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: * Note: nfuncs are not copied as tao and subsolvers share same TaoTerm */
382: bnk->tot_cg_its += bnk->bncg->niter;
383: /* Extract the BNCG function value out and save it into BNK */
384: bnk->f = bnk->bncg_ctx->f;
385: 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) {
386: *terminate = PETSC_TRUE;
387: } else {
388: PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
389: }
390: }
391: PetscFunctionReturn(PETSC_SUCCESS);
392: }
394: /* Routine for computing the Newton step. */
396: PetscErrorCode TaoBNKComputeStep(Tao tao, PetscBool shift, KSPConvergedReason *ksp_reason, PetscInt *step_type)
397: {
398: TAO_BNK *bnk = (TAO_BNK *)tao->data;
399: PetscInt bfgsUpdates = 0;
400: PetscInt kspits;
401: PetscBool is_lmvm;
402: PetscBool kspTR;
404: PetscFunctionBegin;
405: /* If there are no inactive variables left, save some computation and return an adjusted zero step
406: that has (l-x) and (u-x) for lower and upper bounded variables. */
407: if (!bnk->inactive_idx) {
408: PetscCall(VecSet(tao->stepdirection, 0.0));
409: PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));
410: PetscFunctionReturn(PETSC_SUCCESS);
411: }
413: /* Shift the reduced Hessian matrix */
414: if (shift && bnk->pert > 0) {
415: PetscCall(PetscObjectTypeCompare((PetscObject)tao->hessian, MATLMVM, &is_lmvm));
416: if (is_lmvm) {
417: PetscCall(MatShift(tao->hessian, bnk->pert));
418: } else {
419: PetscCall(MatShift(bnk->H_inactive, bnk->pert));
420: if (bnk->H_inactive != bnk->Hpre_inactive) PetscCall(MatShift(bnk->Hpre_inactive, bnk->pert));
421: }
422: }
424: /* Solve the Newton system of equations */
425: tao->ksp_its = 0;
426: PetscCall(VecSet(tao->stepdirection, 0.0));
427: if (bnk->resetksp) {
428: PetscCall(KSPReset(tao->ksp));
429: PetscCall(KSPResetFromOptions(tao->ksp));
430: bnk->resetksp = PETSC_FALSE;
431: }
432: PetscCall(KSPSetOperators(tao->ksp, bnk->H_inactive, bnk->Hpre_inactive));
433: PetscCall(VecCopy(bnk->unprojected_gradient, bnk->Gwork));
434: if (bnk->active_idx) {
435: PetscCall(VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive));
436: PetscCall(VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive));
437: } else {
438: bnk->G_inactive = bnk->unprojected_gradient;
439: bnk->X_inactive = tao->stepdirection;
440: }
441: PetscCall(KSPCGSetRadius(tao->ksp, tao->trust));
442: PetscCall(KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive));
443: PetscCall(KSPGetIterationNumber(tao->ksp, &kspits));
444: tao->ksp_its += kspits;
445: tao->ksp_tot_its += kspits;
446: PetscCall(PetscObjectHasFunction((PetscObject)tao->ksp, "KSPCGGetNormD_C", &kspTR));
447: if (kspTR) {
448: PetscCall(KSPCGGetNormD(tao->ksp, &bnk->dnorm));
450: if (0.0 == tao->trust) {
451: /* Radius was uninitialized; use the norm of the direction */
452: if (bnk->dnorm > 0.0) {
453: tao->trust = bnk->dnorm;
455: /* Modify the radius if it is too large or small */
456: tao->trust = PetscMax(tao->trust, bnk->min_radius);
457: tao->trust = PetscMin(tao->trust, bnk->max_radius);
458: } else {
459: /* The direction was bad; set radius to default value and re-solve
460: the trust-region subproblem to get a direction */
461: tao->trust = tao->trust0;
463: /* Modify the radius if it is too large or small */
464: tao->trust = PetscMax(tao->trust, bnk->min_radius);
465: tao->trust = PetscMin(tao->trust, bnk->max_radius);
467: PetscCall(KSPCGSetRadius(tao->ksp, tao->trust));
468: PetscCall(KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive));
469: PetscCall(KSPGetIterationNumber(tao->ksp, &kspits));
470: tao->ksp_its += kspits;
471: tao->ksp_tot_its += kspits;
472: PetscCall(KSPCGGetNormD(tao->ksp, &bnk->dnorm));
474: PetscCheck(bnk->dnorm != 0.0, PetscObjectComm((PetscObject)tao), PETSC_ERR_PLIB, "Initial direction zero");
475: }
476: }
477: }
478: /* Restore sub vectors back */
479: if (bnk->active_idx) {
480: PetscCall(VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive));
481: PetscCall(VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive));
482: }
483: /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
484: PetscCall(VecScale(tao->stepdirection, -1.0));
485: PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));
487: /* Record convergence reasons */
488: PetscCall(KSPGetConvergedReason(tao->ksp, ksp_reason));
489: if (KSP_CONVERGED_ATOL == *ksp_reason) {
490: ++bnk->ksp_atol;
491: } else if (KSP_CONVERGED_RTOL == *ksp_reason) {
492: ++bnk->ksp_rtol;
493: } else if (KSP_CONVERGED_STEP_LENGTH == *ksp_reason) {
494: ++bnk->ksp_ctol;
495: } else if (KSP_CONVERGED_NEG_CURVE == *ksp_reason) {
496: ++bnk->ksp_negc;
497: } else if (KSP_DIVERGED_DTOL == *ksp_reason) {
498: ++bnk->ksp_dtol;
499: } else if (KSP_DIVERGED_ITS == *ksp_reason) {
500: ++bnk->ksp_iter;
501: } else {
502: ++bnk->ksp_othr;
503: }
505: /* Make sure the BFGS preconditioner is healthy */
506: if (bnk->M) {
507: PetscCall(MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates));
508: if ((KSP_DIVERGED_INDEFINITE_PC == *ksp_reason) && (bfgsUpdates > 0)) {
509: /* Preconditioner is numerically indefinite; reset the approximation. */
510: PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
511: PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
512: }
513: }
514: *step_type = BNK_NEWTON;
515: PetscFunctionReturn(PETSC_SUCCESS);
516: }
518: /* Routine for recomputing the predicted reduction for a given step vector */
520: PetscErrorCode TaoBNKRecomputePred(Tao tao, Vec S, PetscReal *prered)
521: {
522: TAO_BNK *bnk = (TAO_BNK *)tao->data;
524: PetscFunctionBegin;
525: /* Extract subvectors associated with the inactive set */
526: if (bnk->active_idx) {
527: PetscCall(VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive));
528: PetscCall(VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work));
529: PetscCall(VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive));
530: } else {
531: bnk->X_inactive = tao->stepdirection;
532: bnk->inactive_work = bnk->Xwork;
533: bnk->G_inactive = bnk->Gwork;
534: }
535: /* Recompute the predicted decrease based on the quadratic model */
536: PetscCall(MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work));
537: PetscCall(VecAYPX(bnk->inactive_work, -0.5, bnk->G_inactive));
538: PetscCall(VecDot(bnk->inactive_work, bnk->X_inactive, prered));
539: /* Restore the sub vectors */
540: if (bnk->active_idx) {
541: PetscCall(VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive));
542: PetscCall(VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work));
543: PetscCall(VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive));
544: }
545: PetscFunctionReturn(PETSC_SUCCESS);
546: }
548: /* Routine for ensuring that the Newton step is a descent direction.
550: The step direction falls back onto BFGS, scaled gradient and gradient steps
551: in the event that the Newton step fails the test.
552: */
554: PetscErrorCode TaoBNKSafeguardStep(Tao tao, KSPConvergedReason ksp_reason, PetscInt *stepType)
555: {
556: TAO_BNK *bnk = (TAO_BNK *)tao->data;
557: PetscReal gdx, e_min;
558: PetscInt bfgsUpdates;
560: PetscFunctionBegin;
561: switch (*stepType) {
562: case BNK_NEWTON:
563: PetscCall(VecDot(tao->stepdirection, tao->gradient, &gdx));
564: if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) {
565: /* Newton step is not descent or direction produced infinity or NaN
566: Update the perturbation for next time */
567: if (bnk->pert <= 0.0) {
568: PetscBool is_gltr;
570: /* Initialize the perturbation */
571: bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
572: PetscCall(PetscObjectTypeCompare((PetscObject)tao->ksp, KSPGLTR, &is_gltr));
573: if (is_gltr) {
574: PetscCall(KSPGLTRGetMinEig(tao->ksp, &e_min));
575: bnk->pert = PetscMax(bnk->pert, -e_min);
576: }
577: } else {
578: /* Increase the perturbation */
579: bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
580: }
582: if (!bnk->M) {
583: /* We don't have the bfgs matrix around and updated
584: Must use gradient direction in this case */
585: PetscCall(VecCopy(tao->gradient, tao->stepdirection));
586: *stepType = BNK_GRADIENT;
587: } else {
588: /* Attempt to use the BFGS direction */
589: PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));
591: /* Check for success (descent direction)
592: NOTE: Negative gdx here means not a descent direction because
593: the fall-back step is missing a negative sign. */
594: PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx));
595: if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
596: /* BFGS direction is not descent or direction produced not a number
597: We can assert bfgsUpdates > 1 in this case because
598: the first solve produces the scaled gradient direction,
599: which is guaranteed to be descent */
601: /* Use steepest descent direction (scaled) */
602: PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
603: PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
604: PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));
606: *stepType = BNK_SCALED_GRADIENT;
607: } else {
608: PetscCall(MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates));
609: if (1 == bfgsUpdates) {
610: /* The first BFGS direction is always the scaled gradient */
611: *stepType = BNK_SCALED_GRADIENT;
612: } else {
613: *stepType = BNK_BFGS;
614: }
615: }
616: }
617: /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
618: PetscCall(VecScale(tao->stepdirection, -1.0));
619: PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));
620: } else {
621: /* Computed Newton step is descent */
622: switch (ksp_reason) {
623: case KSP_DIVERGED_NANORINF:
624: case KSP_DIVERGED_BREAKDOWN:
625: case KSP_DIVERGED_INDEFINITE_MAT:
626: case KSP_DIVERGED_INDEFINITE_PC:
627: case KSP_CONVERGED_NEG_CURVE:
628: /* Matrix or preconditioner is indefinite; increase perturbation */
629: if (bnk->pert <= 0.0) {
630: PetscBool is_gltr;
632: /* Initialize the perturbation */
633: bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
634: PetscCall(PetscObjectTypeCompare((PetscObject)tao->ksp, KSPGLTR, &is_gltr));
635: if (is_gltr) {
636: PetscCall(KSPGLTRGetMinEig(tao->ksp, &e_min));
637: bnk->pert = PetscMax(bnk->pert, -e_min);
638: }
639: } else {
640: /* Increase the perturbation */
641: bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
642: }
643: break;
645: default:
646: /* Newton step computation is good; decrease perturbation */
647: bnk->pert = PetscMin(bnk->psfac * bnk->pert, bnk->pmsfac * bnk->gnorm);
648: if (bnk->pert < bnk->pmin) bnk->pert = 0.0;
649: break;
650: }
651: *stepType = BNK_NEWTON;
652: }
653: break;
655: case BNK_BFGS:
656: /* Check for success (descent direction) */
657: PetscCall(VecDot(tao->stepdirection, tao->gradient, &gdx));
658: if (gdx >= 0 || PetscIsInfOrNanReal(gdx)) {
659: /* Step is not descent or solve was not successful
660: Use steepest descent direction (scaled) */
661: PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
662: PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
663: PetscCall(MatSolve(bnk->M, tao->gradient, tao->stepdirection));
664: PetscCall(VecScale(tao->stepdirection, -1.0));
665: PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));
666: *stepType = BNK_SCALED_GRADIENT;
667: } else {
668: *stepType = BNK_BFGS;
669: }
670: break;
672: case BNK_SCALED_GRADIENT:
673: break;
675: default:
676: break;
677: }
678: PetscFunctionReturn(PETSC_SUCCESS);
679: }
681: /* Routine for performing a bound-projected More-Thuente line search.
683: Includes fallbacks to BFGS, scaled gradient, and unscaled gradient steps if the
684: Newton step does not produce a valid step length.
685: */
687: PetscErrorCode TaoBNKPerformLineSearch(Tao tao, PetscInt *stepType, PetscReal *steplen, TaoLineSearchConvergedReason *reason)
688: {
689: TAO_BNK *bnk = (TAO_BNK *)tao->data;
690: TaoLineSearchConvergedReason ls_reason;
691: PetscReal e_min, gdx;
692: PetscInt bfgsUpdates;
694: PetscFunctionBegin;
695: /* Perform the linesearch */
696: PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason));
697: PetscCall(TaoAddLineSearchCounts(tao));
699: while (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER && *stepType != BNK_SCALED_GRADIENT && *stepType != BNK_GRADIENT) {
700: /* Linesearch failed, revert solution */
701: bnk->f = bnk->fold;
702: PetscCall(VecCopy(bnk->Xold, tao->solution));
703: PetscCall(VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient));
705: switch (*stepType) {
706: case BNK_NEWTON:
707: /* Failed to obtain acceptable iterate with Newton step
708: Update the perturbation for next time */
709: if (bnk->pert <= 0.0) {
710: PetscBool is_gltr;
712: /* Initialize the perturbation */
713: bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm));
714: PetscCall(PetscObjectTypeCompare((PetscObject)tao->ksp, KSPGLTR, &is_gltr));
715: if (is_gltr) {
716: PetscCall(KSPGLTRGetMinEig(tao->ksp, &e_min));
717: bnk->pert = PetscMax(bnk->pert, -e_min);
718: }
719: } else {
720: /* Increase the perturbation */
721: bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm));
722: }
724: if (!bnk->M) {
725: /* We don't have the bfgs matrix around and being updated
726: Must use gradient direction in this case */
727: PetscCall(VecCopy(bnk->unprojected_gradient, tao->stepdirection));
728: *stepType = BNK_GRADIENT;
729: } else {
730: /* Attempt to use the BFGS direction */
731: PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));
732: /* Check for success (descent direction)
733: NOTE: Negative gdx means not a descent direction because the step here is missing a negative sign. */
734: PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx));
735: if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
736: /* BFGS direction is not descent or direction produced not a number
737: We can assert bfgsUpdates > 1 in this case
738: Use steepest descent direction (scaled) */
739: PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
740: PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
741: PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));
743: bfgsUpdates = 1;
744: *stepType = BNK_SCALED_GRADIENT;
745: } else {
746: PetscCall(MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates));
747: if (1 == bfgsUpdates) {
748: /* The first BFGS direction is always the scaled gradient */
749: *stepType = BNK_SCALED_GRADIENT;
750: } else {
751: *stepType = BNK_BFGS;
752: }
753: }
754: }
755: break;
757: case BNK_BFGS:
758: /* Can only enter if pc_type == BNK_PC_BFGS
759: Failed to obtain acceptable iterate with BFGS step
760: Attempt to use the scaled gradient direction */
761: PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE));
762: PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient));
763: PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection));
765: bfgsUpdates = 1;
766: *stepType = BNK_SCALED_GRADIENT;
767: break;
768: }
769: /* Make sure the safeguarded fall-back step is zero for actively bounded variables */
770: PetscCall(VecScale(tao->stepdirection, -1.0));
771: PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection));
773: /* Perform one last line search with the fall-back step */
774: PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason));
775: PetscCall(TaoAddLineSearchCounts(tao));
776: }
777: *reason = ls_reason;
778: PetscFunctionReturn(PETSC_SUCCESS);
779: }
781: /* Routine for updating the trust radius.
783: Function features three different update methods:
784: 1) Line-search step length based
785: 2) Predicted decrease on the CG quadratic model
786: 3) Interpolation
787: */
789: PetscErrorCode TaoBNKUpdateTrustRadius(Tao tao, PetscReal prered, PetscReal actred, PetscInt updateType, PetscInt stepType, PetscBool *accept)
790: {
791: TAO_BNK *bnk = (TAO_BNK *)tao->data;
793: PetscReal step, kappa;
794: PetscReal gdx, tau_1, tau_2, tau_min, tau_max;
796: PetscFunctionBegin;
797: /* Update trust region radius */
798: *accept = PETSC_FALSE;
799: switch (updateType) {
800: case BNK_UPDATE_STEP:
801: *accept = PETSC_TRUE; /* always accept here because line search succeeded */
802: if (stepType == BNK_NEWTON) {
803: PetscCall(TaoLineSearchGetStepLength(tao->linesearch, &step));
804: if (step < bnk->nu1) {
805: /* Very bad step taken; reduce radius */
806: tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
807: } else if (step < bnk->nu2) {
808: /* Reasonably bad step taken; reduce radius */
809: tao->trust = bnk->omega2 * PetscMin(bnk->dnorm, tao->trust);
810: } else if (step < bnk->nu3) {
811: /* Reasonable step was taken; leave radius alone */
812: if (bnk->omega3 < 1.0) {
813: tao->trust = bnk->omega3 * PetscMin(bnk->dnorm, tao->trust);
814: } else if (bnk->omega3 > 1.0) {
815: tao->trust = PetscMax(bnk->omega3 * bnk->dnorm, tao->trust);
816: }
817: } else if (step < bnk->nu4) {
818: /* Full step taken; increase the radius */
819: tao->trust = PetscMax(bnk->omega4 * bnk->dnorm, tao->trust);
820: } else {
821: /* More than full step taken; increase the radius */
822: tao->trust = PetscMax(bnk->omega5 * bnk->dnorm, tao->trust);
823: }
824: } else {
825: /* Newton step was not good; reduce the radius */
826: tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust);
827: }
828: break;
830: case BNK_UPDATE_REDUCTION:
831: if (stepType == BNK_NEWTON) {
832: if ((prered < 0.0) || PetscIsInfOrNanReal(prered)) {
833: /* The predicted reduction has the wrong sign. This cannot
834: happen in infinite precision arithmetic. Step should
835: be rejected! */
836: tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
837: } else {
838: if (PetscIsInfOrNanReal(actred)) {
839: tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
840: } else {
841: if ((PetscAbsScalar(actred) <= PetscMax(1.0, PetscAbsScalar(bnk->f)) * bnk->epsilon) && (PetscAbsScalar(prered) <= PetscMax(1.0, PetscAbsScalar(bnk->f)) * bnk->epsilon)) {
842: kappa = 1.0;
843: } else {
844: kappa = actred / prered;
845: }
846: /* Accept or reject the step and update radius */
847: if (kappa < bnk->eta1) {
848: /* Reject the step */
849: tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm);
850: } else {
851: /* Accept the step */
852: *accept = PETSC_TRUE;
853: /* Update the trust region radius only if the computed step is at the trust radius boundary */
854: if (bnk->dnorm == tao->trust) {
855: if (kappa < bnk->eta2) {
856: /* Marginal bad step */
857: tao->trust = bnk->alpha2 * tao->trust;
858: } else if (kappa < bnk->eta3) {
859: /* Reasonable step */
860: tao->trust = bnk->alpha3 * tao->trust;
861: } else if (kappa < bnk->eta4) {
862: /* Good step */
863: tao->trust = bnk->alpha4 * tao->trust;
864: } else {
865: /* Very good step */
866: tao->trust = bnk->alpha5 * tao->trust;
867: }
868: }
869: }
870: }
871: }
872: } else {
873: /* Newton step was not good; reduce the radius */
874: tao->trust = bnk->alpha1 * PetscMin(bnk->dnorm, tao->trust);
875: }
876: break;
878: default:
879: if (stepType == BNK_NEWTON) {
880: if (prered < 0.0) {
881: /* The predicted reduction has the wrong sign. This cannot */
882: /* happen in infinite precision arithmetic. Step should */
883: /* be rejected! */
884: tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
885: } else {
886: if (PetscIsInfOrNanReal(actred)) {
887: tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
888: } else {
889: if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) {
890: kappa = 1.0;
891: } else {
892: kappa = actred / prered;
893: }
895: PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx));
896: tau_1 = bnk->theta * gdx / (bnk->theta * gdx - (1.0 - bnk->theta) * prered + actred);
897: tau_2 = bnk->theta * gdx / (bnk->theta * gdx + (1.0 + bnk->theta) * prered - actred);
898: tau_min = PetscMin(tau_1, tau_2);
899: tau_max = PetscMax(tau_1, tau_2);
901: if (kappa >= 1.0 - bnk->mu1) {
902: /* Great agreement */
903: *accept = PETSC_TRUE;
904: if (tau_max < 1.0) {
905: tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
906: } else if (tau_max > bnk->gamma4) {
907: tao->trust = PetscMax(tao->trust, bnk->gamma4 * bnk->dnorm);
908: } else {
909: tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
910: }
911: } else if (kappa >= 1.0 - bnk->mu2) {
912: /* Good agreement */
913: *accept = PETSC_TRUE;
914: if (tau_max < bnk->gamma2) {
915: tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
916: } else if (tau_max > bnk->gamma3) {
917: tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm);
918: } else if (tau_max < 1.0) {
919: tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
920: } else {
921: tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm);
922: }
923: } else {
924: /* Not good agreement */
925: if (tau_min > 1.0) {
926: tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm);
927: } else if (tau_max < bnk->gamma1) {
928: tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
929: } else if ((tau_min < bnk->gamma1) && (tau_max >= 1.0)) {
930: tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm);
931: } else if ((tau_1 >= bnk->gamma1) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1) || (tau_2 >= 1.0))) {
932: tao->trust = tau_1 * PetscMin(tao->trust, bnk->dnorm);
933: } else if ((tau_2 >= bnk->gamma1) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1) || (tau_2 >= 1.0))) {
934: tao->trust = tau_2 * PetscMin(tao->trust, bnk->dnorm);
935: } else {
936: tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm);
937: }
938: }
939: }
940: }
941: } else {
942: /* Newton step was not good; reduce the radius */
943: tao->trust = bnk->gamma1 * PetscMin(bnk->dnorm, tao->trust);
944: }
945: break;
946: }
947: /* Make sure the radius does not violate min and max settings */
948: tao->trust = PetscMin(tao->trust, bnk->max_radius);
949: tao->trust = PetscMax(tao->trust, bnk->min_radius);
950: PetscFunctionReturn(PETSC_SUCCESS);
951: }
953: PetscErrorCode TaoBNKAddStepCounts(Tao tao, PetscInt stepType)
954: {
955: TAO_BNK *bnk = (TAO_BNK *)tao->data;
957: PetscFunctionBegin;
958: switch (stepType) {
959: case BNK_NEWTON:
960: ++bnk->newt;
961: break;
962: case BNK_BFGS:
963: ++bnk->bfgs;
964: break;
965: case BNK_SCALED_GRADIENT:
966: ++bnk->sgrad;
967: break;
968: case BNK_GRADIENT:
969: ++bnk->grad;
970: break;
971: default:
972: break;
973: }
974: PetscFunctionReturn(PETSC_SUCCESS);
975: }
977: PetscErrorCode TaoSetUp_BNK(Tao tao)
978: {
979: TAO_BNK *bnk = (TAO_BNK *)tao->data;
981: PetscFunctionBegin;
982: if (!tao->gradient) PetscCall(VecDuplicate(tao->solution, &tao->gradient));
983: if (!tao->stepdirection) PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));
984: if (!bnk->W) PetscCall(VecDuplicate(tao->solution, &bnk->W));
985: if (!bnk->Xold) PetscCall(VecDuplicate(tao->solution, &bnk->Xold));
986: if (!bnk->Gold) PetscCall(VecDuplicate(tao->solution, &bnk->Gold));
987: if (!bnk->Xwork) PetscCall(VecDuplicate(tao->solution, &bnk->Xwork));
988: if (!bnk->Gwork) PetscCall(VecDuplicate(tao->solution, &bnk->Gwork));
989: if (!bnk->unprojected_gradient) PetscCall(VecDuplicate(tao->solution, &bnk->unprojected_gradient));
990: if (!bnk->unprojected_gradient_old) PetscCall(VecDuplicate(tao->solution, &bnk->unprojected_gradient_old));
991: if (!bnk->Diag_min) PetscCall(VecDuplicate(tao->solution, &bnk->Diag_min));
992: if (!bnk->Diag_max) PetscCall(VecDuplicate(tao->solution, &bnk->Diag_max));
993: PetscCall(TaoSetSolution(bnk->bncg, tao->solution));
994: if (bnk->max_cg_its > 0) {
995: /* Ensure that the important common vectors are shared between BNK and embedded BNCG */
996: bnk->bncg_ctx = (TAO_BNCG *)bnk->bncg->data;
997: PetscCall(PetscObjectReference((PetscObject)bnk->unprojected_gradient_old));
998: PetscCall(VecDestroy(&bnk->bncg_ctx->unprojected_gradient_old));
999: bnk->bncg_ctx->unprojected_gradient_old = bnk->unprojected_gradient_old;
1000: PetscCall(PetscObjectReference((PetscObject)bnk->unprojected_gradient));
1001: PetscCall(VecDestroy(&bnk->bncg_ctx->unprojected_gradient));
1002: bnk->bncg_ctx->unprojected_gradient = bnk->unprojected_gradient;
1003: PetscCall(PetscObjectReference((PetscObject)bnk->Gold));
1004: PetscCall(VecDestroy(&bnk->bncg_ctx->G_old));
1005: bnk->bncg_ctx->G_old = bnk->Gold;
1006: PetscCall(PetscObjectReference((PetscObject)tao->gradient));
1007: PetscCall(VecDestroy(&bnk->bncg->gradient));
1008: bnk->bncg->gradient = tao->gradient;
1009: PetscCall(PetscObjectReference((PetscObject)tao->stepdirection));
1010: PetscCall(VecDestroy(&bnk->bncg->stepdirection));
1011: bnk->bncg->stepdirection = tao->stepdirection;
1012: /* Copy over some settings from BNK into BNCG */
1013: PetscCall(TaoSetMaximumIterations(bnk->bncg, bnk->max_cg_its));
1014: PetscCall(TaoSetTolerances(bnk->bncg, tao->gatol, tao->grtol, tao->gttol));
1015: PetscCall(TaoSetFunctionLowerBound(bnk->bncg, tao->fmin));
1016: PetscCall(TaoSetConvergenceTest(bnk->bncg, tao->ops->convergencetest, tao->cnvP));
1017: {
1018: TaoTerm term;
1019: Vec params;
1020: PetscReal scale;
1021: Mat map;
1023: // Note: tao->objective_term.term and bnk->bncg->objective_term.term will point to same address
1024: PetscCall(TaoGetTerm(tao, &scale, &term, ¶ms, &map));
1025: PetscCall(TaoAddTerm(bnk->bncg, NULL, scale, term, params, map));
1026: }
1027: PetscCall(PetscObjectCopyFortranFunctionPointers((PetscObject)tao, (PetscObject)bnk->bncg));
1028: }
1029: bnk->X_inactive = NULL;
1030: bnk->G_inactive = NULL;
1031: bnk->inactive_work = NULL;
1032: bnk->active_work = NULL;
1033: bnk->inactive_idx = NULL;
1034: bnk->active_idx = NULL;
1035: bnk->active_lower = NULL;
1036: bnk->active_upper = NULL;
1037: bnk->active_fixed = NULL;
1038: bnk->M = NULL;
1039: bnk->H_inactive = NULL;
1040: bnk->Hpre_inactive = NULL;
1041: PetscFunctionReturn(PETSC_SUCCESS);
1042: }
1044: PetscErrorCode TaoDestroy_BNK(Tao tao)
1045: {
1046: TAO_BNK *bnk = (TAO_BNK *)tao->data;
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(PETSC_SUCCESS);
1069: }
1071: PetscErrorCode TaoSetFromOptions_BNK(Tao tao, PetscOptionItems PetscOptionsObject)
1072: {
1073: TAO_BNK *bnk = (TAO_BNK *)tao->data;
1075: PetscFunctionBegin;
1076: PetscOptionsHeadBegin(PetscOptionsObject, "Newton-Krylov method for bound constrained optimization");
1077: PetscCall(PetscOptionsEList("-tao_bnk_init_type", "radius initialization type", "", BNK_INIT, BNK_INIT_TYPES, BNK_INIT[bnk->init_type], &bnk->init_type, NULL));
1078: PetscCall(PetscOptionsEList("-tao_bnk_update_type", "radius update type", "", BNK_UPDATE, BNK_UPDATE_TYPES, BNK_UPDATE[bnk->update_type], &bnk->update_type, NULL));
1079: PetscCall(PetscOptionsEList("-tao_bnk_as_type", "active set estimation method", "", BNK_AS, BNK_AS_TYPES, BNK_AS[bnk->as_type], &bnk->as_type, NULL));
1080: PetscCall(PetscOptionsReal("-tao_bnk_sval", "(developer) Hessian perturbation starting value", "", bnk->sval, &bnk->sval, NULL));
1081: PetscCall(PetscOptionsReal("-tao_bnk_imin", "(developer) minimum initial Hessian perturbation", "", bnk->imin, &bnk->imin, NULL));
1082: PetscCall(PetscOptionsReal("-tao_bnk_imax", "(developer) maximum initial Hessian perturbation", "", bnk->imax, &bnk->imax, NULL));
1083: PetscCall(PetscOptionsReal("-tao_bnk_imfac", "(developer) initial merit factor for Hessian perturbation", "", bnk->imfac, &bnk->imfac, NULL));
1084: PetscCall(PetscOptionsReal("-tao_bnk_pmin", "(developer) minimum Hessian perturbation", "", bnk->pmin, &bnk->pmin, NULL));
1085: PetscCall(PetscOptionsReal("-tao_bnk_pmax", "(developer) maximum Hessian perturbation", "", bnk->pmax, &bnk->pmax, NULL));
1086: PetscCall(PetscOptionsReal("-tao_bnk_pgfac", "(developer) Hessian perturbation growth factor", "", bnk->pgfac, &bnk->pgfac, NULL));
1087: PetscCall(PetscOptionsReal("-tao_bnk_psfac", "(developer) Hessian perturbation shrink factor", "", bnk->psfac, &bnk->psfac, NULL));
1088: PetscCall(PetscOptionsReal("-tao_bnk_pmgfac", "(developer) merit growth factor for Hessian perturbation", "", bnk->pmgfac, &bnk->pmgfac, NULL));
1089: PetscCall(PetscOptionsReal("-tao_bnk_pmsfac", "(developer) merit shrink factor for Hessian perturbation", "", bnk->pmsfac, &bnk->pmsfac, NULL));
1090: PetscCall(PetscOptionsReal("-tao_bnk_eta1", "(developer) threshold for rejecting step (-tao_bnk_update_type reduction)", "", bnk->eta1, &bnk->eta1, NULL));
1091: PetscCall(PetscOptionsReal("-tao_bnk_eta2", "(developer) threshold for accepting marginal step (-tao_bnk_update_type reduction)", "", bnk->eta2, &bnk->eta2, NULL));
1092: PetscCall(PetscOptionsReal("-tao_bnk_eta3", "(developer) threshold for accepting reasonable step (-tao_bnk_update_type reduction)", "", bnk->eta3, &bnk->eta3, NULL));
1093: PetscCall(PetscOptionsReal("-tao_bnk_eta4", "(developer) threshold for accepting good step (-tao_bnk_update_type reduction)", "", bnk->eta4, &bnk->eta4, NULL));
1094: PetscCall(PetscOptionsReal("-tao_bnk_alpha1", "(developer) radius reduction factor for rejected step (-tao_bnk_update_type reduction)", "", bnk->alpha1, &bnk->alpha1, NULL));
1095: PetscCall(PetscOptionsReal("-tao_bnk_alpha2", "(developer) radius reduction factor for marginally accepted bad step (-tao_bnk_update_type reduction)", "", bnk->alpha2, &bnk->alpha2, NULL));
1096: PetscCall(PetscOptionsReal("-tao_bnk_alpha3", "(developer) radius increase factor for reasonable accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha3, &bnk->alpha3, NULL));
1097: PetscCall(PetscOptionsReal("-tao_bnk_alpha4", "(developer) radius increase factor for good accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha4, &bnk->alpha4, NULL));
1098: PetscCall(PetscOptionsReal("-tao_bnk_alpha5", "(developer) radius increase factor for very good accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha5, &bnk->alpha5, NULL));
1099: PetscCall(PetscOptionsReal("-tao_bnk_nu1", "(developer) threshold for small line-search step length (-tao_bnk_update_type step)", "", bnk->nu1, &bnk->nu1, NULL));
1100: PetscCall(PetscOptionsReal("-tao_bnk_nu2", "(developer) threshold for reasonable line-search step length (-tao_bnk_update_type step)", "", bnk->nu2, &bnk->nu2, NULL));
1101: PetscCall(PetscOptionsReal("-tao_bnk_nu3", "(developer) threshold for large line-search step length (-tao_bnk_update_type step)", "", bnk->nu3, &bnk->nu3, NULL));
1102: PetscCall(PetscOptionsReal("-tao_bnk_nu4", "(developer) threshold for very large line-search step length (-tao_bnk_update_type step)", "", bnk->nu4, &bnk->nu4, NULL));
1103: 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));
1104: 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));
1105: PetscCall(PetscOptionsReal("-tao_bnk_omega3", "(developer) radius factor for decent line-search step length (-tao_bnk_update_type step)", "", bnk->omega3, &bnk->omega3, NULL));
1106: 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));
1107: 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));
1108: 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));
1109: PetscCall(PetscOptionsReal("-tao_bnk_mu2_i", "(developer) threshold for accepting good step (-tao_bnk_init_type interpolation)", "", bnk->mu2_i, &bnk->mu2_i, NULL));
1110: 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));
1111: 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));
1112: 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));
1113: 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));
1114: PetscCall(PetscOptionsReal("-tao_bnk_theta_i", "(developer) trust region interpolation factor (-tao_bnk_init_type interpolation)", "", bnk->theta_i, &bnk->theta_i, NULL));
1115: PetscCall(PetscOptionsReal("-tao_bnk_mu1", "(developer) threshold for accepting very good step (-tao_bnk_update_type interpolation)", "", bnk->mu1, &bnk->mu1, NULL));
1116: PetscCall(PetscOptionsReal("-tao_bnk_mu2", "(developer) threshold for accepting good step (-tao_bnk_update_type interpolation)", "", bnk->mu2, &bnk->mu2, NULL));
1117: PetscCall(PetscOptionsReal("-tao_bnk_gamma1", "(developer) radius reduction factor for rejected very bad step (-tao_bnk_update_type interpolation)", "", bnk->gamma1, &bnk->gamma1, NULL));
1118: PetscCall(PetscOptionsReal("-tao_bnk_gamma2", "(developer) radius reduction factor for rejected bad step (-tao_bnk_update_type interpolation)", "", bnk->gamma2, &bnk->gamma2, NULL));
1119: PetscCall(PetscOptionsReal("-tao_bnk_gamma3", "(developer) radius increase factor for accepted good step (-tao_bnk_update_type interpolation)", "", bnk->gamma3, &bnk->gamma3, NULL));
1120: PetscCall(PetscOptionsReal("-tao_bnk_gamma4", "(developer) radius increase factor for accepted very good step (-tao_bnk_update_type interpolation)", "", bnk->gamma4, &bnk->gamma4, NULL));
1121: PetscCall(PetscOptionsReal("-tao_bnk_theta", "(developer) trust region interpolation factor (-tao_bnk_update_type interpolation)", "", bnk->theta, &bnk->theta, NULL));
1122: PetscCall(PetscOptionsReal("-tao_bnk_min_radius", "(developer) lower bound on initial radius", "", bnk->min_radius, &bnk->min_radius, NULL));
1123: PetscCall(PetscOptionsReal("-tao_bnk_max_radius", "(developer) upper bound on radius", "", bnk->max_radius, &bnk->max_radius, NULL));
1124: PetscCall(PetscOptionsReal("-tao_bnk_epsilon", "(developer) tolerance used when computing actual and predicted reduction", "", bnk->epsilon, &bnk->epsilon, NULL));
1125: PetscCall(PetscOptionsReal("-tao_bnk_as_tol", "(developer) initial tolerance used when estimating actively bounded variables", "", bnk->as_tol, &bnk->as_tol, NULL));
1126: PetscCall(PetscOptionsReal("-tao_bnk_as_step", "(developer) step length used when estimating actively bounded variables", "", bnk->as_step, &bnk->as_step, NULL));
1127: 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));
1128: PetscOptionsHeadEnd();
1130: PetscCall(TaoSetOptionsPrefix(bnk->bncg, ((PetscObject)tao)->prefix));
1131: PetscCall(TaoAppendOptionsPrefix(bnk->bncg, "tao_bnk_cg_"));
1132: PetscCall(TaoSetFromOptions(bnk->bncg));
1134: PetscCall(KSPSetOptionsPrefix(tao->ksp, ((PetscObject)tao)->prefix));
1135: PetscCall(KSPAppendOptionsPrefix(tao->ksp, "tao_bnk_"));
1136: PetscCall(KSPSetFromOptions(tao->ksp));
1137: PetscFunctionReturn(PETSC_SUCCESS);
1138: }
1140: PetscErrorCode TaoView_BNK(Tao tao, PetscViewer viewer)
1141: {
1142: TAO_BNK *bnk = (TAO_BNK *)tao->data;
1143: PetscInt nrejects;
1144: PetscBool isascii;
1146: PetscFunctionBegin;
1147: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
1148: if (isascii) {
1149: PetscCall(PetscViewerASCIIPushTab(viewer));
1150: PetscCall(TaoView(bnk->bncg, viewer));
1151: if (bnk->M) {
1152: PetscCall(MatLMVMGetRejectCount(bnk->M, &nrejects));
1153: PetscCall(PetscViewerASCIIPrintf(viewer, "Rejected BFGS updates: %" PetscInt_FMT "\n", nrejects));
1154: }
1155: PetscCall(PetscViewerASCIIPrintf(viewer, "CG steps: %" PetscInt_FMT "\n", bnk->tot_cg_its));
1156: PetscCall(PetscViewerASCIIPrintf(viewer, "Newton steps: %" PetscInt_FMT "\n", bnk->newt));
1157: if (bnk->M) PetscCall(PetscViewerASCIIPrintf(viewer, "BFGS steps: %" PetscInt_FMT "\n", bnk->bfgs));
1158: PetscCall(PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %" PetscInt_FMT "\n", bnk->sgrad));
1159: PetscCall(PetscViewerASCIIPrintf(viewer, "Gradient steps: %" PetscInt_FMT "\n", bnk->grad));
1160: PetscCall(PetscViewerASCIIPrintf(viewer, "KSP termination reasons:\n"));
1161: PetscCall(PetscViewerASCIIPrintf(viewer, " atol: %" PetscInt_FMT "\n", bnk->ksp_atol));
1162: PetscCall(PetscViewerASCIIPrintf(viewer, " rtol: %" PetscInt_FMT "\n", bnk->ksp_rtol));
1163: PetscCall(PetscViewerASCIIPrintf(viewer, " ctol: %" PetscInt_FMT "\n", bnk->ksp_ctol));
1164: PetscCall(PetscViewerASCIIPrintf(viewer, " negc: %" PetscInt_FMT "\n", bnk->ksp_negc));
1165: PetscCall(PetscViewerASCIIPrintf(viewer, " dtol: %" PetscInt_FMT "\n", bnk->ksp_dtol));
1166: PetscCall(PetscViewerASCIIPrintf(viewer, " iter: %" PetscInt_FMT "\n", bnk->ksp_iter));
1167: PetscCall(PetscViewerASCIIPrintf(viewer, " othr: %" PetscInt_FMT "\n", bnk->ksp_othr));
1168: PetscCall(PetscViewerASCIIPopTab(viewer));
1169: }
1170: PetscFunctionReturn(PETSC_SUCCESS);
1171: }
1173: /*MC
1174: TAOBNK - Shared base-type for Bounded Newton-Krylov type algorithms.
1175: At each iteration, the BNK methods solve the symmetric
1176: system of equations to obtain the step direction $d_k$:
1177: $ H_k d_k = -g_k $
1178: for free variables only. The step can be globalized either through
1179: trust-region methods, or a line search, or a heuristic mixture of both.
1181: Options Database Keys:
1182: + -tao_bnk_max_cg_its - maximum number of bounded conjugate-gradient iterations taken in each Newton loop
1183: . -tao_bnk_init_type - trust radius initialization method ("constant", "direction", "interpolation")
1184: . -tao_bnk_update_type - trust radius update method ("step", "direction", "interpolation")
1185: . -tao_bnk_as_type - active-set estimation method ("none", "bertsekas")
1186: . -tao_bnk_as_tol - (developer) initial tolerance used in estimating bounded active variables (-as_type bertsekas)
1187: . -tao_bnk_as_step - (developer) trial step length used in estimating bounded active variables (-as_type bertsekas)
1188: . -tao_bnk_sval - (developer) Hessian perturbation starting value
1189: . -tao_bnk_imin - (developer) minimum initial Hessian perturbation
1190: . -tao_bnk_imax - (developer) maximum initial Hessian perturbation
1191: . -tao_bnk_pmin - (developer) minimum Hessian perturbation
1192: . -tao_bnk_pmax - (developer) aximum Hessian perturbation
1193: . -tao_bnk_pgfac - (developer) Hessian perturbation growth factor
1194: . -tao_bnk_psfac - (developer) Hessian perturbation shrink factor
1195: . -tao_bnk_imfac - (developer) initial merit factor for Hessian perturbation
1196: . -tao_bnk_pmgfac - (developer) merit growth factor for Hessian perturbation
1197: . -tao_bnk_pmsfac - (developer) merit shrink factor for Hessian perturbation
1198: . -tao_bnk_eta1 - (developer) threshold for rejecting step (-update_type reduction)
1199: . -tao_bnk_eta2 - (developer) threshold for accepting marginal step (-update_type reduction)
1200: . -tao_bnk_eta3 - (developer) threshold for accepting reasonable step (-update_type reduction)
1201: . -tao_bnk_eta4 - (developer) threshold for accepting good step (-update_type reduction)
1202: . -tao_bnk_alpha1 - (developer) radius reduction factor for rejected step (-update_type reduction)
1203: . -tao_bnk_alpha2 - (developer) radius reduction factor for marginally accepted bad step (-update_type reduction)
1204: . -tao_bnk_alpha3 - (developer) radius increase factor for reasonable accepted step (-update_type reduction)
1205: . -tao_bnk_alpha4 - (developer) radius increase factor for good accepted step (-update_type reduction)
1206: . -tao_bnk_alpha5 - (developer) radius increase factor for very good accepted step (-update_type reduction)
1207: . -tao_bnk_epsilon - (developer) tolerance for small pred/actual ratios that trigger automatic step acceptance (-update_type reduction)
1208: . -tao_bnk_mu1 - (developer) threshold for accepting very good step (-update_type interpolation)
1209: . -tao_bnk_mu2 - (developer) threshold for accepting good step (-update_type interpolation)
1210: . -tao_bnk_gamma1 - (developer) radius reduction factor for rejected very bad step (-update_type interpolation)
1211: . -tao_bnk_gamma2 - (developer) radius reduction factor for rejected bad step (-update_type interpolation)
1212: . -tao_bnk_gamma3 - (developer) radius increase factor for accepted good step (-update_type interpolation)
1213: . -tao_bnk_gamma4 - (developer) radius increase factor for accepted very good step (-update_type interpolation)
1214: . -tao_bnk_theta - (developer) trust region interpolation factor (-update_type interpolation)
1215: . -tao_bnk_nu1 - (developer) threshold for small line-search step length (-update_type step)
1216: . -tao_bnk_nu2 - (developer) threshold for reasonable line-search step length (-update_type step)
1217: . -tao_bnk_nu3 - (developer) threshold for large line-search step length (-update_type step)
1218: . -tao_bnk_nu4 - (developer) threshold for very large line-search step length (-update_type step)
1219: . -tao_bnk_omega1 - (developer) radius reduction factor for very small line-search step length (-update_type step)
1220: . -tao_bnk_omega2 - (developer) radius reduction factor for small line-search step length (-update_type step)
1221: . -tao_bnk_omega3 - (developer) radius factor for decent line-search step length (-update_type step)
1222: . -tao_bnk_omega4 - (developer) radius increase factor for large line-search step length (-update_type step)
1223: . -tao_bnk_omega5 - (developer) radius increase factor for very large line-search step length (-update_type step)
1224: . -tao_bnk_mu1_i - (developer) threshold for accepting very good step (-init_type interpolation)
1225: . -tao_bnk_mu2_i - (developer) threshold for accepting good step (-init_type interpolation)
1226: . -tao_bnk_gamma1_i - (developer) radius reduction factor for rejected very bad step (-init_type interpolation)
1227: . -tao_bnk_gamma2_i - (developer) radius reduction factor for rejected bad step (-init_type interpolation)
1228: . -tao_bnk_gamma3_i - (developer) radius increase factor for accepted good step (-init_type interpolation)
1229: . -tao_bnk_gamma4_i - (developer) radius increase factor for accepted very good step (-init_type interpolation)
1230: - -tao_bnk_theta_i - (developer) trust region interpolation factor (-init_type interpolation)
1232: Level: beginner
1234: The various algorithmic factors can only be supplied via the options database
1236: .seealso: `Tao`, `TAONLS`, `TAONTL`, `TAONM`, `TaoType`, `TaoCreate()`
1237: M*/
1239: PetscErrorCode TaoCreate_BNK(Tao tao)
1240: {
1241: TAO_BNK *bnk;
1242: PC pc;
1244: PetscFunctionBegin;
1245: PetscCall(PetscNew(&bnk));
1247: tao->ops->setup = TaoSetUp_BNK;
1248: tao->ops->view = TaoView_BNK;
1249: tao->ops->setfromoptions = TaoSetFromOptions_BNK;
1250: tao->ops->destroy = TaoDestroy_BNK;
1251: tao->uses_gradient = PETSC_TRUE;
1252: tao->uses_hessian_matrices = PETSC_TRUE;
1254: /* Override default settings (unless already changed) */
1255: PetscCall(TaoParametersInitialize(tao));
1256: PetscObjectParameterSetDefault(tao, max_it, 50);
1257: PetscObjectParameterSetDefault(tao, trust0, 100.0);
1259: tao->data = (void *)bnk;
1261: /* Hessian shifting parameters */
1262: bnk->computehessian = TaoBNKComputeHessian;
1263: bnk->computestep = TaoBNKComputeStep;
1265: bnk->sval = 0.0;
1266: bnk->imin = 1.0e-4;
1267: bnk->imax = 1.0e+2;
1268: bnk->imfac = 1.0e-1;
1270: bnk->pmin = 1.0e-12;
1271: bnk->pmax = 1.0e+2;
1272: bnk->pgfac = 1.0e+1;
1273: bnk->psfac = 4.0e-1;
1274: bnk->pmgfac = 1.0e-1;
1275: bnk->pmsfac = 1.0e-1;
1277: /* Default values for trust-region radius update based on steplength */
1278: bnk->nu1 = 0.25;
1279: bnk->nu2 = 0.50;
1280: bnk->nu3 = 1.00;
1281: bnk->nu4 = 1.25;
1283: bnk->omega1 = 0.25;
1284: bnk->omega2 = 0.50;
1285: bnk->omega3 = 1.00;
1286: bnk->omega4 = 2.00;
1287: bnk->omega5 = 4.00;
1289: /* Default values for trust-region radius update based on reduction */
1290: bnk->eta1 = 1.0e-4;
1291: bnk->eta2 = 0.25;
1292: bnk->eta3 = 0.50;
1293: bnk->eta4 = 0.90;
1295: bnk->alpha1 = 0.25;
1296: bnk->alpha2 = 0.50;
1297: bnk->alpha3 = 1.00;
1298: bnk->alpha4 = 2.00;
1299: bnk->alpha5 = 4.00;
1301: /* Default values for trust-region radius update based on interpolation */
1302: bnk->mu1 = 0.10;
1303: bnk->mu2 = 0.50;
1305: bnk->gamma1 = 0.25;
1306: bnk->gamma2 = 0.50;
1307: bnk->gamma3 = 2.00;
1308: bnk->gamma4 = 4.00;
1310: bnk->theta = 0.05;
1312: /* Default values for trust region initialization based on interpolation */
1313: bnk->mu1_i = 0.35;
1314: bnk->mu2_i = 0.50;
1316: bnk->gamma1_i = 0.0625;
1317: bnk->gamma2_i = 0.5;
1318: bnk->gamma3_i = 2.0;
1319: bnk->gamma4_i = 5.0;
1321: bnk->theta_i = 0.25;
1323: /* Remaining parameters */
1324: bnk->max_cg_its = 0;
1325: bnk->min_radius = 1.0e-10;
1326: bnk->max_radius = 1.0e10;
1327: bnk->epsilon = PetscPowReal(PETSC_MACHINE_EPSILON, 2.0 / 3.0);
1328: bnk->as_tol = 1.0e-3;
1329: bnk->as_step = 1.0e-3;
1330: bnk->dmin = 1.0e-6;
1331: bnk->dmax = 1.0e6;
1333: bnk->M = NULL;
1334: bnk->bfgs_pre = NULL;
1335: bnk->init_type = BNK_INIT_INTERPOLATION;
1336: bnk->update_type = BNK_UPDATE_REDUCTION;
1337: bnk->as_type = BNK_AS_BERTSEKAS;
1339: /* Create the embedded BNCG solver */
1340: PetscCall(TaoCreate(PetscObjectComm((PetscObject)tao), &bnk->bncg));
1341: PetscCall(PetscObjectIncrementTabLevel((PetscObject)bnk->bncg, (PetscObject)tao, 1));
1342: PetscCall(TaoSetType(bnk->bncg, TAOBNCG));
1344: /* Create the line search */
1345: PetscCall(TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch));
1346: PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1));
1347: PetscCall(TaoLineSearchSetType(tao->linesearch, TAOLINESEARCHMT));
1348: PetscCall(TaoLineSearchUseTaoRoutines(tao->linesearch, tao));
1350: /* Set linear solver to default for symmetric matrices */
1351: PetscCall(KSPCreate(((PetscObject)tao)->comm, &tao->ksp));
1352: PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1));
1353: PetscCall(KSPSetType(tao->ksp, KSPSTCG));
1354: PetscCall(KSPGetPC(tao->ksp, &pc));
1355: PetscCall(PCSetType(pc, PCLMVM));
1356: PetscFunctionReturn(PETSC_SUCCESS);
1357: }