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