1 #include <petsctaolinesearch.h> 2 #include <../src/tao/bound/impls/bnk/bnk.h> 3 #include <petscksp.h> 4 5 static const char *BNK_INIT[64] = {"constant", "direction", "interpolation"}; 6 static const char *BNK_UPDATE[64] = {"step", "reduction", "interpolation"}; 7 static const char *BNK_AS[64] = {"none", "bertsekas"}; 8 9 /* Extracts from the full Hessian the part associated with the current bnk->inactive_idx and set the PCLMVM preconditioner */ 10 11 static PetscErrorCode TaoBNKComputeSubHessian(Tao tao) 12 { 13 TAO_BNK *bnk = (TAO_BNK *)tao->data; 14 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 } 36 37 /* Initializes the KSP solver, the BFGS preconditioner, and the initial trust radius estimation */ 38 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; 51 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)); 57 58 /* Project the initial point onto the feasible region */ 59 PetscCall(TaoBoundSolution(tao->solution, tao->XL, tao->XU, 0.0, &nDiff, tao->solution)); 60 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)); 67 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); 76 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; 85 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; 92 93 /* Initialize the Hessian perturbation */ 94 bnk->pert = bnk->sval; 95 96 /* Reset initial steplength to zero (this helps BNCG reset its direction internally) */ 97 PetscCall(VecSet(tao->stepdirection, 0.0)); 98 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)); 113 114 /* 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)); 117 118 /* 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; 128 129 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; 136 137 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 } 144 145 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 } 164 165 /* 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 } 186 187 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); 191 192 if (PetscAbsScalar(kappa - (PetscReal)1.0) <= bnk->mu1_i) { 193 /* Great agreement */ 194 max_radius = PetscMax(max_radius, tao->trust); 195 196 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); 206 207 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 } 233 234 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); 262 263 /* 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; 267 268 default: 269 /* Norm of the first direction will initialize radius */ 270 tao->trust = 0.0; 271 break; 272 } 273 } 274 PetscFunctionReturn(PETSC_SUCCESS); 275 } 276 277 /* Computes the exact Hessian and extracts its subHessian */ 278 279 PetscErrorCode TaoBNKComputeHessian(Tao tao) 280 { 281 TAO_BNK *bnk = (TAO_BNK *)tao->data; 282 283 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 } 292 293 /* Routine for estimating the active set */ 294 295 PetscErrorCode TaoBNKEstimateActiveSet(Tao tao, PetscInt asType) 296 { 297 TAO_BNK *bnk = (TAO_BNK *)tao->data; 298 PetscBool hessComputed, diagExists, hadactive; 299 300 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; 309 310 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; 334 335 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 } 341 342 /* Routine for bounding the step direction */ 343 344 PetscErrorCode TaoBNKBoundStep(Tao tao, PetscInt asType, Vec step) 345 { 346 TAO_BNK *bnk = (TAO_BNK *)tao->data; 347 348 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 } 361 362 /* Routine for taking a finite number of BNCG iterations to 363 accelerate Newton convergence. 364 365 In practice, this approach simply trades off Hessian evaluations 366 for more gradient evaluations. 367 */ 368 369 PetscErrorCode TaoBNKTakeCGSteps(Tao tao, PetscBool *terminate) 370 { 371 TAO_BNK *bnk = (TAO_BNK *)tao->data; 372 373 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 } 396 397 /* Routine for computing the Newton step. */ 398 399 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; 406 407 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 } 415 416 /* 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 } 426 427 /* 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)); 452 453 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; 457 458 /* 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; 465 466 /* 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); 469 470 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)); 476 477 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)); 489 490 /* 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 } 507 508 /* 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 } 520 521 /* Routine for recomputing the predicted reduction for a given step vector */ 522 523 PetscErrorCode TaoBNKRecomputePred(Tao tao, Vec S, PetscReal *prered) 524 { 525 TAO_BNK *bnk = (TAO_BNK *)tao->data; 526 527 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 } 550 551 /* Routine for ensuring that the Newton step is a descent direction. 552 553 The step direction falls back onto BFGS, scaled gradient and gradient steps 554 in the event that the Newton step fails the test. 555 */ 556 557 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; 562 563 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; 572 573 /* 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 } 584 585 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)); 593 594 /* 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 */ 603 604 /* 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)); 608 609 *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; 634 635 /* 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; 647 648 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; 657 658 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; 674 675 case BNK_SCALED_GRADIENT: 676 break; 677 678 default: 679 break; 680 } 681 PetscFunctionReturn(PETSC_SUCCESS); 682 } 683 684 /* Routine for performing a bound-projected More-Thuente line search. 685 686 Includes fallbacks to BFGS, scaled gradient, and unscaled gradient steps if the 687 Newton step does not produce a valid step length. 688 */ 689 690 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; 696 697 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)); 701 702 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)); 707 708 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; 714 715 /* 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 } 726 727 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)); 745 746 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; 759 760 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)); 767 768 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)); 775 776 /* 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 } 783 784 /* Routine for updating the trust radius. 785 786 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 */ 791 792 PetscErrorCode TaoBNKUpdateTrustRadius(Tao tao, PetscReal prered, PetscReal actred, PetscInt updateType, PetscInt stepType, PetscBool *accept) 793 { 794 TAO_BNK *bnk = (TAO_BNK *)tao->data; 795 796 PetscReal step, kappa; 797 PetscReal gdx, tau_1, tau_2, tau_min, tau_max; 798 799 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; 832 833 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; 880 881 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 } 897 898 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); 903 904 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 } 955 956 PetscErrorCode TaoBNKAddStepCounts(Tao tao, PetscInt stepType) 957 { 958 TAO_BNK *bnk = (TAO_BNK *)tao->data; 959 960 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 } 979 980 PetscErrorCode TaoSetUp_BNK(Tao tao) 981 { 982 TAO_BNK *bnk = (TAO_BNK *)tao->data; 983 984 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 } 1039 1040 PetscErrorCode TaoDestroy_BNK(Tao tao) 1041 { 1042 TAO_BNK *bnk = (TAO_BNK *)tao->data; 1043 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 } 1066 1067 PetscErrorCode TaoSetFromOptions_BNK(Tao tao, PetscOptionItems PetscOptionsObject) 1068 { 1069 TAO_BNK *bnk = (TAO_BNK *)tao->data; 1070 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(); 1125 1126 PetscCall(TaoSetOptionsPrefix(bnk->bncg, ((PetscObject)tao)->prefix)); 1127 PetscCall(TaoAppendOptionsPrefix(bnk->bncg, "tao_bnk_cg_")); 1128 PetscCall(TaoSetFromOptions(bnk->bncg)); 1129 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 } 1135 1136 PetscErrorCode TaoView_BNK(Tao tao, PetscViewer viewer) 1137 { 1138 TAO_BNK *bnk = (TAO_BNK *)tao->data; 1139 PetscInt nrejects; 1140 PetscBool isascii; 1141 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 } 1168 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. 1176 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) 1227 1228 Level: beginner 1229 M*/ 1230 1231 PetscErrorCode TaoCreate_BNK(Tao tao) 1232 { 1233 TAO_BNK *bnk; 1234 PC pc; 1235 1236 PetscFunctionBegin; 1237 PetscCall(PetscNew(&bnk)); 1238 1239 tao->ops->setup = TaoSetUp_BNK; 1240 tao->ops->view = TaoView_BNK; 1241 tao->ops->setfromoptions = TaoSetFromOptions_BNK; 1242 tao->ops->destroy = TaoDestroy_BNK; 1243 1244 /* Override default settings (unless already changed) */ 1245 PetscCall(TaoParametersInitialize(tao)); 1246 PetscObjectParameterSetDefault(tao, max_it, 50); 1247 PetscObjectParameterSetDefault(tao, trust0, 100.0); 1248 1249 tao->data = (void *)bnk; 1250 1251 /* Hessian shifting parameters */ 1252 bnk->computehessian = TaoBNKComputeHessian; 1253 bnk->computestep = TaoBNKComputeStep; 1254 1255 bnk->sval = 0.0; 1256 bnk->imin = 1.0e-4; 1257 bnk->imax = 1.0e+2; 1258 bnk->imfac = 1.0e-1; 1259 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; 1266 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; 1272 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; 1278 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; 1284 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; 1290 1291 /* Default values for trust-region radius update based on interpolation */ 1292 bnk->mu1 = 0.10; 1293 bnk->mu2 = 0.50; 1294 1295 bnk->gamma1 = 0.25; 1296 bnk->gamma2 = 0.50; 1297 bnk->gamma3 = 2.00; 1298 bnk->gamma4 = 4.00; 1299 1300 bnk->theta = 0.05; 1301 1302 /* Default values for trust region initialization based on interpolation */ 1303 bnk->mu1_i = 0.35; 1304 bnk->mu2_i = 0.50; 1305 1306 bnk->gamma1_i = 0.0625; 1307 bnk->gamma2_i = 0.5; 1308 bnk->gamma3_i = 2.0; 1309 bnk->gamma4_i = 5.0; 1310 1311 bnk->theta_i = 0.25; 1312 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; 1322 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; 1328 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)); 1333 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)); 1339 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 } 1348