp_atol;
576   } else if (KSP_CONVERGED_RTOL == *ksp_reason) {
577     ++bnk->ksp_rtol;
578   } else if (KSP_CONVERGED_CG_CONSTRAINED == *ksp_reason) {
579     ++bnk->ksp_ctol;
580   } else if (KSP_CONVERGED_CG_NEG_CURVE == *ksp_reason) {
581     ++bnk->ksp_negc;
582   } else if (KSP_DIVERGED_DTOL == *ksp_reason) {
583     ++bnk->ksp_dtol;
584   } else if (KSP_DIVERGED_ITS == *ksp_reason) {
585     ++bnk->ksp_iter;
586   } else {
587     ++bnk->ksp_othr;
588   }
589 
590   /* Make sure the BFGS preconditioner is healthy */
591   if (bnk->pc_type == BNK_PC_BFGS) {
592     ierr = MatLMVMGetUpdates(bnk->M, &bfgsUpdates);CHKERRQ(ierr);
593     if ((KSP_DIVERGED_INDEFINITE_PC == *ksp_reason) && (bfgsUpdates > 1)) {
594       /* Preconditioner is numerically indefinite; reset the approximation. */
595       delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
596       ierr = MatLMVMSetDelta(bnk->M,delta);CHKERRQ(ierr);
597       ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
598       ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
599     }
600   }
601   PetscFunctionReturn(0);
602 }
603 
604 /*------------------------------------------------------------*/
605 
606 /* Routine for recomputing the predicted reduction for a given step vector */
607 
608 PetscErrorCode TaoBNKRecomputePred(Tao tao, Vec S, PetscReal *prered)
609 {
610   PetscErrorCode               ierr;
611   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
612 
613   PetscFunctionBegin;
614   /* Extract subvectors associated with the inactive set */
615   if (bnk->inactive_idx){
616     ierr = VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr);
617     ierr = VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);CHKERRQ(ierr);
618     ierr = VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr);
619   } else {
620     bnk->X_inactive = tao->stepdirection;
621     bnk->inactive_work = bnk->Xwork;
622     bnk->G_inactive = bnk->Gwork;
623   }
624   /* Recompute the predicted decrease based on the quadratic model */
625   ierr = MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work);CHKERRQ(ierr);
626   ierr = VecAYPX(bnk->inactive_work, -0.5, bnk->G_inactive);CHKERRQ(ierr);
627   ierr = VecDot(bnk->inactive_work, bnk->X_inactive, prered);
628   /* Restore the sub vectors */
629   if (bnk->inactive_idx){
630     ierr = VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive);CHKERRQ(ierr);
631     ierr = VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work);CHKERRQ(ierr);
632     ierr = VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive);CHKERRQ(ierr);
633   }
634   PetscFunctionReturn(0);
635 }
636 
637 /*------------------------------------------------------------*/
638 
639 /* Routine for ensuring that the Newton step is a descent direction.
640 
641    The step direction falls back onto BFGS, scaled gradient and gradient steps
642    in the event that the Newton step fails the test.
643 */
644 
645 PetscErrorCode TaoBNKSafeguardStep(Tao tao, KSPConvergedReason ksp_reason, PetscInt *stepType)
646 {
647   PetscErrorCode               ierr;
648   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
649 
650   PetscReal                    gdx, delta, e_min;
651   PetscInt                     bfgsUpdates;
652 
653   PetscFunctionBegin;
654   ierr = VecDot(tao->stepdirection, tao->gradient, &gdx);CHKERRQ(ierr);
655   if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) {
656     /* Newton step is not descent or direction produced Inf or NaN
657        Update the perturbation for next time */
658     if (bnk->pert <= 0.0) {
659       /* Initialize the perturbation */
660       bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
661       if (bnk->is_gltr) {
662         ierr = KSPCGGLTRGetMinEig(tao->ksp,&e_min);CHKERRQ(ierr);
663         bnk->pert = PetscMax(bnk->pert, -e_min);
664       }
665     } else {
666       /* Increase the perturbation */
667       bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
668     }
669 
670     if (BNK_PC_BFGS != bnk->pc_type) {
671       /* We don't have the bfgs matrix around and updated
672          Must use gradient direction in this case */
673       ierr = VecCopy(tao->gradient, tao->stepdirection);CHKERRQ(ierr);
674       *stepType = BNK_GRADIENT;
675     } else {
676       /* Attempt to use the BFGS direction */
677       ierr = MatLMVMSetInactive(bnk->M, NULL);CHKERRQ(ierr);
678       ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
679 
680       /* Check for success (descent direction)
681          NOTE: Negative gdx here means not a descent direction because
682          the fall-back step is missing a negative sign. */
683       ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr);
684       if ((gdx <= 0) || PetscIsInfOrNanReal(gdx)) {
685         /* BFGS direction is not descent or direction produced not a number
686            We can assert bfgsUpdates > 1 in this case because
687            the first solve produces the scaled gradient direction,
688            which is guaranteed to be descent */
689 
690         /* Use steepest descent direction (scaled) */
691         delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
692         ierr = MatLMVMSetDelta(bnk->M, delta);CHKERRQ(ierr);
693         ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
694         ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
695         ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
696 
697         *stepType = BNK_SCALED_GRADIENT;
698       } else {
699         ierr = MatLMVMGetUpdates(bnk->M, &bfgsUpdates);CHKERRQ(ierr);
700         if (1 == bfgsUpdates) {
701           /* The first BFGS direction is always the scaled gradient */
702           *stepType = BNK_SCALED_GRADIENT;
703         } else {
704           *stepType = BNK_BFGS;
705         }
706       }
707     }
708     /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
709     ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
710     ierr = TaoBNKBoundStep(tao, tao->stepdirection);CHKERRQ(ierr);
711   } else {
712     /* Computed Newton step is descent */
713     switch (ksp_reason) {
714     case KSP_DIVERGED_NANORINF:
715     case KSP_DIVERGED_BREAKDOWN:
716     case KSP_DIVERGED_INDEFINITE_MAT:
717     case KSP_DIVERGED_INDEFINITE_PC:
718     case KSP_CONVERGED_CG_NEG_CURVE:
719       /* Matrix or preconditioner is indefinite; increase perturbation */
720       if (bnk->pert <= 0.0) {
721         /* Initialize the perturbation */
722         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
723         if (bnk->is_gltr) {
724           ierr = KSPCGGLTRGetMinEig(tao->ksp, &e_min);CHKERRQ(ierr);
725           bnk->pert = PetscMax(bnk->pert, -e_min);
726         }
727       } else {
728         /* Increase the perturbation */
729         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
730       }
731       break;
732 
733     default:
734       /* Newton step computation is good; decrease perturbation */
735       bnk->pert = PetscMin(bnk->psfac * bnk->pert, bnk->pmsfac * bnk->gnorm);
736       if (bnk->pert < bnk->pmin) {
737         bnk->pert = 0.0;
738       }
739       break;
740     }
741     *stepType = BNK_NEWTON;
742   }
743   PetscFunctionReturn(0);
744 }
745 
746 /*------------------------------------------------------------*/
747 
748 /* Routine for performing a bound-projected More-Thuente line search.
749 
750   Includes fallbacks to BFGS, scaled gradient, and unscaled gradient steps if the
751   Newton step does not produce a valid step length.
752 */
753 
754 PetscErrorCode TaoBNKPerformLineSearch(Tao tao, PetscInt stepType, PetscReal *steplen, TaoLineSearchConvergedReason *reason)
755 {
756   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
757   PetscErrorCode ierr;
758   TaoLineSearchConvergedReason ls_reason;
759 
760   PetscReal      e_min, gdx, delta;
761   PetscInt       bfgsUpdates;
762 
763   PetscFunctionBegin;
764   /* Perform the linesearch */
765   ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason);CHKERRQ(ierr);
766   ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
767 
768   while (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER && (stepType != BNK_GRADIENT || stepType !=BNK_SCALED_GRADIENT)) {
769     /* Linesearch failed, revert solution */
770     bnk->f = bnk->fold;
771     ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr);
772     ierr = VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);CHKERRQ(ierr);
773 
774     switch(stepType) {
775     case BNK_NEWTON:
776       /* Failed to obtain acceptable iterate with Newton step
777          Update the perturbation for next time */
778       if (bnk->pert <= 0.0) {
779         /* Initialize the perturbation */
780         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
781         if (bnk->is_gltr) {
782           ierr = KSPCGGLTRGetMinEig(tao->ksp,&e_min);CHKERRQ(ierr);
783           bnk->pert = PetscMax(bnk->pert, -e_min);
784         }
785       } else {
786         /* Increase the perturbation */
787         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
788       }
789 
790       if (BNK_PC_BFGS != bnk->pc_type) {
791         /* We don't have the bfgs matrix around and being updated
792            Must use gradient direction in this case */
793         ierr = VecCopy(tao->gradient, tao->stepdirection);CHKERRQ(ierr);
794         stepType = BNK_GRADIENT;
795       } else {
796         /* Attempt to use the BFGS direction */
797         ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
798         /* Check for success (descent direction)
799            NOTE: Negative gdx means not a descent direction because the step here is missing a negative sign. */
800         ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr);
801         if ((gdx <= 0) || PetscIsInfOrNanReal(gdx)) {
802           /* BFGS direction is not descent or direction produced not a number
803              We can assert bfgsUpdates > 1 in this case
804              Use steepest descent direction (scaled) */
805           delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
806           ierr = MatLMVMSetDelta(bnk->M, delta);CHKERRQ(ierr);
807           ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
808           ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
809           ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
810 
811           bfgsUpdates = 1;
812           stepType = BNK_SCALED_GRADIENT;
813         } else {
814           ierr = MatLMVMGetUpdates(bnk->M, &bfgsUpdates);CHKERRQ(ierr);
815           if (1 == bfgsUpdates) {
816             /* The first BFGS direction is always the scaled gradient */
817             stepType = BNK_SCALED_GRADIENT;
818           } else {
819             stepType = BNK_BFGS;
820           }
821         }
822       }
823       break;
824 
825     case BNK_BFGS:
826       /* Can only enter if pc_type == BNK_PC_BFGS
827          Failed to obtain acceptable iterate with BFGS step
828          Attempt to use the scaled gradient direction */
829       delta = 2.0 * PetscMax(1.0, PetscAbsScalar(bnk->f)) / (bnk->gnorm*bnk->gnorm);
830       ierr = MatLMVMSetDelta(bnk->M, delta);CHKERRQ(ierr);
831       ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
832       ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
833       ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
834 
835       bfgsUpdates = 1;
836       stepType = BNK_SCALED_GRADIENT;
837       break;
838 
839     case BNK_SCALED_GRADIENT:
840       /* Can only enter if pc_type == BNK_PC_BFGS
841          The scaled gradient step did not produce a new iterate;
842          attemp to use the gradient direction.
843          Need to make sure we are not using a different diagonal scaling */
844       ierr = MatLMVMSetScale(bnk->M,0);CHKERRQ(ierr);
845       ierr = MatLMVMSetDelta(bnk->M,1.0);CHKERRQ(ierr);
846       ierr = MatLMVMReset(bnk->M);CHKERRQ(ierr);
847       ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
848       ierr = MatLMVMSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
849 
850       bfgsUpdates = 1;
851       stepType = BNK_GRADIENT;
852       break;
853     }
854     /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
855     ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
856     ierr = TaoBNKBoundStep(tao, tao->stepdirection);CHKERRQ(ierr);
857 
858     /* Perform one last line search with the fall-back step */
859     ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason);CHKERRQ(ierr);
860     ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
861   }
862   *reason = ls_reason;
863   PetscFunctionReturn(0);
864 }
865 
866 /*------------------------------------------------------------*/
867 
868 /* Routine for updating the trust radius.
869 
870   Function features three different update methods:
871   1) Line-search step length based
872   2) Predicted decrease on the CG quadratic model
873   3) Interpolation
874 */
875 
876 PetscErrorCode TaoBNKUpdateTrustRadius(Tao tao, PetscReal prered, PetscReal actred, PetscInt updateType, PetscInt stepType, PetscBool *accept)
877 {
878   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
879   PetscErrorCode ierr;
880 
881   PetscReal      step, kappa;
882   PetscReal      gdx, tau_1, tau_2, tau_min, tau_max;
883 
884   PetscFunctionBegin;
885   /* Update trust region radius */
886   *accept = PETSC_FALSE;
887   switch(updateType) {
888   case BNK_UPDATE_STEP:
889     *accept = PETSC_TRUE; /* always accept here because line search succeeded */
890     if (stepType == BNK_NEWTON) {
891       ierr = TaoLineSearchGetStepLength(tao->linesearch, &step);CHKERRQ(ierr);
892       if (step < bnk->nu1) {
893         /* Very bad step taken; reduce radius */
894         tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
895       } else if (step < bnk->nu2) {
896         /* Reasonably bad step taken; reduce radius */
897         tao->trust = bnk->omega2 * PetscMin(bnk->dnorm, tao->trust);
898       } else if (step < bnk->nu3) {
899         /*  Reasonable step was taken; leave radius alone */
900         if (bnk->omega3 < 1.0) {
901           tao->trust = bnk->omega3 * PetscMin(bnk->dnorm, tao->trust);
902         } else if (bnk->omega3 > 1.0) {
903           tao->trust = PetscMax(bnk->omega3 * bnk->dnorm, tao->trust);
904         }
905       } else if (step < bnk->nu4) {
906         /*  Full step taken; increase the radius */
907         tao->trust = PetscMax(bnk->omega4 * bnk->dnorm, tao->trust);
908       } else {
909         /*  More than full step taken; increase the radius */
910         tao->trust = PetscMax(bnk->omega5 * bnk->dnorm, tao->trust);
911       }
912     } else {
913       /*  Newton step was not good; reduce the radius */
914       tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
915     }
916     break;
917 
918   case BNK_UPDATE_REDUCTION:
919     if (stepType == BNK_NEWTON) {
920       if (prered < 0.0) {
921         /* The predicted reduction has the wrong sign.  This cannot
922            happen in infinite precision arithmetic.  Step should
923            be rejected! */
924         tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
925       }
926       else {
927         if (PetscIsInfOrNanReal(actred)) {
928           tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
929         } else {
930           if ((PetscAbsScalar(actred) <= PetscMax(1.0, PetscAbsScalar(bnk->f))*bnk->epsilon) &&
931               (PetscAbsScalar(prered) <= PetscMax(1.0, PetscAbsScalar(bnk->f))*bnk->epsilon)) {
932             kappa = 1.0;
933           }
934           else {
935             kappa = actred / prered;
936           }
937 
938           /* Accept or reject the step and update radius */
939           if (kappa < bnk->eta1) {
940             /* Reject the step */
941             tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
942           }
943           else {
944             /* Accept the step */
945             *accept = PETSC_TRUE;
946             /* Update the trust region radius only if the computed step is at the trust radius boundary */
947             if (bnk->dnorm == tao->trust) {
948               if (kappa < bnk->eta2) {
949                 /* Marginal bad step */
950                 tao->trust = bnk->alpha2 * tao->trust;
951               }
952               else if (kappa < bnk->eta3) {
953                 /* Reasonable step */
954                 tao->trust = bnk->alpha3 * tao->trust;
955               }
956               else if (kappa < bnk->eta4) {
957                 /* Good step */
958                 tao->trust = bnk->alpha4 * tao->trust;
959               }
960               else {
961                 /* Very good step */
962                 tao->trust = bnk->alpha5 * tao->trust;
963               }
964             }
965           }
966         }
967       }
968     } else {
969       /*  Newton step was not good; reduce the radius */
970       tao->trust = bnk->alpha1 * PetscMin(bnk->dnorm, tao->trust);
971     }
972     break;
973 
974   default:
975     if (stepType == BNK_NEWTON) {
976       if (prered < 0.0) {
977         /*  The predicted reduction has the wrong sign.  This cannot */
978         /*  happen in infinite precision arithmetic.  Step should */
979         /*  be rejected! */
980         tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
981       } else {
982         if (PetscIsInfOrNanReal(actred)) {
983           tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
984         } else {
985           if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) {
986             kappa = 1.0;
987           } else {
988             kappa = actred / prered;
989           }
990 
991           ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr);
992           tau_1 = bnk->theta * gdx / (bnk->theta * gdx - (1.0 - bnk->theta) * prered + actred);
993           tau_2 = bnk->theta * gdx / (bnk->theta * gdx + (1.0 + bnk->theta) * prered - actred);
994           tau_min = PetscMin(tau_1, tau_2);
995           tau_max = PetscMax(tau_1, tau_2);
996 
997           if (kappa >= 1.0 - bnk->mu1) {
998             /*  Great agreement */
999             *accept = PETSC_TRUE;
1000             if (tau_max < 1.0) {
1001               tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
1002             } else if (tau_max > bnk->gamma4) {
1003               tao->trust = PetscMax(tao->trust, bnk->gamma4 * bnk->dnorm);
1004             } else {
1005               tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
1006             }
1007           } else if (kappa >= 1.0 - bnk->mu2) {
1008             /*  Good agreement */
1009             *accept = PETSC_TRUE;
1010             if (tau_max < bnk->gamma2) {
1011               tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
1012             } else if (tau_max > bnk->gamma3) {
1013               tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
1014             } else if (tau_max < 1.0) {
1015               tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
1016             } else {
1017               tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
1018             }
1019           } else {
1020             /*  Not good agreement */
1021             if (tau_min > 1.0) {
1022               tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
1023             } else if (tau_max < bnk->gamma1) {
1024               tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
1025             } else if ((tau_min < bnk->gamma1) && (tau_max >= 1.0)) {
1026               tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
1027             } else if ((tau_1 >= bnk->gamma1) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1) || (tau_2 >= 1.0))) {
1028               tao->trust = tau_1 * PetscMin(tao->trust, bnk->dnorm);
1029             } else if ((tau_2 >= bnk->gamma1) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1) || (tau_2 >= 1.0))) {
1030               tao->trust = tau_2 * PetscMin(tao->trust, bnk->dnorm);
1031             } else {
1032               tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
1033             }
1034           }
1035         }
1036       }
1037     } else {
1038       /*  Newton step was not good; reduce the radius */
1039       tao->trust = bnk->gamma1 * PetscMin(bnk->dnorm, tao->trust);
1040     }
1041     break;
1042   }
1043   /* Make sure the radius does not violate min and max settings */
1044   tao->trust = PetscMin(tao->trust, bnk->max_radius);
1045   tao->trust = PetscMax(tao->trust, bnk->min_radius);
1046   PetscFunctionReturn(0);
1047 }
1048 
1049 /* ---------------------------------------------------------- */
1050 
1051 PetscErrorCode TaoBNKAddStepCounts(Tao tao, PetscInt stepType)
1052 {
1053   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1054 
1055   PetscFunctionBegin;
1056   switch (stepType) {
1057   case BNK_NEWTON:
1058     ++bnk->newt;
1059     break;
1060   case BNK_BFGS:
1061     ++bnk->bfgs;
1062     break;
1063   case BNK_SCALED_GRADIENT:
1064     ++bnk->sgrad;
1065     break;
1066   case BNK_GRADIENT:
1067     ++bnk->grad;
1068     break;
1069   default:
1070     break;
1071   }
1072   PetscFunctionReturn(0);
1073 }
1074 
1075 /* ---------------------------------------------------------- */
1076 
1077 PetscErrorCode TaoSetUp_BNK(Tao tao)
1078 {
1079   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1080   PetscErrorCode ierr;
1081   KSPType        ksp_type;
1082 
1083   PetscFunctionBegin;
1084   if (!tao->gradient) {ierr = VecDuplicate(tao->solution,&tao->gradient);CHKERRQ(ierr);}
1085   if (!tao->stepdirection) {ierr = VecDuplicate(tao->solution,&tao->stepdirection);CHKERRQ(ierr);}
1086   if (!bnk->W) {ierr = VecDuplicate(tao->solution,&bnk->W);CHKERRQ(ierr);}
1087   if (!bnk->Xold) {ierr = VecDuplicate(tao->solution,&bnk->Xold);CHKERRQ(ierr);}
1088   if (!bnk->Gold) {ierr = VecDuplicate(tao->solution,&bnk->Gold);CHKERRQ(ierr);}
1089   if (!bnk->Xwork) {ierr = VecDuplicate(tao->solution,&bnk->Xwork);CHKERRQ(ierr);}
1090   if (!bnk->Gwork) {ierr = VecDuplicate(tao->solution,&bnk->Gwork);CHKERRQ(ierr);}
1091   if (!bnk->unprojected_gradient) {ierr = VecDuplicate(tao->solution,&bnk->unprojected_gradient);CHKERRQ(ierr);}
1092   if (!bnk->unprojected_gradient_old) {ierr = VecDuplicate(tao->solution,&bnk->unprojected_gradient_old);CHKERRQ(ierr);}
1093   if (!bnk->Diag_min) {ierr = VecDuplicate(tao->solution,&bnk->Diag_min);CHKERRQ(ierr);}
1094   if (!bnk->Diag_max) {ierr = VecDuplicate(tao->solution,&bnk->Diag_max);CHKERRQ(ierr);}
1095   if (!bnk->bncg_sol && bnk->max_cg_its > 0) {ierr = VecDuplicate(tao->solution,&bnk->bncg_sol);CHKERRQ(ierr);}
1096   bnk->Diag = 0;
1097   bnk->Diag_red = 0;
1098   bnk->X_inactive = 0;
1099   bnk->G_inactive = 0;
1100   bnk->inactive_work = 0;
1101   bnk->active_work = 0;
1102   bnk->inactive_idx = 0;
1103   bnk->active_idx = 0;
1104   bnk->active_lower = 0;
1105   bnk->active_upper = 0;
1106   bnk->active_fixed = 0;
1107   bnk->M = 0;
1108   bnk->H_inactive = 0;
1109   bnk->Hpre_inactive = 0;
1110   ierr = KSPGetType(tao->ksp,&ksp_type);CHKERRQ(ierr);
1111   ierr = PetscStrcmp(ksp_type,KSPCGNASH,&bnk->is_nash);CHKERRQ(ierr);
1112   ierr = PetscStrcmp(ksp_type,KSPCGSTCG,&bnk->is_stcg);CHKERRQ(ierr);
1113   ierr = PetscStrcmp(ksp_type,KSPCGGLTR,&bnk->is_gltr);CHKERRQ(ierr);
1114   PetscFunctionReturn(0);
1115 }
1116 
1117 /*------------------------------------------------------------*/
1118 
1119 static PetscErrorCode TaoDestroy_BNK(Tao tao)
1120 {
1121   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1122   PetscErrorCode ierr;
1123 
1124   PetscFunctionBegin;
1125   if (tao->setupcalled) {
1126     ierr = VecDestroy(&bnk->W);CHKERRQ(ierr);
1127     ierr = VecDestroy(&bnk->Xold);CHKERRQ(ierr);
1128     ierr = VecDestroy(&bnk->Gold);CHKERRQ(ierr);
1129     ierr = VecDestroy(&bnk->Xwork);CHKERRQ(ierr);
1130     ierr = VecDestroy(&bnk->Gwork);CHKERRQ(ierr);
1131     ierr = VecDestroy(&bnk->unprojected_gradient);CHKERRQ(ierr);
1132     ierr = VecDestroy(&bnk->unprojected_gradient_old);CHKERRQ(ierr);
1133     ierr = VecDestroy(&bnk->Diag_min);CHKERRQ(ierr);
1134     ierr = VecDestroy(&bnk->Diag_max);CHKERRQ(ierr);
1135     if (bnk->max_cg_its > 0) {
1136       ierr = TaoDestroy(&bnk->bncg);CHKERRQ(ierr);
1137       ierr = VecDestroy(&bnk->bncg_sol);CHKERRQ(ierr);
1138     }
1139   }
1140   ierr = VecDestroy(&bnk->Diag);CHKERRQ(ierr);
1141   ierr = MatDestroy(&bnk->M);CHKERRQ(ierr);
1142   if (bnk->Hpre_inactive != tao->hessian_pre && bnk->Hpre_inactive != bnk->H_inactive) {ierr = MatDestroy(&bnk->Hpre_inactive);CHKERRQ(ierr);}
1143   if (bnk->H_inactive != tao->hessian) {ierr = MatDestroy(&bnk->H_inactive);CHKERRQ(ierr);}
1144   ierr = PetscFree(tao->data);CHKERRQ(ierr);
1145   PetscFunctionReturn(0);
1146 }
1147 
1148 /*------------------------------------------------------------*/
1149 
1150 static PetscErrorCode TaoSetFromOptions_BNK(PetscOptionItems *PetscOptionsObject,Tao tao)
1151 {
1152   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1153   PetscErrorCode ierr;
1154 
1155   PetscFunctionBegin;
1156   ierr = PetscOptionsHead(PetscOptionsObject,"Newton line search method for unconstrained optimization");CHKERRQ(ierr);
1157   ierr = PetscOptionsEList("-tao_bnk_pc_type", "pc type", "", BNK_PC, BNK_PC_TYPES, BNK_PC[bnk->pc_type], &bnk->pc_type, 0);CHKERRQ(ierr);
1158   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);
1159   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);
1160   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);
1161   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);
1162   ierr = PetscOptionsReal("-tao_bnk_sval", "perturbation starting value", "", bnk->sval, &bnk->sval,NULL);CHKERRQ(ierr);
1163   ierr = PetscOptionsReal("-tao_bnk_imin", "minimum initial perturbation", "", bnk->imin, &bnk->imin,NULL);CHKERRQ(ierr);
1164   ierr = PetscOptionsReal("-tao_bnk_imax", "maximum initial perturbation", "", bnk->imax, &bnk->imax,NULL);CHKERRQ(ierr);
1165   ierr = PetscOptionsReal("-tao_bnk_imfac", "initial merit factor", "", bnk->imfac, &bnk->imfac,NULL);CHKERRQ(ierr);
1166   ierr = PetscOptionsReal("-tao_bnk_pmin", "minimum perturbation", "", bnk->pmin, &bnk->pmin,NULL);CHKERRQ(ierr);
1167   ierr = PetscOptionsReal("-tao_bnk_pmax", "maximum perturbation", "", bnk->pmax, &bnk->pmax,NULL);CHKERRQ(ierr);
1168   ierr = PetscOptionsReal("-tao_bnk_pgfac", "growth factor", "", bnk->pgfac, &bnk->pgfac,NULL);CHKERRQ(ierr);
1169   ierr = PetscOptionsReal("-tao_bnk_psfac", "shrink factor", "", bnk->psfac, &bnk->psfac,NULL);CHKERRQ(ierr);
1170   ierr = PetscOptionsReal("-tao_bnk_pmgfac", "merit growth factor", "", bnk->pmgfac, &bnk->pmgfac,NULL);CHKERRQ(ierr);
1171   ierr = PetscOptionsReal("-tao_bnk_pmsfac", "merit shrink factor", "", bnk->pmsfac, &bnk->pmsfac,NULL);CHKERRQ(ierr);
1172   ierr = PetscOptionsReal("-tao_bnk_eta1", "poor steplength; reduce radius", "", bnk->eta1, &bnk->eta1,NULL);CHKERRQ(ierr);
1173   ierr = PetscOptionsReal("-tao_bnk_eta2", "reasonable steplength; leave radius alone", "", bnk->eta2, &bnk->eta2,NULL);CHKERRQ(ierr);
1174   ierr = PetscOptionsReal("-tao_bnk_eta3", "good steplength; increase radius", "", bnk->eta3, &bnk->eta3,NULL);CHKERRQ(ierr);
1175   ierr = PetscOptionsReal("-tao_bnk_eta4", "excellent steplength; greatly increase radius", "", bnk->eta4, &bnk->eta4,NULL);CHKERRQ(ierr);
1176   ierr = PetscOptionsReal("-tao_bnk_alpha1", "", "", bnk->alpha1, &bnk->alpha1,NULL);CHKERRQ(ierr);
1177   ierr = PetscOptionsReal("-tao_bnk_alpha2", "", "", bnk->alpha2, &bnk->alpha2,NULL);CHKERRQ(ierr);
1178   ierr = PetscOptionsReal("-tao_bnk_alpha3", "", "", bnk->alpha3, &bnk->alpha3,NULL);CHKERRQ(ierr);
1179   ierr = PetscOptionsReal("-tao_bnk_alpha4", "", "", bnk->alpha4, &bnk->alpha4,NULL);CHKERRQ(ierr);
1180   ierr = PetscOptionsReal("-tao_bnk_alpha5", "", "", bnk->alpha5, &bnk->alpha5,NULL);CHKERRQ(ierr);
1181   ierr = PetscOptionsReal("-tao_bnk_nu1", "poor steplength; reduce radius", "", bnk->nu1, &bnk->nu1,NULL);CHKERRQ(ierr);
1182   ierr = PetscOptionsReal("-tao_bnk_nu2", "reasonable steplength; leave radius alone", "", bnk->nu2, &bnk->nu2,NULL);CHKERRQ(ierr);
1183   ierr = PetscOptionsReal("-tao_bnk_nu3", "good steplength; increase radius", "", bnk->nu3, &bnk->nu3,NULL);CHKERRQ(ierr);
1184   ierr = PetscOptionsReal("-tao_bnk_nu4", "excellent steplength; greatly increase radius", "", bnk->nu4, &bnk->nu4,NULL);CHKERRQ(ierr);
1185   ierr = PetscOptionsReal("-tao_bnk_omega1", "", "", bnk->omega1, &bnk->omega1,NULL);CHKERRQ(ierr);
1186   ierr = PetscOptionsReal("-tao_bnk_omega2", "", "", bnk->omega2, &bnk->omega2,NULL);CHKERRQ(ierr);
1187   ierr = PetscOptionsReal("-tao_bnk_omega3", "", "", bnk->omega3, &bnk->omega3,NULL);CHKERRQ(ierr);
1188   ierr = PetscOptionsReal("-tao_bnk_omega4", "", "", bnk->omega4, &bnk->omega4,NULL);CHKERRQ(ierr);
1189   ierr = PetscOptionsReal("-tao_bnk_omega5", "", "", bnk->omega5, &bnk->omega5,NULL);CHKERRQ(ierr);
1190   ierr = PetscOptionsReal("-tao_bnk_mu1_i", "", "", bnk->mu1_i, &bnk->mu1_i,NULL);CHKERRQ(ierr);
1191   ierr = PetscOptionsReal("-tao_bnk_mu2_i", "", "", bnk->mu2_i, &bnk->mu2_i,NULL);CHKERRQ(ierr);
1192   ierr = PetscOptionsReal("-tao_bnk_gamma1_i", "", "", bnk->gamma1_i, &bnk->gamma1_i,NULL);CHKERRQ(ierr);
1193   ierr = PetscOptionsReal("-tao_bnk_gamma2_i", "", "", bnk->gamma2_i, &bnk->gamma2_i,NULL);CHKERRQ(ierr);
1194   ierr = PetscOptionsReal("-tao_bnk_gamma3_i", "", "", bnk->gamma3_i, &bnk->gamma3_i,NULL);CHKERRQ(ierr);
1195   ierr = PetscOptionsReal("-tao_bnk_gamma4_i", "", "", bnk->gamma4_i, &bnk->gamma4_i,NULL);CHKERRQ(ierr);
1196   ierr = PetscOptionsReal("-tao_bnk_theta_i", "", "", bnk->theta_i, &bnk->theta_i,NULL);CHKERRQ(ierr);
1197   ierr = PetscOptionsReal("-tao_bnk_mu1", "", "", bnk->mu1, &bnk->mu1,NULL);CHKERRQ(ierr);
1198   ierr = PetscOptionsReal("-tao_bnk_mu2", "", "", bnk->mu2, &bnk->mu2,NULL);CHKERRQ(ierr);
1199   ierr = PetscOptionsReal("-tao_bnk_gamma1", "", "", bnk->gamma1, &bnk->gamma1,NULL);CHKERRQ(ierr);
1200   ierr = PetscOptionsReal("-tao_bnk_gamma2", "", "", bnk->gamma2, &bnk->gamma2,NULL);CHKERRQ(ierr);
1201   ierr = PetscOptionsReal("-tao_bnk_gamma3", "", "", bnk->gamma3, &bnk->gamma3,NULL);CHKERRQ(ierr);
1202   ierr = PetscOptionsReal("-tao_bnk_gamma4", "", "", bnk->gamma4, &bnk->gamma4,NULL);CHKERRQ(ierr);
1203   ierr = PetscOptionsReal("-tao_bnk_theta", "", "", bnk->theta, &bnk->theta,NULL);CHKERRQ(ierr);
1204   ierr = PetscOptionsReal("-tao_bnk_min_radius", "lower bound on initial radius", "", bnk->min_radius, &bnk->min_radius,NULL);CHKERRQ(ierr);
1205   ierr = PetscOptionsReal("-tao_bnk_max_radius", "upper bound on radius", "", bnk->max_radius, &bnk->max_radius,NULL);CHKERRQ(ierr);
1206   ierr = PetscOptionsReal("-tao_bnk_epsilon", "tolerance used when computing actual and predicted reduction", "", bnk->epsilon, &bnk->epsilon,NULL);CHKERRQ(ierr);
1207   ierr = PetscOptionsReal("-tao_bnk_as_tol", "initial tolerance used when estimating actively bounded variables", "", bnk->as_tol, &bnk->as_tol,NULL);CHKERRQ(ierr);
1208   ierr = PetscOptionsReal("-tao_bnk_as_step", "step length used when estimating actively bounded variables", "", bnk->as_step, &bnk->as_step,NULL);CHKERRQ(ierr);
1209   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);
1210   ierr = PetscOptionsTail();CHKERRQ(ierr);
1211   ierr = TaoLineSearchSetFromOptions(tao->linesearch);CHKERRQ(ierr);
1212   ierr = KSPSetFromOptions(tao->ksp);CHKERRQ(ierr);
1213   PetscFunctionReturn(0);
1214 }
1215 
1216 /*------------------------------------------------------------*/
1217 
1218 static PetscErrorCode TaoView_BNK(Tao tao, PetscViewer viewer)
1219 {
1220   TAO_BNK        *bnk = (TAO_BNK *)tao->data;
1221   PetscInt       nrejects;
1222   PetscBool      isascii;
1223   PetscErrorCode ierr;
1224 
1225   PetscFunctionBegin;
1226   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);
1227   if (isascii) {
1228     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1229     if (BNK_PC_BFGS == bnk->pc_type && bnk->M) {
1230       ierr = MatLMVMGetRejects(bnk->M,&nrejects);CHKERRQ(ierr);
1231       ierr = PetscViewerASCIIPrintf(viewer, "Rejected matrix updates: %D\n",nrejects);CHKERRQ(ierr);
1232     }
1233     ierr = PetscViewerASCIIPrintf(viewer, "Newton steps: %D\n", bnk->newt);CHKERRQ(ierr);
1234     ierr = PetscViewerASCIIPrintf(viewer, "BFGS steps: %D\n", bnk->bfgs);CHKERRQ(ierr);
1235     ierr = PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %D\n", bnk->sgrad);CHKERRQ(ierr);
1236     ierr = PetscViewerASCIIPrintf(viewer, "Gradient steps: %D\n", bnk->grad);CHKERRQ(ierr);
1237     ierr = PetscViewerASCIIPrintf(viewer, "KSP termination reasons:\n");CHKERRQ(ierr);
1238     ierr = PetscViewerASCIIPrintf(viewer, "  atol: %D\n", bnk->ksp_atol);CHKERRQ(ierr);
1239     ierr = PetscViewerASCIIPrintf(viewer, "  rtol: %D\n", bnk->ksp_rtol);CHKERRQ(ierr);
1240     ierr = PetscViewerASCIIPrintf(viewer, "  ctol: %D\n", bnk->ksp_ctol);CHKERRQ(ierr);
1241     ierr = PetscViewerASCIIPrintf(viewer, "  negc: %D\n", bnk->ksp_negc);CHKERRQ(ierr);
1242     ierr = PetscViewerASCIIPrintf(viewer, "  dtol: %D\n", bnk->ksp_dtol);CHKERRQ(ierr);
1243     ierr = PetscViewerASCIIPrintf(viewer, "  iter: %D\n", bnk->ksp_iter);CHKERRQ(ierr);
1244     ierr = PetscViewerASCIIPrintf(viewer, "  othr: %D\n", bnk->ksp_othr);CHKERRQ(ierr);
1245     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1246   }
1247   PetscFunctionReturn(0);
1248 }
1249 
1250 /* ---------------------------------------------------------- */
1251 
1252 /*MC
1253   TAOBNK - Shared base-type for Bounded Newton-Krylov type algorithms.
1254   At each iteration, the BNK methods solve the symmetric
1255   system of equations to obtain the step diretion dk:
1256               Hk dk = -gk
1257   for free variables only. The step can be globalized either through
1258   trust-region methods, or a line search, or a heuristic mixture of both.
1259 
1260     Options Database Keys:
1261 + -tao_bnk_pc_type - "none","ahess","bfgs","petsc"
1262 . -tao_bnk_bfgs_scale_type - "ahess","phess","bfgs"
1263 . -tao_bnk_init_type - "constant","direction","interpolation"
1264 . -tao_bnk_update_type - "step","direction","interpolation"
1265 . -tao_bnk_as_type - "none","bertsekas"
1266 . -tao_bnk_sval - perturbation starting value
1267 . -tao_bnk_imin - minimum initial perturbation
1268 . -tao_bnk_imax - maximum initial perturbation
1269 . -tao_bnk_pmin - minimum perturbation
1270 . -tao_bnk_pmax - maximum perturbation
1271 . -tao_bnk_pgfac - growth factor
1272 . -tao_bnk_psfac - shrink factor
1273 . -tao_bnk_imfac - initial merit factor
1274 . -tao_bnk_pmgfac - merit growth factor
1275 . -tao_bnk_pmsfac - merit shrink factor
1276 . -tao_bnk_eta1 - poor steplength; reduce radius
1277 . -tao_bnk_eta2 - reasonable steplength; leave radius
1278 . -tao_bnk_eta3 - good steplength; increase readius
1279 . -tao_bnk_eta4 - excellent steplength; greatly increase radius
1280 . -tao_bnk_alpha1 - alpha1 reduction
1281 . -tao_bnk_alpha2 - alpha2 reduction
1282 . -tao_bnk_alpha3 - alpha3 reduction
1283 . -tao_bnk_alpha4 - alpha4 reduction
1284 . -tao_bnk_alpha - alpha5 reduction
1285 . -tao_bnk_mu1 - mu1 interpolation update
1286 . -tao_bnk_mu2 - mu2 interpolation update
1287 . -tao_bnk_gamma1 - gamma1 interpolation update
1288 . -tao_bnk_gamma2 - gamma2 interpolation update
1289 . -tao_bnk_gamma3 - gamma3 interpolation update
1290 . -tao_bnk_gamma4 - gamma4 interpolation update
1291 . -tao_bnk_theta - theta interpolation update
1292 . -tao_bnk_omega1 - omega1 step update
1293 . -tao_bnk_omega2 - omega2 step update
1294 . -tao_bnk_omega3 - omega3 step update
1295 . -tao_bnk_omega4 - omega4 step update
1296 . -tao_bnk_omega5 - omega5 step update
1297 . -tao_bnk_mu1_i -  mu1 interpolation init factor
1298 . -tao_bnk_mu2_i -  mu2 interpolation init factor
1299 . -tao_bnk_gamma1_i -  gamma1 interpolation init factor
1300 . -tao_bnk_gamma2_i -  gamma2 interpolation init factor
1301 . -tao_bnk_gamma3_i -  gamma3 interpolation init factor
1302 . -tao_bnk_gamma4_i -  gamma4 interpolation init factor
1303 . -tao_bnk_theta_i -  theta interpolation init factor
1304 - -tao_bnk_bound_tol -  initial tolerance used in estimating bounded active variables
1305 
1306   Level: beginner
1307 M*/
1308 
1309 PetscErrorCode TaoCreate_BNK(Tao tao)
1310 {
1311   TAO_BNK        *bnk;
1312   const char     *morethuente_type = TAOLINESEARCHMT;
1313   PetscErrorCode ierr;
1314 
1315   PetscFunctionBegin;
1316   ierr = PetscNewLog(tao,&bnk);CHKERRQ(ierr);
1317 
1318   tao->ops->setup = TaoSetUp_BNK;
1319   tao->ops->view = TaoView_BNK;
1320   tao->ops->setfromoptions = TaoSetFromOptions_BNK;
1321   tao->ops->destroy = TaoDestroy_BNK;
1322 
1323   /*  Override default settings (unless already changed) */
1324   if (!tao->max_it_changed) tao->max_it = 50;
1325   if (!tao->trust0_changed) tao->trust0 = 100.0;
1326 
1327   tao->data = (void*)bnk;
1328 
1329   /*  Hessian shifting parameters */
1330   bnk->sval   = 0.0;
1331   bnk->imin   = 1.0e-4;
1332   bnk->imax   = 1.0e+2;
1333   bnk->imfac  = 1.0e-1;
1334 
1335   bnk->pmin   = 1.0e-12;
1336   bnk->pmax   = 1.0e+2;
1337   bnk->pgfac  = 1.0e+1;
1338   bnk->psfac  = 4.0e-1;
1339   bnk->pmgfac = 1.0e-1;
1340   bnk->pmsfac = 1.0e-1;
1341 
1342   /*  Default values for trust-region radius update based on steplength */
1343   bnk->nu1 = 0.25;
1344   bnk->nu2 = 0.50;
1345   bnk->nu3 = 1.00;
1346   bnk->nu4 = 1.25;
1347 
1348   bnk->omega1 = 0.25;
1349   bnk->omega2 = 0.50;
1350   bnk->omega3 = 1.00;
1351   bnk->omega4 = 2.00;
1352   bnk->omega5 = 4.00;
1353 
1354   /*  Default values for trust-region radius update based on reduction */
1355   bnk->eta1 = 1.0e-4;
1356   bnk->eta2 = 0.25;
1357   bnk->eta3 = 0.50;
1358   bnk->eta4 = 0.90;
1359 
1360   bnk->alpha1 = 0.25;
1361   bnk->alpha2 = 0.50;
1362   bnk->alpha3 = 1.00;
1363   bnk->alpha4 = 2.00;
1364   bnk->alpha5 = 4.00;
1365 
1366   /*  Default values for trust-region radius update based on interpolation */
1367   bnk->mu1 = 0.10;
1368   bnk->mu2 = 0.50;
1369 
1370   bnk->gamma1 = 0.25;
1371   bnk->gamma2 = 0.50;
1372   bnk->gamma3 = 2.00;
1373   bnk->gamma4 = 4.00;
1374 
1375   bnk->theta = 0.05;
1376 
1377   /*  Default values for trust region initialization based on interpolation */
1378   bnk->mu1_i = 0.35;
1379   bnk->mu2_i = 0.50;
1380 
1381   bnk->gamma1_i = 0.0625;
1382   bnk->gamma2_i = 0.5;
1383   bnk->gamma3_i = 2.0;
1384   bnk->gamma4_i = 5.0;
1385 
1386   bnk->theta_i = 0.25;
1387 
1388   /*  Remaining parameters */
1389   bnk->max_cg_its = 0;
1390   bnk->min_radius = 1.0e-10;
1391   bnk->max_radius = 1.0e10;
1392   bnk->epsilon = PetscPowReal(PETSC_MACHINE_EPSILON, 2.0/3.0);
1393   bnk->as_tol = 1.0e-3;
1394   bnk->as_step = 1.0e-3;
1395   bnk->dmin = 1.0e-6;
1396   bnk->dmax = 1.0e6;
1397 
1398   bnk->pc_type         = BNK_PC_BFGS;
1399   bnk->bfgs_scale_type = BFGS_SCALE_PHESS;
1400   bnk->init_type       = BNK_INIT_INTERPOLATION;
1401   bnk->update_type     = BNK_UPDATE_INTERPOLATION;
1402   bnk->as_type         = BNK_AS_BERTSEKAS;
1403 
1404   /* Create the line search */
1405   ierr = TaoLineSearchCreate(((PetscObject)tao)->comm,&tao->linesearch);CHKERRQ(ierr);
1406   ierr = PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);CHKERRQ(ierr);
1407   ierr = TaoLineSearchSetType(tao->linesearch,morethuente_type);CHKERRQ(ierr);
1408   ierr = TaoLineSearchUseTaoRoutines(tao->linesearch,tao);CHKERRQ(ierr);
1409   ierr = TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);CHKERRQ(ierr);
1410 
1411   /*  Set linear solver to default for symmetric matrices */
1412   ierr = KSPCreate(((PetscObject)tao)->comm,&tao->ksp);CHKERRQ(ierr);
1413   ierr = PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1);CHKERRQ(ierr);
1414   ierr = KSPSetOptionsPrefix(tao->ksp,tao->hdr.prefix);CHKERRQ(ierr);
1415   ierr = KSPSetType(tao->ksp,KSPCGSTCG);CHKERRQ(ierr);
1416   PetscFunctionReturn(0);
1417 }
1418