xref: /petsc/src/tao/bound/impls/bnk/bnk.c (revision d2522c19e8fa9bca20aaca277941d9a63e71db6a)
1 #include <petsctaolinesearch.h>
2 #include <../src/tao/bound/impls/bnk/bnk.h>
3 #include <petscksp.h>
4 
5 static const char *BNK_INIT[64]   = {"constant", "direction", "interpolation"};
6 static const char *BNK_UPDATE[64] = {"step", "reduction", "interpolation"};
7 static const char *BNK_AS[64]     = {"none", "bertsekas"};
8 
9 /*------------------------------------------------------------*/
10 
11 /* Routine for initializing the KSP solver, the BFGS preconditioner, and the initial trust radius estimation */
12 
13 PetscErrorCode TaoBNKInitialize(Tao tao, PetscInt initType, PetscBool *needH) {
14   TAO_BNK          *bnk = (TAO_BNK *)tao->data;
15   PC                pc;
16   PetscReal         f_min, ftrial, prered, actred, kappa, sigma, resnorm;
17   PetscReal         tau, tau_1, tau_2, tau_max, tau_min, max_radius;
18   PetscBool         is_bfgs, is_jacobi, is_symmetric, sym_set;
19   PetscInt          n, N, nDiff;
20   PetscInt          i_max = 5;
21   PetscInt          j_max = 1;
22   PetscInt          i, j;
23   PetscVoidFunction kspTR;
24 
25   PetscFunctionBegin;
26   /* Project the current point onto the feasible set */
27   PetscCall(TaoComputeVariableBounds(tao));
28   PetscCall(TaoSetVariableBounds(bnk->bncg, tao->XL, tao->XU));
29   if (tao->bounded) PetscCall(TaoLineSearchSetVariableBounds(tao->linesearch, tao->XL, tao->XU));
30 
31   /* Project the initial point onto the feasible region */
32   PetscCall(TaoBoundSolution(tao->solution, tao->XL, tao->XU, 0.0, &nDiff, tao->solution));
33 
34   /* Check convergence criteria */
35   PetscCall(TaoComputeObjectiveAndGradient(tao, tao->solution, &bnk->f, bnk->unprojected_gradient));
36   PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
37   PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient));
38   PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
39   PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm));
40 
41   /* Test the initial point for convergence */
42   PetscCall(VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W));
43   PetscCall(VecNorm(bnk->W, NORM_2, &resnorm));
44   PetscCheck(!PetscIsInfOrNanReal(bnk->f) && !PetscIsInfOrNanReal(resnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
45   PetscCall(TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its));
46   PetscCall(TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, 1.0));
47   PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
48   if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
49 
50   /* Reset KSP stopping reason counters */
51   bnk->ksp_atol = 0;
52   bnk->ksp_rtol = 0;
53   bnk->ksp_dtol = 0;
54   bnk->ksp_ctol = 0;
55   bnk->ksp_negc = 0;
56   bnk->ksp_iter = 0;
57   bnk->ksp_othr = 0;
58 
59   /* Reset accepted step type counters */
60   bnk->tot_cg_its = 0;
61   bnk->newt       = 0;
62   bnk->bfgs       = 0;
63   bnk->sgrad      = 0;
64   bnk->grad       = 0;
65 
66   /* Initialize the Hessian perturbation */
67   bnk->pert = bnk->sval;
68 
69   /* Reset initial steplength to zero (this helps BNCG reset its direction internally) */
70   PetscCall(VecSet(tao->stepdirection, 0.0));
71 
72   /* Allocate the vectors needed for the BFGS approximation */
73   PetscCall(KSPGetPC(tao->ksp, &pc));
74   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCLMVM, &is_bfgs));
75   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCJACOBI, &is_jacobi));
76   if (is_bfgs) {
77     bnk->bfgs_pre = pc;
78     PetscCall(PCLMVMGetMatLMVM(bnk->bfgs_pre, &bnk->M));
79     PetscCall(VecGetLocalSize(tao->solution, &n));
80     PetscCall(VecGetSize(tao->solution, &N));
81     PetscCall(MatSetSizes(bnk->M, n, n, N, N));
82     PetscCall(MatLMVMAllocate(bnk->M, tao->solution, bnk->unprojected_gradient));
83     PetscCall(MatIsSymmetricKnown(bnk->M, &sym_set, &is_symmetric));
84     PetscCheck(sym_set && is_symmetric, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_INCOMP, "LMVM matrix in the LMVM preconditioner must be symmetric.");
85   } else if (is_jacobi) PetscCall(PCJacobiSetUseAbs(pc, PETSC_TRUE));
86 
87   /* Prepare the min/max vectors for safeguarding diagonal scales */
88   PetscCall(VecSet(bnk->Diag_min, bnk->dmin));
89   PetscCall(VecSet(bnk->Diag_max, bnk->dmax));
90 
91   /* Initialize trust-region radius.  The initialization is only performed
92      when we are using Nash, Steihaug-Toint or the Generalized Lanczos method. */
93   *needH = PETSC_TRUE;
94   PetscCall(PetscObjectQueryFunction((PetscObject)tao->ksp, "KSPCGSetRadius_C", &kspTR));
95   if (kspTR) {
96     switch (initType) {
97     case BNK_INIT_CONSTANT:
98       /* Use the initial radius specified */
99       tao->trust = tao->trust0;
100       break;
101 
102     case BNK_INIT_INTERPOLATION:
103       /* Use interpolation based on the initial Hessian */
104       max_radius = 0.0;
105       tao->trust = tao->trust0;
106       for (j = 0; j < j_max; ++j) {
107         f_min = bnk->f;
108         sigma = 0.0;
109 
110         if (*needH) {
111           /* Compute the Hessian at the new step, and extract the inactive subsystem */
112           PetscCall((*bnk->computehessian)(tao));
113           PetscCall(TaoBNKEstimateActiveSet(tao, BNK_AS_NONE));
114           PetscCall(MatDestroy(&bnk->H_inactive));
115           if (bnk->active_idx) {
116             PetscCall(MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive));
117           } else {
118             PetscCall(PetscObjectReference((PetscObject)tao->hessian));
119             bnk->H_inactive = tao->hessian;
120           }
121           *needH = PETSC_FALSE;
122         }
123 
124         for (i = 0; i < i_max; ++i) {
125           /* Take a steepest descent step and snap it to bounds */
126           PetscCall(VecCopy(tao->solution, bnk->Xold));
127           PetscCall(VecAXPY(tao->solution, -tao->trust / bnk->gnorm, tao->gradient));
128           PetscCall(TaoBoundSolution(tao->solution, tao->XL, tao->XU, 0.0, &nDiff, tao->solution));
129           /* Compute the step we actually accepted */
130           PetscCall(VecCopy(tao->solution, bnk->W));
131           PetscCall(VecAXPY(bnk->W, -1.0, bnk->Xold));
132           /* Compute the objective at the trial */
133           PetscCall(TaoComputeObjective(tao, tao->solution, &ftrial));
134           PetscCheck(!PetscIsInfOrNanReal(bnk->f), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
135           PetscCall(VecCopy(bnk->Xold, tao->solution));
136           if (PetscIsInfOrNanReal(ftrial)) {
137             tau = bnk->gamma1_i;
138           } else {
139             if (ftrial < f_min) {
140               f_min = ftrial;
141               sigma = -tao->trust / bnk->gnorm;
142             }
143 
144             /* Compute the predicted and actual reduction */
145             if (bnk->active_idx) {
146               PetscCall(VecGetSubVector(bnk->W, bnk->inactive_idx, &bnk->X_inactive));
147               PetscCall(VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work));
148             } else {
149               bnk->X_inactive    = bnk->W;
150               bnk->inactive_work = bnk->Xwork;
151             }
152             PetscCall(MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work));
153             PetscCall(VecDot(bnk->X_inactive, bnk->inactive_work, &prered));
154             if (bnk->active_idx) {
155               PetscCall(VecRestoreSubVector(bnk->W, bnk->inactive_idx, &bnk->X_inactive));
156               PetscCall(VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work));
157             }
158             prered = tao->trust * (bnk->gnorm - 0.5 * tao->trust * prered / (bnk->gnorm * bnk->gnorm));
159             actred = bnk->f - ftrial;
160             if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) {
161               kappa = 1.0;
162             } else {
163               kappa = actred / prered;
164             }
165 
166             tau_1   = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust + (1.0 - bnk->theta_i) * prered - actred);
167             tau_2   = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust - (1.0 + bnk->theta_i) * prered + actred);
168             tau_min = PetscMin(tau_1, tau_2);
169             tau_max = PetscMax(tau_1, tau_2);
170 
171             if (PetscAbsScalar(kappa - (PetscReal)1.0) <= bnk->mu1_i) {
172               /*  Great agreement */
173               max_radius = PetscMax(max_radius, tao->trust);
174 
175               if (tau_max < 1.0) {
176                 tau = bnk->gamma3_i;
177               } else if (tau_max > bnk->gamma4_i) {
178                 tau = bnk->gamma4_i;
179               } else {
180                 tau = tau_max;
181               }
182             } else if (PetscAbsScalar(kappa - (PetscReal)1.0) <= bnk->mu2_i) {
183               /*  Good agreement */
184               max_radius = PetscMax(max_radius, tao->trust);
185 
186               if (tau_max < bnk->gamma2_i) {
187                 tau = bnk->gamma2_i;
188               } else if (tau_max > bnk->gamma3_i) {
189                 tau = bnk->gamma3_i;
190               } else {
191                 tau = tau_max;
192               }
193             } else {
194               /*  Not good agreement */
195               if (tau_min > 1.0) {
196                 tau = bnk->gamma2_i;
197               } else if (tau_max < bnk->gamma1_i) {
198                 tau = bnk->gamma1_i;
199               } else if ((tau_min < bnk->gamma1_i) && (tau_max >= 1.0)) {
200                 tau = bnk->gamma1_i;
201               } else if ((tau_1 >= bnk->gamma1_i) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
202                 tau = tau_1;
203               } else if ((tau_2 >= bnk->gamma1_i) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1_i) || (tau_2 >= 1.0))) {
204                 tau = tau_2;
205               } else {
206                 tau = tau_max;
207               }
208             }
209           }
210           tao->trust = tau * tao->trust;
211         }
212 
213         if (f_min < bnk->f) {
214           /* We accidentally found a solution better than the initial, so accept it */
215           bnk->f = f_min;
216           PetscCall(VecCopy(tao->solution, bnk->Xold));
217           PetscCall(VecAXPY(tao->solution, sigma, tao->gradient));
218           PetscCall(TaoBoundSolution(tao->solution, tao->XL, tao->XU, 0.0, &nDiff, tao->solution));
219           PetscCall(VecCopy(tao->solution, tao->stepdirection));
220           PetscCall(VecAXPY(tao->stepdirection, -1.0, bnk->Xold));
221           PetscCall(TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient));
222           PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
223           PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient));
224           PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
225           /* Compute gradient at the new iterate and flip switch to compute the Hessian later */
226           PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm));
227           *needH = PETSC_TRUE;
228           /* Test the new step for convergence */
229           PetscCall(VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W));
230           PetscCall(VecNorm(bnk->W, NORM_2, &resnorm));
231           PetscCheck(!PetscIsInfOrNanReal(resnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
232           PetscCall(TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its));
233           PetscCall(TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, 1.0));
234           PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
235           if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
236           /* active BNCG recycling early because we have a stepdirection computed */
237           PetscCall(TaoSetRecycleHistory(bnk->bncg, PETSC_TRUE));
238         }
239       }
240       tao->trust = PetscMax(tao->trust, max_radius);
241 
242       /* Ensure that the trust radius is within the limits */
243       tao->trust = PetscMax(tao->trust, bnk->min_radius);
244       tao->trust = PetscMin(tao->trust, bnk->max_radius);
245       break;
246 
247     default:
248       /* Norm of the first direction will initialize radius */
249       tao->trust = 0.0;
250       break;
251     }
252   }
253   PetscFunctionReturn(0);
254 }
255 
256 /*------------------------------------------------------------*/
257 
258 /* Routine for computing the exact Hessian and preparing the preconditioner at the new iterate */
259 
260 PetscErrorCode TaoBNKComputeHessian(Tao tao) {
261   TAO_BNK *bnk = (TAO_BNK *)tao->data;
262 
263   PetscFunctionBegin;
264   /* Compute the Hessian */
265   PetscCall(TaoComputeHessian(tao, tao->solution, tao->hessian, tao->hessian_pre));
266   /* Add a correction to the BFGS preconditioner */
267   if (bnk->M) PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
268   /* Prepare the reduced sub-matrices for the inactive set */
269   PetscCall(MatDestroy(&bnk->Hpre_inactive));
270   PetscCall(MatDestroy(&bnk->H_inactive));
271   if (bnk->active_idx) {
272     PetscCall(MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive));
273     if (tao->hessian == tao->hessian_pre) {
274       PetscCall(PetscObjectReference((PetscObject)bnk->H_inactive));
275       bnk->Hpre_inactive = bnk->H_inactive;
276     } else {
277       PetscCall(MatCreateSubMatrix(tao->hessian_pre, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->Hpre_inactive));
278     }
279     if (bnk->bfgs_pre) PetscCall(PCLMVMSetIS(bnk->bfgs_pre, bnk->inactive_idx));
280   } else {
281     PetscCall(PetscObjectReference((PetscObject)tao->hessian));
282     bnk->H_inactive = tao->hessian;
283     if (tao->hessian == tao->hessian_pre) {
284       PetscCall(PetscObjectReference((PetscObject)bnk->H_inactive));
285       bnk->Hpre_inactive = bnk->H_inactive;
286     } else {
287       PetscCall(PetscObjectReference((PetscObject)tao->hessian_pre));
288       bnk->Hpre_inactive = tao->hessian_pre;
289     }
290     if (bnk->bfgs_pre) PetscCall(PCLMVMClearIS(bnk->bfgs_pre));
291   }
292   PetscFunctionReturn(0);
293 }
294 
295 /*------------------------------------------------------------*/
296 
297 /* Routine for estimating the active set */
298 
299 PetscErrorCode TaoBNKEstimateActiveSet(Tao tao, PetscInt asType) {
300   TAO_BNK  *bnk = (TAO_BNK *)tao->data;
301   PetscBool hessComputed, diagExists, hadactive;
302 
303   PetscFunctionBegin;
304   hadactive = bnk->active_idx ? PETSC_TRUE : PETSC_FALSE;
305   switch (asType) {
306   case BNK_AS_NONE:
307     PetscCall(ISDestroy(&bnk->inactive_idx));
308     PetscCall(VecWhichInactive(tao->XL, tao->solution, bnk->unprojected_gradient, tao->XU, PETSC_TRUE, &bnk->inactive_idx));
309     PetscCall(ISDestroy(&bnk->active_idx));
310     PetscCall(ISComplementVec(bnk->inactive_idx, tao->solution, &bnk->active_idx));
311     break;
312 
313   case BNK_AS_BERTSEKAS:
314     /* Compute the trial step vector with which we will estimate the active set at the next iteration */
315     if (bnk->M) {
316       /* If the BFGS preconditioner matrix is available, we will construct a trial step with it */
317       PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, bnk->W));
318     } else {
319       hessComputed = diagExists = PETSC_FALSE;
320       if (tao->hessian) { PetscCall(MatAssembled(tao->hessian, &hessComputed)); }
321       if (hessComputed) { PetscCall(MatHasOperation(tao->hessian, MATOP_GET_DIAGONAL, &diagExists)); }
322       if (diagExists) {
323         /* BFGS preconditioner doesn't exist so let's invert the absolute diagonal of the Hessian instead onto the gradient */
324         PetscCall(MatGetDiagonal(tao->hessian, bnk->Xwork));
325         PetscCall(VecAbs(bnk->Xwork));
326         PetscCall(VecMedian(bnk->Diag_min, bnk->Xwork, bnk->Diag_max, bnk->Xwork));
327         PetscCall(VecReciprocal(bnk->Xwork));
328         PetscCall(VecPointwiseMult(bnk->W, bnk->Xwork, bnk->unprojected_gradient));
329       } else {
330         /* If the Hessian or its diagonal does not exist, we will simply use gradient step */
331         PetscCall(VecCopy(bnk->unprojected_gradient, bnk->W));
332       }
333     }
334     PetscCall(VecScale(bnk->W, -1.0));
335     PetscCall(TaoEstimateActiveBounds(tao->solution, tao->XL, tao->XU, bnk->unprojected_gradient, bnk->W, bnk->Xwork, bnk->as_step, &bnk->as_tol, &bnk->active_lower, &bnk->active_upper, &bnk->active_fixed, &bnk->active_idx, &bnk->inactive_idx));
336     break;
337 
338   default: break;
339   }
340   bnk->resetksp = (PetscBool)(bnk->active_idx || hadactive); /* inactive Hessian size may have changed, need to reset operators */
341   PetscFunctionReturn(0);
342 }
343 
344 /*------------------------------------------------------------*/
345 
346 /* Routine for bounding the step direction */
347 
348 PetscErrorCode TaoBNKBoundStep(Tao tao, PetscInt asType, Vec step) {
349   TAO_BNK *bnk = (TAO_BNK *)tao->data;
350 
351   PetscFunctionBegin;
352   switch (asType) {
353   case BNK_AS_NONE: PetscCall(VecISSet(step, bnk->active_idx, 0.0)); break;
354 
355   case BNK_AS_BERTSEKAS: PetscCall(TaoBoundStep(tao->solution, tao->XL, tao->XU, bnk->active_lower, bnk->active_upper, bnk->active_fixed, 1.0, step)); break;
356 
357   default: break;
358   }
359   PetscFunctionReturn(0);
360 }
361 
362 /*------------------------------------------------------------*/
363 
364 /* Routine for taking a finite number of BNCG iterations to
365    accelerate Newton convergence.
366 
367    In practice, this approach simply trades off Hessian evaluations
368    for more gradient evaluations.
369 */
370 
371 PetscErrorCode TaoBNKTakeCGSteps(Tao tao, PetscBool *terminate) {
372   TAO_BNK *bnk = (TAO_BNK *)tao->data;
373 
374   PetscFunctionBegin;
375   *terminate = PETSC_FALSE;
376   if (bnk->max_cg_its > 0) {
377     /* Copy the current function value (important vectors are already shared) */
378     bnk->bncg_ctx->f = bnk->f;
379     /* Take some small finite number of BNCG iterations */
380     PetscCall(TaoSolve(bnk->bncg));
381     /* Add the number of gradient and function evaluations to the total */
382     tao->nfuncs += bnk->bncg->nfuncs;
383     tao->nfuncgrads += bnk->bncg->nfuncgrads;
384     tao->ngrads += bnk->bncg->ngrads;
385     tao->nhess += bnk->bncg->nhess;
386     bnk->tot_cg_its += bnk->bncg->niter;
387     /* Extract the BNCG function value out and save it into BNK */
388     bnk->f = bnk->bncg_ctx->f;
389     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) {
390       *terminate = PETSC_TRUE;
391     } else {
392       PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
393     }
394   }
395   PetscFunctionReturn(0);
396 }
397 
398 /*------------------------------------------------------------*/
399 
400 /* Routine for computing the Newton step. */
401 
402 PetscErrorCode TaoBNKComputeStep(Tao tao, PetscBool shift, KSPConvergedReason *ksp_reason, PetscInt *step_type) {
403   TAO_BNK          *bnk         = (TAO_BNK *)tao->data;
404   PetscInt          bfgsUpdates = 0;
405   PetscInt          kspits;
406   PetscBool         is_lmvm;
407   PetscVoidFunction kspTR;
408 
409   PetscFunctionBegin;
410   /* If there are no inactive variables left, save some computation and return an adjusted zero step
411      that has (l-x) and (u-x) for lower and upper bounded variables. */
412   if (!bnk->inactive_idx) {
413     PetscCall(VecSet(tao->stepdirection, 0.0));
414     PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));
415     PetscFunctionReturn(0);
416   }
417 
418   /* Shift the reduced Hessian matrix */
419   if (shift && bnk->pert > 0) {
420     PetscCall(PetscObjectTypeCompare((PetscObject)tao->hessian, MATLMVM, &is_lmvm));
421     if (is_lmvm) {
422       PetscCall(MatShift(tao->hessian, bnk->pert));
423     } else {
424       PetscCall(MatShift(bnk->H_inactive, bnk->pert));
425       if (bnk->H_inactive != bnk->Hpre_inactive) { PetscCall(MatShift(bnk->Hpre_inactive, bnk->pert)); }
426     }
427   }
428 
429   /* Solve the Newton system of equations */
430   tao->ksp_its = 0;
431   PetscCall(VecSet(tao->stepdirection, 0.0));
432   if (bnk->resetksp) {
433     PetscCall(KSPReset(tao->ksp));
434     PetscCall(KSPResetFromOptions(tao->ksp));
435     bnk->resetksp = PETSC_FALSE;
436   }
437   PetscCall(KSPSetOperators(tao->ksp, bnk->H_inactive, bnk->Hpre_inactive));
438   PetscCall(VecCopy(bnk->unprojected_gradient, bnk->Gwork));
439   if (bnk->active_idx) {
440     PetscCall(VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive));
441     PetscCall(VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive));
442   } else {
443     bnk->G_inactive = bnk->unprojected_gradient;
444     bnk->X_inactive = tao->stepdirection;
445   }
446   PetscCall(KSPCGSetRadius(tao->ksp, tao->trust));
447   PetscCall(KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive));
448   PetscCall(KSPGetIterationNumber(tao->ksp, &kspits));
449   tao->ksp_its += kspits;
450   tao->ksp_tot_its += kspits;
451   PetscCall(PetscObjectQueryFunction((PetscObject)tao->ksp, "KSPCGGetNormD_C", &kspTR));
452   if (kspTR) {
453     PetscCall(KSPCGGetNormD(tao->ksp, &bnk->dnorm));
454 
455     if (0.0 == tao->trust) {
456       /* Radius was uninitialized; use the norm of the direction */
457       if (bnk->dnorm > 0.0) {
458         tao->trust = bnk->dnorm;
459 
460         /* Modify the radius if it is too large or small */
461         tao->trust = PetscMax(tao->trust, bnk->min_radius);
462         tao->trust = PetscMin(tao->trust, bnk->max_radius);
463       } else {
464         /* The direction was bad; set radius to default value and re-solve
465            the trust-region subproblem to get a direction */
466         tao->trust = tao->trust0;
467 
468         /* Modify the radius if it is too large or small */
469         tao->trust = PetscMax(tao->trust, bnk->min_radius);
470         tao->trust = PetscMin(tao->trust, bnk->max_radius);
471 
472         PetscCall(KSPCGSetRadius(tao->ksp, tao->trust));
473         PetscCall(KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive));
474         PetscCall(KSPGetIterationNumber(tao->ksp, &kspits));
475         tao->ksp_its += kspits;
476         tao->ksp_tot_its += kspits;
477         PetscCall(KSPCGGetNormD(tao->ksp, &bnk->dnorm));
478 
479         PetscCheck(bnk->dnorm != 0.0, PetscObjectComm((PetscObject)tao), PETSC_ERR_PLIB, "Initial direction zero");
480       }
481     }
482   }
483   /* Restore sub vectors back */
484   if (bnk->active_idx) {
485     PetscCall(VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive));
486     PetscCall(VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive));
487   }
488   /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
489   PetscCall(VecScale(tao->stepdirection, -1.0));
490   PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));
491 
492   /* Record convergence reasons */
493   PetscCall(KSPGetConvergedReason(tao->ksp, ksp_reason));
494   if (KSP_CONVERGED_ATOL == *ksp_reason) {
495     ++bnk->ksp_atol;
496   } else if (KSP_CONVERGED_RTOL == *ksp_reason) {
497     ++bnk->ksp_rtol;
498   } else if (KSP_CONVERGED_CG_CONSTRAINED == *ksp_reason) {
499     ++bnk->ksp_ctol;
500   } else if (KSP_CONVERGED_CG_NEG_CURVE == *ksp_reason) {
501     ++bnk->ksp_negc;
502   } else if (KSP_DIVERGED_DTOL == *ksp_reason) {
503     ++bnk->ksp_dtol;
504   } else if (KSP_DIVERGED_ITS == *ksp_reason) {
505     ++bnk->ksp_iter;
506   } else {
507     ++bnk->ksp_othr;
508   }
509 
510   /* Make sure the BFGS preconditioner is healthy */
511   if (bnk->M) {
512     PetscCall(MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates));
513     if ((KSP_DIVERGED_INDEFINITE_PC == *ksp_reason) && (bfgsUpdates > 0)) {
514       /* Preconditioner is numerically indefinite; reset the approximation. */
515       PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
516       PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
517     }
518   }
519   *step_type = BNK_NEWTON;
520   PetscFunctionReturn(0);
521 }
522 
523 /*------------------------------------------------------------*/
524 
525 /* Routine for recomputing the predicted reduction for a given step vector */
526 
527 PetscErrorCode TaoBNKRecomputePred(Tao tao, Vec S, PetscReal *prered) {
528   TAO_BNK *bnk = (TAO_BNK *)tao->data;
529 
530   PetscFunctionBegin;
531   /* Extract subvectors associated with the inactive set */
532   if (bnk->active_idx) {
533     PetscCall(VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive));
534     PetscCall(VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work));
535     PetscCall(VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive));
536   } else {
537     bnk->X_inactive    = tao->stepdirection;
538     bnk->inactive_work = bnk->Xwork;
539     bnk->G_inactive    = bnk->Gwork;
540   }
541   /* Recompute the predicted decrease based on the quadratic model */
542   PetscCall(MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work));
543   PetscCall(VecAYPX(bnk->inactive_work, -0.5, bnk->G_inactive));
544   PetscCall(VecDot(bnk->inactive_work, bnk->X_inactive, prered));
545   /* Restore the sub vectors */
546   if (bnk->active_idx) {
547     PetscCall(VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive));
548     PetscCall(VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work));
549     PetscCall(VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive));
550   }
551   PetscFunctionReturn(0);
552 }
553 
554 /*------------------------------------------------------------*/
555 
556 /* Routine for ensuring that the Newton step is a descent direction.
557 
558    The step direction falls back onto BFGS, scaled gradient and gradient steps
559    in the event that the Newton step fails the test.
560 */
561 
562 PetscErrorCode TaoBNKSafeguardStep(Tao tao, KSPConvergedReason ksp_reason, PetscInt *stepType) {
563   TAO_BNK  *bnk = (TAO_BNK *)tao->data;
564   PetscReal gdx, e_min;
565   PetscInt  bfgsUpdates;
566 
567   PetscFunctionBegin;
568   switch (*stepType) {
569   case BNK_NEWTON:
570     PetscCall(VecDot(tao->stepdirection, tao->gradient, &gdx));
571     if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) {
572       /* Newton step is not descent or direction produced Inf or NaN
573         Update the perturbation for next time */
574       if (bnk->pert <= 0.0) {
575         PetscBool is_gltr;
576 
577         /* Initialize the perturbation */
578         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
579         PetscCall(PetscObjectTypeCompare((PetscObject)(tao->ksp), KSPGLTR, &is_gltr));
580         if (is_gltr) {
581           PetscCall(KSPGLTRGetMinEig(tao->ksp, &e_min));
582           bnk->pert = PetscMax(bnk->pert, -e_min);
583         }
584       } else {
585         /* Increase the perturbation */
586         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
587       }
588 
589       if (!bnk->M) {
590         /* We don't have the bfgs matrix around and updated
591           Must use gradient direction in this case */
592         PetscCall(VecCopy(tao->gradient, tao->stepdirection));
593         *stepType = BNK_GRADIENT;
594       } else {
595         /* Attempt to use the BFGS direction */
596         PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));
597 
598         /* Check for success (descent direction)
599           NOTE: Negative gdx here means not a descent direction because
600           the fall-back step is missing a negative sign. */
601         PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx));
602         if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
603           /* BFGS direction is not descent or direction produced not a number
604             We can assert bfgsUpdates > 1 in this case because
605             the first solve produces the scaled gradient direction,
606             which is guaranteed to be descent */
607 
608           /* Use steepest descent direction (scaled) */
609           PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
610           PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
611           PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));
612 
613           *stepType = BNK_SCALED_GRADIENT;
614         } else {
615           PetscCall(MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates));
616           if (1 == bfgsUpdates) {
617             /* The first BFGS direction is always the scaled gradient */
618             *stepType = BNK_SCALED_GRADIENT;
619           } else {
620             *stepType = BNK_BFGS;
621           }
622         }
623       }
624       /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
625       PetscCall(VecScale(tao->stepdirection, -1.0));
626       PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));
627     } else {
628       /* Computed Newton step is descent */
629       switch (ksp_reason) {
630       case KSP_DIVERGED_NANORINF:
631       case KSP_DIVERGED_BREAKDOWN:
632       case KSP_DIVERGED_INDEFINITE_MAT:
633       case KSP_DIVERGED_INDEFINITE_PC:
634       case KSP_CONVERGED_CG_NEG_CURVE:
635         /* Matrix or preconditioner is indefinite; increase perturbation */
636         if (bnk->pert <= 0.0) {
637           PetscBool is_gltr;
638 
639           /* Initialize the perturbation */
640           bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
641           PetscCall(PetscObjectTypeCompare((PetscObject)(tao->ksp), KSPGLTR, &is_gltr));
642           if (is_gltr) {
643             PetscCall(KSPGLTRGetMinEig(tao->ksp, &e_min));
644             bnk->pert = PetscMax(bnk->pert, -e_min);
645           }
646         } else {
647           /* Increase the perturbation */
648           bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
649         }
650         break;
651 
652       default:
653         /* Newton step computation is good; decrease perturbation */
654         bnk->pert = PetscMin(bnk->psfac * bnk->pert, bnk->pmsfac * bnk->gnorm);
655         if (bnk->pert < bnk->pmin) { bnk->pert = 0.0; }
656         break;
657       }
658       *stepType = BNK_NEWTON;
659     }
660     break;
661 
662   case BNK_BFGS:
663     /* Check for success (descent direction) */
664     PetscCall(VecDot(tao->stepdirection, tao->gradient, &gdx));
665     if (gdx >= 0 || PetscIsInfOrNanReal(gdx)) {
666       /* Step is not descent or solve was not successful
667          Use steepest descent direction (scaled) */
668       PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
669       PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
670       PetscCall(MatSolve(bnk->M, tao->gradient, tao->stepdirection));
671       PetscCall(VecScale(tao->stepdirection, -1.0));
672       PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));
673       *stepType = BNK_SCALED_GRADIENT;
674     } else {
675       *stepType = BNK_BFGS;
676     }
677     break;
678 
679   case BNK_SCALED_GRADIENT: break;
680 
681   default: break;
682   }
683 
684   PetscFunctionReturn(0);
685 }
686 
687 /*------------------------------------------------------------*/
688 
689 /* Routine for performing a bound-projected More-Thuente line search.
690 
691   Includes fallbacks to BFGS, scaled gradient, and unscaled gradient steps if the
692   Newton step does not produce a valid step length.
693 */
694 
695 PetscErrorCode TaoBNKPerformLineSearch(Tao tao, PetscInt *stepType, PetscReal *steplen, TaoLineSearchConvergedReason *reason) {
696   TAO_BNK                     *bnk = (TAO_BNK *)tao->data;
697   TaoLineSearchConvergedReason ls_reason;
698   PetscReal                    e_min, gdx;
699   PetscInt                     bfgsUpdates;
700 
701   PetscFunctionBegin;
702   /* Perform the linesearch */
703   PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason));
704   PetscCall(TaoAddLineSearchCounts(tao));
705 
706   while (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER && *stepType != BNK_SCALED_GRADIENT && *stepType != BNK_GRADIENT) {
707     /* Linesearch failed, revert solution */
708     bnk->f = bnk->fold;
709     PetscCall(VecCopy(bnk->Xold, tao->solution));
710     PetscCall(VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient));
711 
712     switch (*stepType) {
713     case BNK_NEWTON:
714       /* Failed to obtain acceptable iterate with Newton step
715          Update the perturbation for next time */
716       if (bnk->pert <= 0.0) {
717         PetscBool is_gltr;
718 
719         /* Initialize the perturbation */
720         bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
721         PetscCall(PetscObjectTypeCompare((PetscObject)(tao->ksp), KSPGLTR, &is_gltr));
722         if (is_gltr) {
723           PetscCall(KSPGLTRGetMinEig(tao->ksp, &e_min));
724           bnk->pert = PetscMax(bnk->pert, -e_min);
725         }
726       } else {
727         /* Increase the perturbation */
728         bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
729       }
730 
731       if (!bnk->M) {
732         /* We don't have the bfgs matrix around and being updated
733            Must use gradient direction in this case */
734         PetscCall(VecCopy(bnk->unprojected_gradient, tao->stepdirection));
735         *stepType = BNK_GRADIENT;
736       } else {
737         /* Attempt to use the BFGS direction */
738         PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));
739         /* Check for success (descent direction)
740            NOTE: Negative gdx means not a descent direction because the step here is missing a negative sign. */
741         PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx));
742         if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
743           /* BFGS direction is not descent or direction produced not a number
744              We can assert bfgsUpdates > 1 in this case
745              Use steepest descent direction (scaled) */
746           PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
747           PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
748           PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));
749 
750           bfgsUpdates = 1;
751           *stepType   = BNK_SCALED_GRADIENT;
752         } else {
753           PetscCall(MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates));
754           if (1 == bfgsUpdates) {
755             /* The first BFGS direction is always the scaled gradient */
756             *stepType = BNK_SCALED_GRADIENT;
757           } else {
758             *stepType = BNK_BFGS;
759           }
760         }
761       }
762       break;
763 
764     case BNK_BFGS:
765       /* Can only enter if pc_type == BNK_PC_BFGS
766          Failed to obtain acceptable iterate with BFGS step
767          Attempt to use the scaled gradient direction */
768       PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
769       PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
770       PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));
771 
772       bfgsUpdates = 1;
773       *stepType   = BNK_SCALED_GRADIENT;
774       break;
775     }
776     /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
777     PetscCall(VecScale(tao->stepdirection, -1.0));
778     PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));
779 
780     /* Perform one last line search with the fall-back step */
781     PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason));
782     PetscCall(TaoAddLineSearchCounts(tao));
783   }
784   *reason = ls_reason;
785   PetscFunctionReturn(0);
786 }
787 
788 /*------------------------------------------------------------*/
789 
790 /* Routine for updating the trust radius.
791 
792   Function features three different update methods:
793   1) Line-search step length based
794   2) Predicted decrease on the CG quadratic model
795   3) Interpolation
796 */
797 
798 PetscErrorCode TaoBNKUpdateTrustRadius(Tao tao, PetscReal prered, PetscReal actred, PetscInt updateType, PetscInt stepType, PetscBool *accept) {
799   TAO_BNK *bnk = (TAO_BNK *)tao->data;
800 
801   PetscReal step, kappa;
802   PetscReal gdx, tau_1, tau_2, tau_min, tau_max;
803 
804   PetscFunctionBegin;
805   /* Update trust region radius */
806   *accept = PETSC_FALSE;
807   switch (updateType) {
808   case BNK_UPDATE_STEP:
809     *accept = PETSC_TRUE; /* always accept here because line search succeeded */
810     if (stepType == BNK_NEWTON) {
811       PetscCall(TaoLineSearchGetStepLength(tao->linesearch, &step));
812       if (step < bnk->nu1) {
813         /* Very bad step taken; reduce radius */
814         tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
815       } else if (step < bnk->nu2) {
816         /* Reasonably bad step taken; reduce radius */
817         tao->trust = bnk->omega2 * PetscMin(bnk->dnorm, tao->trust);
818       } else if (step < bnk->nu3) {
819         /*  Reasonable step was taken; leave radius alone */
820         if (bnk->omega3 < 1.0) {
821           tao->trust = bnk->omega3 * PetscMin(bnk->dnorm, tao->trust);
822         } else if (bnk->omega3 > 1.0) {
823           tao->trust = PetscMax(bnk->omega3 * bnk->dnorm, tao->trust);
824         }
825       } else if (step < bnk->nu4) {
826         /*  Full step taken; increase the radius */
827         tao->trust = PetscMax(bnk->omega4 * bnk->dnorm, tao->trust);
828       } else {
829         /*  More than full step taken; increase the radius */
830         tao->trust = PetscMax(bnk->omega5 * bnk->dnorm, tao->trust);
831       }
832     } else {
833       /*  Newton step was not good; reduce the radius */
834       tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
835     }
836     break;
837 
838   case BNK_UPDATE_REDUCTION:
839     if (stepType == BNK_NEWTON) {
840       if ((prered < 0.0) || PetscIsInfOrNanReal(prered)) {
841         /* The predicted reduction has the wrong sign.  This cannot
842            happen in infinite precision arithmetic.  Step should
843            be rejected! */
844         tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
845       } else {
846         if (PetscIsInfOrNanReal(actred)) {
847           tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
848         } else {
849           if ((PetscAbsScalar(actred) <= PetscMax(1.0, PetscAbsScalar(bnk->f)) * bnk->epsilon) && (PetscAbsScalar(prered) <= PetscMax(1.0, PetscAbsScalar(bnk->f)) * bnk->epsilon)) {
850             kappa = 1.0;
851           } else {
852             kappa = actred / prered;
853           }
854           /* Accept or reject the step and update radius */
855           if (kappa < bnk->eta1) {
856             /* Reject the step */
857             tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
858           } else {
859             /* Accept the step */
860             *accept = PETSC_TRUE;
861             /* Update the trust region radius only if the computed step is at the trust radius boundary */
862             if (bnk->dnorm == tao->trust) {
863               if (kappa < bnk->eta2) {
864                 /* Marginal bad step */
865                 tao->trust = bnk->alpha2 * tao->trust;
866               } else if (kappa < bnk->eta3) {
867                 /* Reasonable step */
868                 tao->trust = bnk->alpha3 * tao->trust;
869               } else if (kappa < bnk->eta4) {
870                 /* Good step */
871                 tao->trust = bnk->alpha4 * tao->trust;
872               } else {
873                 /* Very good step */
874                 tao->trust = bnk->alpha5 * tao->trust;
875               }
876             }
877           }
878         }
879       }
880     } else {
881       /*  Newton step was not good; reduce the radius */
882       tao->trust = bnk->alpha1 * PetscMin(bnk->dnorm, tao->trust);
883     }
884     break;
885 
886   default:
887     if (stepType == BNK_NEWTON) {
888       if (prered < 0.0) {
889         /*  The predicted reduction has the wrong sign.  This cannot */
890         /*  happen in infinite precision arithmetic.  Step should */
891         /*  be rejected! */
892         tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
893       } else {
894         if (PetscIsInfOrNanReal(actred)) {
895           tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
896         } else {
897           if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) {
898             kappa = 1.0;
899           } else {
900             kappa = actred / prered;
901           }
902 
903           PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx));
904           tau_1   = bnk->theta * gdx / (bnk->theta * gdx - (1.0 - bnk->theta) * prered + actred);
905           tau_2   = bnk->theta * gdx / (bnk->theta * gdx + (1.0 + bnk->theta) * prered - actred);
906           tau_min = PetscMin(tau_1, tau_2);
907           tau_max = PetscMax(tau_1, tau_2);
908 
909           if (kappa >= 1.0 - bnk->mu1) {
910             /*  Great agreement */
911             *accept = PETSC_TRUE;
912             if (tau_max < 1.0) {
913               tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
914             } else if (tau_max > bnk->gamma4) {
915               tao->trust = PetscMax(tao->trust, bnk->gamma4 * bnk->dnorm);
916             } else {
917               tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
918             }
919           } else if (kappa >= 1.0 - bnk->mu2) {
920             /*  Good agreement */
921             *accept = PETSC_TRUE;
922             if (tau_max < bnk->gamma2) {
923               tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
924             } else if (tau_max > bnk->gamma3) {
925               tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
926             } else if (tau_max < 1.0) {
927               tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
928             } else {
929               tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
930             }
931           } else {
932             /*  Not good agreement */
933             if (tau_min > 1.0) {
934               tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
935             } else if (tau_max < bnk->gamma1) {
936               tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
937             } else if ((tau_min < bnk->gamma1) && (tau_max >= 1.0)) {
938               tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
939             } else if ((tau_1 >= bnk->gamma1) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1) || (tau_2 >= 1.0))) {
940               tao->trust = tau_1 * PetscMin(tao->trust, bnk->dnorm);
941             } else if ((tau_2 >= bnk->gamma1) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1) || (tau_2 >= 1.0))) {
942               tao->trust = tau_2 * PetscMin(tao->trust, bnk->dnorm);
943             } else {
944               tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
945             }
946           }
947         }
948       }
949     } else {
950       /*  Newton step was not good; reduce the radius */
951       tao->trust = bnk->gamma1 * PetscMin(bnk->dnorm, tao->trust);
952     }
953     break;
954   }
955   /* Make sure the radius does not violate min and max settings */
956   tao->trust = PetscMin(tao->trust, bnk->max_radius);
957   tao->trust = PetscMax(tao->trust, bnk->min_radius);
958   PetscFunctionReturn(0);
959 }
960 
961 /* ---------------------------------------------------------- */
962 
963 PetscErrorCode TaoBNKAddStepCounts(Tao tao, PetscInt stepType) {
964   TAO_BNK *bnk = (TAO_BNK *)tao->data;
965 
966   PetscFunctionBegin;
967   switch (stepType) {
968   case BNK_NEWTON: ++bnk->newt; break;
969   case BNK_BFGS: ++bnk->bfgs; break;
970   case BNK_SCALED_GRADIENT: ++bnk->sgrad; break;
971   case BNK_GRADIENT: ++bnk->grad; break;
972   default: break;
973   }
974   PetscFunctionReturn(0);
975 }
976 
977 /* ---------------------------------------------------------- */
978 
979 PetscErrorCode TaoSetUp_BNK(Tao tao) {
980   TAO_BNK *bnk = (TAO_BNK *)tao->data;
981   PetscInt i;
982 
983   PetscFunctionBegin;
984   if (!tao->gradient) { PetscCall(VecDuplicate(tao->solution, &tao->gradient)); }
985   if (!tao->stepdirection) { PetscCall(VecDuplicate(tao->solution, &tao->stepdirection)); }
986   if (!bnk->W) { PetscCall(VecDuplicate(tao->solution, &bnk->W)); }
987   if (!bnk->Xold) { PetscCall(VecDuplicate(tao->solution, &bnk->Xold)); }
988   if (!bnk->Gold) { PetscCall(VecDuplicate(tao->solution, &bnk->Gold)); }
989   if (!bnk->Xwork) { PetscCall(VecDuplicate(tao->solution, &bnk->Xwork)); }
990   if (!bnk->Gwork) { PetscCall(VecDuplicate(tao->solution, &bnk->Gwork)); }
991   if (!bnk->unprojected_gradient) { PetscCall(VecDuplicate(tao->solution, &bnk->unprojected_gradient)); }
992   if (!bnk->unprojected_gradient_old) { PetscCall(VecDuplicate(tao->solution, &bnk->unprojected_gradient_old)); }
993   if (!bnk->Diag_min) { PetscCall(VecDuplicate(tao->solution, &bnk->Diag_min)); }
994   if (!bnk->Diag_max) { PetscCall(VecDuplicate(tao->solution, &bnk->Diag_max)); }
995   if (bnk->max_cg_its > 0) {
996     /* Ensure that the important common vectors are shared between BNK and embedded BNCG */
997     bnk->bncg_ctx = (TAO_BNCG *)bnk->bncg->data;
998     PetscCall(PetscObjectReference((PetscObject)(bnk->unprojected_gradient_old)));
999     PetscCall(VecDestroy(&bnk->bncg_ctx->unprojected_gradient_old));
1000     bnk->bncg_ctx->unprojected_gradient_old = bnk->unprojected_gradient_old;
1001     PetscCall(PetscObjectReference((PetscObject)(bnk->unprojected_gradient)));
1002     PetscCall(VecDestroy(&bnk->bncg_ctx->unprojected_gradient));
1003     bnk->bncg_ctx->unprojected_gradient = bnk->unprojected_gradient;
1004     PetscCall(PetscObjectReference((PetscObject)(bnk->Gold)));
1005     PetscCall(VecDestroy(&bnk->bncg_ctx->G_old));
1006     bnk->bncg_ctx->G_old = bnk->Gold;
1007     PetscCall(PetscObjectReference((PetscObject)(tao->gradient)));
1008     PetscCall(VecDestroy(&bnk->bncg->gradient));
1009     bnk->bncg->gradient = tao->gradient;
1010     PetscCall(PetscObjectReference((PetscObject)(tao->stepdirection)));
1011     PetscCall(VecDestroy(&bnk->bncg->stepdirection));
1012     bnk->bncg->stepdirection = tao->stepdirection;
1013     PetscCall(TaoSetSolution(bnk->bncg, tao->solution));
1014     /* Copy over some settings from BNK into BNCG */
1015     PetscCall(TaoSetMaximumIterations(bnk->bncg, bnk->max_cg_its));
1016     PetscCall(TaoSetTolerances(bnk->bncg, tao->gatol, tao->grtol, tao->gttol));
1017     PetscCall(TaoSetFunctionLowerBound(bnk->bncg, tao->fmin));
1018     PetscCall(TaoSetConvergenceTest(bnk->bncg, tao->ops->convergencetest, tao->cnvP));
1019     PetscCall(TaoSetObjective(bnk->bncg, tao->ops->computeobjective, tao->user_objP));
1020     PetscCall(TaoSetGradient(bnk->bncg, NULL, tao->ops->computegradient, tao->user_gradP));
1021     PetscCall(TaoSetObjectiveAndGradient(bnk->bncg, NULL, tao->ops->computeobjectiveandgradient, tao->user_objgradP));
1022     PetscCall(PetscObjectCopyFortranFunctionPointers((PetscObject)tao, (PetscObject)(bnk->bncg)));
1023     for (i = 0; i < tao->numbermonitors; ++i) {
1024       PetscCall(TaoSetMonitor(bnk->bncg, tao->monitor[i], tao->monitorcontext[i], tao->monitordestroy[i]));
1025       PetscCall(PetscObjectReference((PetscObject)(tao->monitorcontext[i])));
1026     }
1027   }
1028   bnk->X_inactive    = NULL;
1029   bnk->G_inactive    = NULL;
1030   bnk->inactive_work = NULL;
1031   bnk->active_work   = NULL;
1032   bnk->inactive_idx  = NULL;
1033   bnk->active_idx    = NULL;
1034   bnk->active_lower  = NULL;
1035   bnk->active_upper  = NULL;
1036   bnk->active_fixed  = NULL;
1037   bnk->M             = NULL;
1038   bnk->H_inactive    = NULL;
1039   bnk->Hpre_inactive = NULL;
1040   PetscFunctionReturn(0);
1041 }
1042 
1043 /*------------------------------------------------------------*/
1044 
1045 PetscErrorCode TaoDestroy_BNK(Tao tao) {
1046   TAO_BNK *bnk = (TAO_BNK *)tao->data;
1047 
1048   PetscFunctionBegin;
1049   PetscCall(VecDestroy(&bnk->W));
1050   PetscCall(VecDestroy(&bnk->Xold));
1051   PetscCall(VecDestroy(&bnk->Gold));
1052   PetscCall(VecDestroy(&bnk->Xwork));
1053   PetscCall(VecDestroy(&bnk->Gwork));
1054   PetscCall(VecDestroy(&bnk->unprojected_gradient));
1055   PetscCall(VecDestroy(&bnk->unprojected_gradient_old));
1056   PetscCall(VecDestroy(&bnk->Diag_min));
1057   PetscCall(VecDestroy(&bnk->Diag_max));
1058   PetscCall(ISDestroy(&bnk->active_lower));
1059   PetscCall(ISDestroy(&bnk->active_upper));
1060   PetscCall(ISDestroy(&bnk->active_fixed));
1061   PetscCall(ISDestroy(&bnk->active_idx));
1062   PetscCall(ISDestroy(&bnk->inactive_idx));
1063   PetscCall(MatDestroy(&bnk->Hpre_inactive));
1064   PetscCall(MatDestroy(&bnk->H_inactive));
1065   PetscCall(TaoDestroy(&bnk->bncg));
1066   PetscCall(KSPDestroy(&tao->ksp));
1067   PetscCall(PetscFree(tao->data));
1068   PetscFunctionReturn(0);
1069 }
1070 
1071 /*------------------------------------------------------------*/
1072 
1073 PetscErrorCode TaoSetFromOptions_BNK(Tao tao, PetscOptionItems *PetscOptionsObject) {
1074   TAO_BNK *bnk = (TAO_BNK *)tao->data;
1075 
1076   PetscFunctionBegin;
1077   PetscOptionsHeadBegin(PetscOptionsObject, "Newton-Krylov method for bound constrained optimization");
1078   PetscCall(PetscOptionsEList("-tao_bnk_init_type", "radius initialization type", "", BNK_INIT, BNK_INIT_TYPES, BNK_INIT[bnk->init_type], &bnk->init_type, NULL));
1079   PetscCall(PetscOptionsEList("-tao_bnk_update_type", "radius update type", "", BNK_UPDATE, BNK_UPDATE_TYPES, BNK_UPDATE[bnk->update_type], &bnk->update_type, NULL));
1080   PetscCall(PetscOptionsEList("-tao_bnk_as_type", "active set estimation method", "", BNK_AS, BNK_AS_TYPES, BNK_AS[bnk->as_type], &bnk->as_type, NULL));
1081   PetscCall(PetscOptionsReal("-tao_bnk_sval", "(developer) Hessian perturbation starting value", "", bnk->sval, &bnk->sval, NULL));
1082   PetscCall(PetscOptionsReal("-tao_bnk_imin", "(developer) minimum initial Hessian perturbation", "", bnk->imin, &bnk->imin, NULL));
1083   PetscCall(PetscOptionsReal("-tao_bnk_imax", "(developer) maximum initial Hessian perturbation", "", bnk->imax, &bnk->imax, NULL));
1084   PetscCall(PetscOptionsReal("-tao_bnk_imfac", "(developer) initial merit factor for Hessian perturbation", "", bnk->imfac, &bnk->imfac, NULL));
1085   PetscCall(PetscOptionsReal("-tao_bnk_pmin", "(developer) minimum Hessian perturbation", "", bnk->pmin, &bnk->pmin, NULL));
1086   PetscCall(PetscOptionsReal("-tao_bnk_pmax", "(developer) maximum Hessian perturbation", "", bnk->pmax, &bnk->pmax, NULL));
1087   PetscCall(PetscOptionsReal("-tao_bnk_pgfac", "(developer) Hessian perturbation growth factor", "", bnk->pgfac, &bnk->pgfac, NULL));
1088   PetscCall(PetscOptionsReal("-tao_bnk_psfac", "(developer) Hessian perturbation shrink factor", "", bnk->psfac, &bnk->psfac, NULL));
1089   PetscCall(PetscOptionsReal("-tao_bnk_pmgfac", "(developer) merit growth factor for Hessian perturbation", "", bnk->pmgfac, &bnk->pmgfac, NULL));
1090   PetscCall(PetscOptionsReal("-tao_bnk_pmsfac", "(developer) merit shrink factor for Hessian perturbation", "", bnk->pmsfac, &bnk->pmsfac, NULL));
1091   PetscCall(PetscOptionsReal("-tao_bnk_eta1", "(developer) threshold for rejecting step (-tao_bnk_update_type reduction)", "", bnk->eta1, &bnk->eta1, NULL));
1092   PetscCall(PetscOptionsReal("-tao_bnk_eta2", "(developer) threshold for accepting marginal step (-tao_bnk_update_type reduction)", "", bnk->eta2, &bnk->eta2, NULL));
1093   PetscCall(PetscOptionsReal("-tao_bnk_eta3", "(developer) threshold for accepting reasonable step (-tao_bnk_update_type reduction)", "", bnk->eta3, &bnk->eta3, NULL));
1094   PetscCall(PetscOptionsReal("-tao_bnk_eta4", "(developer) threshold for accepting good step (-tao_bnk_update_type reduction)", "", bnk->eta4, &bnk->eta4, NULL));
1095   PetscCall(PetscOptionsReal("-tao_bnk_alpha1", "(developer) radius reduction factor for rejected step (-tao_bnk_update_type reduction)", "", bnk->alpha1, &bnk->alpha1, NULL));
1096   PetscCall(PetscOptionsReal("-tao_bnk_alpha2", "(developer) radius reduction factor for marginally accepted bad step (-tao_bnk_update_type reduction)", "", bnk->alpha2, &bnk->alpha2, NULL));
1097   PetscCall(PetscOptionsReal("-tao_bnk_alpha3", "(developer) radius increase factor for reasonable accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha3, &bnk->alpha3, NULL));
1098   PetscCall(PetscOptionsReal("-tao_bnk_alpha4", "(developer) radius increase factor for good accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha4, &bnk->alpha4, NULL));
1099   PetscCall(PetscOptionsReal("-tao_bnk_alpha5", "(developer) radius increase factor for very good accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha5, &bnk->alpha5, NULL));
1100   PetscCall(PetscOptionsReal("-tao_bnk_nu1", "(developer) threshold for small line-search step length (-tao_bnk_update_type step)", "", bnk->nu1, &bnk->nu1, NULL));
1101   PetscCall(PetscOptionsReal("-tao_bnk_nu2", "(developer) threshold for reasonable line-search step length (-tao_bnk_update_type step)", "", bnk->nu2, &bnk->nu2, NULL));
1102   PetscCall(PetscOptionsReal("-tao_bnk_nu3", "(developer) threshold for large line-search step length (-tao_bnk_update_type step)", "", bnk->nu3, &bnk->nu3, NULL));
1103   PetscCall(PetscOptionsReal("-tao_bnk_nu4", "(developer) threshold for very large line-search step length (-tao_bnk_update_type step)", "", bnk->nu4, &bnk->nu4, NULL));
1104   PetscCall(PetscOptionsReal("-tao_bnk_omega1", "(developer) radius reduction factor for very small line-search step length (-tao_bnk_update_type step)", "", bnk->omega1, &bnk->omega1, NULL));
1105   PetscCall(PetscOptionsReal("-tao_bnk_omega2", "(developer) radius reduction factor for small line-search step length (-tao_bnk_update_type step)", "", bnk->omega2, &bnk->omega2, NULL));
1106   PetscCall(PetscOptionsReal("-tao_bnk_omega3", "(developer) radius factor for decent line-search step length (-tao_bnk_update_type step)", "", bnk->omega3, &bnk->omega3, NULL));
1107   PetscCall(PetscOptionsReal("-tao_bnk_omega4", "(developer) radius increase factor for large line-search step length (-tao_bnk_update_type step)", "", bnk->omega4, &bnk->omega4, NULL));
1108   PetscCall(PetscOptionsReal("-tao_bnk_omega5", "(developer) radius increase factor for very large line-search step length (-tao_bnk_update_type step)", "", bnk->omega5, &bnk->omega5, NULL));
1109   PetscCall(PetscOptionsReal("-tao_bnk_mu1_i", "(developer) threshold for accepting very good step (-tao_bnk_init_type interpolation)", "", bnk->mu1_i, &bnk->mu1_i, NULL));
1110   PetscCall(PetscOptionsReal("-tao_bnk_mu2_i", "(developer) threshold for accepting good step (-tao_bnk_init_type interpolation)", "", bnk->mu2_i, &bnk->mu2_i, NULL));
1111   PetscCall(PetscOptionsReal("-tao_bnk_gamma1_i", "(developer) radius reduction factor for rejected very bad step (-tao_bnk_init_type interpolation)", "", bnk->gamma1_i, &bnk->gamma1_i, NULL));
1112   PetscCall(PetscOptionsReal("-tao_bnk_gamma2_i", "(developer) radius reduction factor for rejected bad step (-tao_bnk_init_type interpolation)", "", bnk->gamma2_i, &bnk->gamma2_i, NULL));
1113   PetscCall(PetscOptionsReal("-tao_bnk_gamma3_i", "(developer) radius increase factor for accepted good step (-tao_bnk_init_type interpolation)", "", bnk->gamma3_i, &bnk->gamma3_i, NULL));
1114   PetscCall(PetscOptionsReal("-tao_bnk_gamma4_i", "(developer) radius increase factor for accepted very good step (-tao_bnk_init_type interpolation)", "", bnk->gamma4_i, &bnk->gamma4_i, NULL));
1115   PetscCall(PetscOptionsReal("-tao_bnk_theta_i", "(developer) trust region interpolation factor (-tao_bnk_init_type interpolation)", "", bnk->theta_i, &bnk->theta_i, NULL));
1116   PetscCall(PetscOptionsReal("-tao_bnk_mu1", "(developer) threshold for accepting very good step (-tao_bnk_update_type interpolation)", "", bnk->mu1, &bnk->mu1, NULL));
1117   PetscCall(PetscOptionsReal("-tao_bnk_mu2", "(developer) threshold for accepting good step (-tao_bnk_update_type interpolation)", "", bnk->mu2, &bnk->mu2, NULL));
1118   PetscCall(PetscOptionsReal("-tao_bnk_gamma1", "(developer) radius reduction factor for rejected very bad step (-tao_bnk_update_type interpolation)", "", bnk->gamma1, &bnk->gamma1, NULL));
1119   PetscCall(PetscOptionsReal("-tao_bnk_gamma2", "(developer) radius reduction factor for rejected bad step (-tao_bnk_update_type interpolation)", "", bnk->gamma2, &bnk->gamma2, NULL));
1120   PetscCall(PetscOptionsReal("-tao_bnk_gamma3", "(developer) radius increase factor for accepted good step (-tao_bnk_update_type interpolation)", "", bnk->gamma3, &bnk->gamma3, NULL));
1121   PetscCall(PetscOptionsReal("-tao_bnk_gamma4", "(developer) radius increase factor for accepted very good step (-tao_bnk_update_type interpolation)", "", bnk->gamma4, &bnk->gamma4, NULL));
1122   PetscCall(PetscOptionsReal("-tao_bnk_theta", "(developer) trust region interpolation factor (-tao_bnk_update_type interpolation)", "", bnk->theta, &bnk->theta, NULL));
1123   PetscCall(PetscOptionsReal("-tao_bnk_min_radius", "(developer) lower bound on initial radius", "", bnk->min_radius, &bnk->min_radius, NULL));
1124   PetscCall(PetscOptionsReal("-tao_bnk_max_radius", "(developer) upper bound on radius", "", bnk->max_radius, &bnk->max_radius, NULL));
1125   PetscCall(PetscOptionsReal("-tao_bnk_epsilon", "(developer) tolerance used when computing actual and predicted reduction", "", bnk->epsilon, &bnk->epsilon, NULL));
1126   PetscCall(PetscOptionsReal("-tao_bnk_as_tol", "(developer) initial tolerance used when estimating actively bounded variables", "", bnk->as_tol, &bnk->as_tol, NULL));
1127   PetscCall(PetscOptionsReal("-tao_bnk_as_step", "(developer) step length used when estimating actively bounded variables", "", bnk->as_step, &bnk->as_step, NULL));
1128   PetscCall(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));
1129   PetscOptionsHeadEnd();
1130 
1131   PetscCall(TaoSetOptionsPrefix(bnk->bncg, ((PetscObject)(tao))->prefix));
1132   PetscCall(TaoAppendOptionsPrefix(bnk->bncg, "tao_bnk_cg_"));
1133   PetscCall(TaoSetFromOptions(bnk->bncg));
1134 
1135   PetscCall(KSPSetOptionsPrefix(tao->ksp, ((PetscObject)(tao))->prefix));
1136   PetscCall(KSPAppendOptionsPrefix(tao->ksp, "tao_bnk_"));
1137   PetscCall(KSPSetFromOptions(tao->ksp));
1138   PetscFunctionReturn(0);
1139 }
1140 
1141 /*------------------------------------------------------------*/
1142 
1143 PetscErrorCode TaoView_BNK(Tao tao, PetscViewer viewer) {
1144   TAO_BNK  *bnk = (TAO_BNK *)tao->data;
1145   PetscInt  nrejects;
1146   PetscBool isascii;
1147 
1148   PetscFunctionBegin;
1149   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
1150   if (isascii) {
1151     PetscCall(PetscViewerASCIIPushTab(viewer));
1152     if (bnk->M) {
1153       PetscCall(MatLMVMGetRejectCount(bnk->M, &nrejects));
1154       PetscCall(PetscViewerASCIIPrintf(viewer, "Rejected BFGS updates: %" PetscInt_FMT "\n", nrejects));
1155     }
1156     PetscCall(PetscViewerASCIIPrintf(viewer, "CG steps: %" PetscInt_FMT "\n", bnk->tot_cg_its));
1157     PetscCall(PetscViewerASCIIPrintf(viewer, "Newton steps: %" PetscInt_FMT "\n", bnk->newt));
1158     if (bnk->M) { PetscCall(PetscViewerASCIIPrintf(viewer, "BFGS steps: %" PetscInt_FMT "\n", bnk->bfgs)); }
1159     PetscCall(PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %" PetscInt_FMT "\n", bnk->sgrad));
1160     PetscCall(PetscViewerASCIIPrintf(viewer, "Gradient steps: %" PetscInt_FMT "\n", bnk->grad));
1161     PetscCall(PetscViewerASCIIPrintf(viewer, "KSP termination reasons:\n"));
1162     PetscCall(PetscViewerASCIIPrintf(viewer, "  atol: %" PetscInt_FMT "\n", bnk->ksp_atol));
1163     PetscCall(PetscViewerASCIIPrintf(viewer, "  rtol: %" PetscInt_FMT "\n", bnk->ksp_rtol));
1164     PetscCall(PetscViewerASCIIPrintf(viewer, "  ctol: %" PetscInt_FMT "\n", bnk->ksp_ctol));
1165     PetscCall(PetscViewerASCIIPrintf(viewer, "  negc: %" PetscInt_FMT "\n", bnk->ksp_negc));
1166     PetscCall(PetscViewerASCIIPrintf(viewer, "  dtol: %" PetscInt_FMT "\n", bnk->ksp_dtol));
1167     PetscCall(PetscViewerASCIIPrintf(viewer, "  iter: %" PetscInt_FMT "\n", bnk->ksp_iter));
1168     PetscCall(PetscViewerASCIIPrintf(viewer, "  othr: %" PetscInt_FMT "\n", bnk->ksp_othr));
1169     PetscCall(PetscViewerASCIIPopTab(viewer));
1170   }
1171   PetscFunctionReturn(0);
1172 }
1173 
1174 /* ---------------------------------------------------------- */
1175 
1176 /*MC
1177   TAOBNK - Shared base-type for Bounded Newton-Krylov type algorithms.
1178   At each iteration, the BNK methods solve the symmetric
1179   system of equations to obtain the step diretion dk:
1180               Hk dk = -gk
1181   for free variables only. The step can be globalized either through
1182   trust-region methods, or a line search, or a heuristic mixture of both.
1183 
1184     Options Database Keys:
1185 + -tao_bnk_max_cg_its - maximum number of bounded conjugate-gradient iterations taken in each Newton loop
1186 . -tao_bnk_init_type - trust radius initialization method ("constant", "direction", "interpolation")
1187 . -tao_bnk_update_type - trust radius update method ("step", "direction", "interpolation")
1188 . -tao_bnk_as_type - active-set estimation method ("none", "bertsekas")
1189 . -tao_bnk_as_tol - (developer) initial tolerance used in estimating bounded active variables (-as_type bertsekas)
1190 . -tao_bnk_as_step - (developer) trial step length used in estimating bounded active variables (-as_type bertsekas)
1191 . -tao_bnk_sval - (developer) Hessian perturbation starting value
1192 . -tao_bnk_imin - (developer) minimum initial Hessian perturbation
1193 . -tao_bnk_imax - (developer) maximum initial Hessian perturbation
1194 . -tao_bnk_pmin - (developer) minimum Hessian perturbation
1195 . -tao_bnk_pmax - (developer) aximum Hessian perturbation
1196 . -tao_bnk_pgfac - (developer) Hessian perturbation growth factor
1197 . -tao_bnk_psfac - (developer) Hessian perturbation shrink factor
1198 . -tao_bnk_imfac - (developer) initial merit factor for Hessian perturbation
1199 . -tao_bnk_pmgfac - (developer) merit growth factor for Hessian perturbation
1200 . -tao_bnk_pmsfac - (developer) merit shrink factor for Hessian perturbation
1201 . -tao_bnk_eta1 - (developer) threshold for rejecting step (-update_type reduction)
1202 . -tao_bnk_eta2 - (developer) threshold for accepting marginal step (-update_type reduction)
1203 . -tao_bnk_eta3 - (developer) threshold for accepting reasonable step (-update_type reduction)
1204 . -tao_bnk_eta4 - (developer) threshold for accepting good step (-update_type reduction)
1205 . -tao_bnk_alpha1 - (developer) radius reduction factor for rejected step (-update_type reduction)
1206 . -tao_bnk_alpha2 - (developer) radius reduction factor for marginally accepted bad step (-update_type reduction)
1207 . -tao_bnk_alpha3 - (developer) radius increase factor for reasonable accepted step (-update_type reduction)
1208 . -tao_bnk_alpha4 - (developer) radius increase factor for good accepted step (-update_type reduction)
1209 . -tao_bnk_alpha5 - (developer) radius increase factor for very good accepted step (-update_type reduction)
1210 . -tao_bnk_epsilon - (developer) tolerance for small pred/actual ratios that trigger automatic step acceptance (-update_type reduction)
1211 . -tao_bnk_mu1 - (developer) threshold for accepting very good step (-update_type interpolation)
1212 . -tao_bnk_mu2 - (developer) threshold for accepting good step (-update_type interpolation)
1213 . -tao_bnk_gamma1 - (developer) radius reduction factor for rejected very bad step (-update_type interpolation)
1214 . -tao_bnk_gamma2 - (developer) radius reduction factor for rejected bad step (-update_type interpolation)
1215 . -tao_bnk_gamma3 - (developer) radius increase factor for accepted good step (-update_type interpolation)
1216 . -tao_bnk_gamma4 - (developer) radius increase factor for accepted very good step (-update_type interpolation)
1217 . -tao_bnk_theta - (developer) trust region interpolation factor (-update_type interpolation)
1218 . -tao_bnk_nu1 - (developer) threshold for small line-search step length (-update_type step)
1219 . -tao_bnk_nu2 - (developer) threshold for reasonable line-search step length (-update_type step)
1220 . -tao_bnk_nu3 - (developer) threshold for large line-search step length (-update_type step)
1221 . -tao_bnk_nu4 - (developer) threshold for very large line-search step length (-update_type step)
1222 . -tao_bnk_omega1 - (developer) radius reduction factor for very small line-search step length (-update_type step)
1223 . -tao_bnk_omega2 - (developer) radius reduction factor for small line-search step length (-update_type step)
1224 . -tao_bnk_omega3 - (developer) radius factor for decent line-search step length (-update_type step)
1225 . -tao_bnk_omega4 - (developer) radius increase factor for large line-search step length (-update_type step)
1226 . -tao_bnk_omega5 - (developer) radius increase factor for very large line-search step length (-update_type step)
1227 . -tao_bnk_mu1_i -  (developer) threshold for accepting very good step (-init_type interpolation)
1228 . -tao_bnk_mu2_i -  (developer) threshold for accepting good step (-init_type interpolation)
1229 . -tao_bnk_gamma1_i - (developer) radius reduction factor for rejected very bad step (-init_type interpolation)
1230 . -tao_bnk_gamma2_i - (developer) radius reduction factor for rejected bad step (-init_type interpolation)
1231 . -tao_bnk_gamma3_i - (developer) radius increase factor for accepted good step (-init_type interpolation)
1232 . -tao_bnk_gamma4_i - (developer) radius increase factor for accepted very good step (-init_type interpolation)
1233 - -tao_bnk_theta_i - (developer) trust region interpolation factor (-init_type interpolation)
1234 
1235   Level: beginner
1236 M*/
1237 
1238 PetscErrorCode TaoCreate_BNK(Tao tao) {
1239   TAO_BNK *bnk;
1240   PC       pc;
1241 
1242   PetscFunctionBegin;
1243   PetscCall(PetscNewLog(tao, &bnk));
1244 
1245   tao->ops->setup          = TaoSetUp_BNK;
1246   tao->ops->view           = TaoView_BNK;
1247   tao->ops->setfromoptions = TaoSetFromOptions_BNK;
1248   tao->ops->destroy        = TaoDestroy_BNK;
1249 
1250   /*  Override default settings (unless already changed) */
1251   if (!tao->max_it_changed) tao->max_it = 50;
1252   if (!tao->trust0_changed) tao->trust0 = 100.0;
1253 
1254   tao->data = (void *)bnk;
1255 
1256   /*  Hessian shifting parameters */
1257   bnk->computehessian = TaoBNKComputeHessian;
1258   bnk->computestep    = TaoBNKComputeStep;
1259 
1260   bnk->sval  = 0.0;
1261   bnk->imin  = 1.0e-4;
1262   bnk->imax  = 1.0e+2;
1263   bnk->imfac = 1.0e-1;
1264 
1265   bnk->pmin   = 1.0e-12;
1266   bnk->pmax   = 1.0e+2;
1267   bnk->pgfac  = 1.0e+1;
1268   bnk->psfac  = 4.0e-1;
1269   bnk->pmgfac = 1.0e-1;
1270   bnk->pmsfac = 1.0e-1;
1271 
1272   /*  Default values for trust-region radius update based on steplength */
1273   bnk->nu1 = 0.25;
1274   bnk->nu2 = 0.50;
1275   bnk->nu3 = 1.00;
1276   bnk->nu4 = 1.25;
1277 
1278   bnk->omega1 = 0.25;
1279   bnk->omega2 = 0.50;
1280   bnk->omega3 = 1.00;
1281   bnk->omega4 = 2.00;
1282   bnk->omega5 = 4.00;
1283 
1284   /*  Default values for trust-region radius update based on reduction */
1285   bnk->eta1 = 1.0e-4;
1286   bnk->eta2 = 0.25;
1287   bnk->eta3 = 0.50;
1288   bnk->eta4 = 0.90;
1289 
1290   bnk->alpha1 = 0.25;
1291   bnk->alpha2 = 0.50;
1292   bnk->alpha3 = 1.00;
1293   bnk->alpha4 = 2.00;
1294   bnk->alpha5 = 4.00;
1295 
1296   /*  Default values for trust-region radius update based on interpolation */
1297   bnk->mu1 = 0.10;
1298   bnk->mu2 = 0.50;
1299 
1300   bnk->gamma1 = 0.25;
1301   bnk->gamma2 = 0.50;
1302   bnk->gamma3 = 2.00;
1303   bnk->gamma4 = 4.00;
1304 
1305   bnk->theta = 0.05;
1306 
1307   /*  Default values for trust region initialization based on interpolation */
1308   bnk->mu1_i = 0.35;
1309   bnk->mu2_i = 0.50;
1310 
1311   bnk->gamma1_i = 0.0625;
1312   bnk->gamma2_i = 0.5;
1313   bnk->gamma3_i = 2.0;
1314   bnk->gamma4_i = 5.0;
1315 
1316   bnk->theta_i = 0.25;
1317 
1318   /*  Remaining parameters */
1319   bnk->max_cg_its = 0;
1320   bnk->min_radius = 1.0e-10;
1321   bnk->max_radius = 1.0e10;
1322   bnk->epsilon    = PetscPowReal(PETSC_MACHINE_EPSILON, 2.0 / 3.0);
1323   bnk->as_tol     = 1.0e-3;
1324   bnk->as_step    = 1.0e-3;
1325   bnk->dmin       = 1.0e-6;
1326   bnk->dmax       = 1.0e6;
1327 
1328   bnk->M           = NULL;
1329   bnk->bfgs_pre    = NULL;
1330   bnk->init_type   = BNK_INIT_INTERPOLATION;
1331   bnk->update_type = BNK_UPDATE_REDUCTION;
1332   bnk->as_type     = BNK_AS_BERTSEKAS;
1333 
1334   /* Create the embedded BNCG solver */
1335   PetscCall(TaoCreate(PetscObjectComm((PetscObject)tao), &bnk->bncg));
1336   PetscCall(PetscObjectIncrementTabLevel((PetscObject)bnk->bncg, (PetscObject)tao, 1));
1337   PetscCall(TaoSetType(bnk->bncg, TAOBNCG));
1338 
1339   /* Create the line search */
1340   PetscCall(TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch));
1341   PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1));
1342   PetscCall(TaoLineSearchSetType(tao->linesearch, TAOLINESEARCHMT));
1343   PetscCall(TaoLineSearchUseTaoRoutines(tao->linesearch, tao));
1344 
1345   /*  Set linear solver to default for symmetric matrices */
1346   PetscCall(KSPCreate(((PetscObject)tao)->comm, &tao->ksp));
1347   PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1));
1348   PetscCall(KSPSetType(tao->ksp, KSPSTCG));
1349   PetscCall(KSPGetPC(tao->ksp, &pc));
1350   PetscCall(PCSetType(pc, PCLMVM));
1351   PetscFunctionReturn(0);
1352 }
1353