1 #include <petsctaolinesearch.h> 2 #include <../src/tao/bound/impls/bnk/bnk.h> 3 #include <petscksp.h> 4 5 static const char *BNK_INIT[64] = {"constant", "direction", "interpolation"}; 6 static const char *BNK_UPDATE[64] = {"step", "reduction", "interpolation"}; 7 static const char *BNK_AS[64] = {"none", "bertsekas"}; 8 9 /*------------------------------------------------------------*/ 10 11 /* Routine for initializing the KSP solver, the BFGS preconditioner, and the initial trust radius estimation */ 12 13 PetscErrorCode TaoBNKInitialize(Tao tao, PetscInt initType, PetscBool *needH) 14 { 15 TAO_BNK *bnk = (TAO_BNK *)tao->data; 16 PC pc; 17 PetscReal f_min, ftrial, prered, actred, kappa, sigma, resnorm; 18 PetscReal tau, tau_1, tau_2, tau_max, tau_min, max_radius; 19 PetscBool is_bfgs, is_jacobi, is_symmetric, sym_set; 20 PetscInt n, N, nDiff; 21 PetscInt i_max = 5; 22 PetscInt j_max = 1; 23 PetscInt i, j; 24 PetscVoidFunction kspTR; 25 26 PetscFunctionBegin; 27 /* Project the current point onto the feasible set */ 28 PetscCall(TaoComputeVariableBounds(tao)); 29 PetscCall(TaoSetVariableBounds(bnk->bncg, tao->XL, tao->XU)); 30 if (tao->bounded) { 31 PetscCall(TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU)); 32 } 33 34 /* Project the initial point onto the feasible region */ 35 PetscCall(TaoBoundSolution(tao->solution, tao->XL,tao->XU, 0.0, &nDiff, tao->solution)); 36 37 /* Check convergence criteria */ 38 PetscCall(TaoComputeObjectiveAndGradient(tao, tao->solution, &bnk->f, bnk->unprojected_gradient)); 39 PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type)); 40 PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient)); 41 PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0)); 42 PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm)); 43 44 /* Test the initial point for convergence */ 45 PetscCall(VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W)); 46 PetscCall(VecNorm(bnk->W, NORM_2, &resnorm)); 47 PetscCheck(!PetscIsInfOrNanReal(bnk->f) && !PetscIsInfOrNanReal(resnorm),PetscObjectComm((PetscObject)tao),PETSC_ERR_USER, "User provided compute function generated Inf or NaN"); 48 PetscCall(TaoLogConvergenceHistory(tao,bnk->f,resnorm,0.0,tao->ksp_its)); 49 PetscCall(TaoMonitor(tao,tao->niter,bnk->f,resnorm,0.0,1.0)); 50 PetscCall((*tao->ops->convergencetest)(tao,tao->cnvP)); 51 if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0); 52 53 /* Reset KSP stopping reason counters */ 54 bnk->ksp_atol = 0; 55 bnk->ksp_rtol = 0; 56 bnk->ksp_dtol = 0; 57 bnk->ksp_ctol = 0; 58 bnk->ksp_negc = 0; 59 bnk->ksp_iter = 0; 60 bnk->ksp_othr = 0; 61 62 /* Reset accepted step type counters */ 63 bnk->tot_cg_its = 0; 64 bnk->newt = 0; 65 bnk->bfgs = 0; 66 bnk->sgrad = 0; 67 bnk->grad = 0; 68 69 /* Initialize the Hessian perturbation */ 70 bnk->pert = bnk->sval; 71 72 /* Reset initial steplength to zero (this helps BNCG reset its direction internally) */ 73 PetscCall(VecSet(tao->stepdirection, 0.0)); 74 75 /* Allocate the vectors needed for the BFGS approximation */ 76 PetscCall(KSPGetPC(tao->ksp, &pc)); 77 PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCLMVM, &is_bfgs)); 78 PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCJACOBI, &is_jacobi)); 79 if (is_bfgs) { 80 bnk->bfgs_pre = pc; 81 PetscCall(PCLMVMGetMatLMVM(bnk->bfgs_pre, &bnk->M)); 82 PetscCall(VecGetLocalSize(tao->solution, &n)); 83 PetscCall(VecGetSize(tao->solution, &N)); 84 PetscCall(MatSetSizes(bnk->M, n, n, N, N)); 85 PetscCall(MatLMVMAllocate(bnk->M, tao->solution, bnk->unprojected_gradient)); 86 PetscCall(MatIsSymmetricKnown(bnk->M, &sym_set, &is_symmetric)); 87 PetscCheck(sym_set && is_symmetric,PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_INCOMP, "LMVM matrix in the LMVM preconditioner must be symmetric."); 88 } else if (is_jacobi) { 89 PetscCall(PCJacobiSetUseAbs(pc,PETSC_TRUE)); 90 } 91 92 /* Prepare the min/max vectors for safeguarding diagonal scales */ 93 PetscCall(VecSet(bnk->Diag_min, bnk->dmin)); 94 PetscCall(VecSet(bnk->Diag_max, bnk->dmax)); 95 96 /* Initialize trust-region radius. The initialization is only performed 97 when we are using Nash, Steihaug-Toint or the Generalized Lanczos method. */ 98 *needH = PETSC_TRUE; 99 PetscCall(PetscObjectQueryFunction((PetscObject)tao->ksp,"KSPCGSetRadius_C",&kspTR)); 100 if (kspTR) { 101 switch (initType) { 102 case BNK_INIT_CONSTANT: 103 /* Use the initial radius specified */ 104 tao->trust = tao->trust0; 105 break; 106 107 case BNK_INIT_INTERPOLATION: 108 /* Use interpolation based on the initial Hessian */ 109 max_radius = 0.0; 110 tao->trust = tao->trust0; 111 for (j = 0; j < j_max; ++j) { 112 f_min = bnk->f; 113 sigma = 0.0; 114 115 if (*needH) { 116 /* Compute the Hessian at the new step, and extract the inactive subsystem */ 117 PetscCall((*bnk->computehessian)(tao)); 118 PetscCall(TaoBNKEstimateActiveSet(tao, BNK_AS_NONE)); 119 PetscCall(MatDestroy(&bnk->H_inactive)); 120 if (bnk->active_idx) { 121 PetscCall(MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive)); 122 } else { 123 PetscCall(PetscObjectReference((PetscObject)tao->hessian)); 124 bnk->H_inactive = tao->hessian; 125 } 126 *needH = PETSC_FALSE; 127 } 128 129 for (i = 0; i < i_max; ++i) { 130 /* Take a steepest descent step and snap it to bounds */ 131 PetscCall(VecCopy(tao->solution, bnk->Xold)); 132 PetscCall(VecAXPY(tao->solution, -tao->trust/bnk->gnorm, tao->gradient)); 133 PetscCall(TaoBoundSolution(tao->solution, tao->XL,tao->XU, 0.0, &nDiff, tao->solution)); 134 /* Compute the step we actually accepted */ 135 PetscCall(VecCopy(tao->solution, bnk->W)); 136 PetscCall(VecAXPY(bnk->W, -1.0, bnk->Xold)); 137 /* Compute the objective at the trial */ 138 PetscCall(TaoComputeObjective(tao, tao->solution, &ftrial)); 139 PetscCheck(!PetscIsInfOrNanReal(bnk->f),PetscObjectComm((PetscObject)tao),PETSC_ERR_USER, "User provided compute function generated Inf or NaN"); 140 PetscCall(VecCopy(bnk->Xold, tao->solution)); 141 if (PetscIsInfOrNanReal(ftrial)) { 142 tau = bnk->gamma1_i; 143 } else { 144 if (ftrial < f_min) { 145 f_min = ftrial; 146 sigma = -tao->trust / bnk->gnorm; 147 } 148 149 /* Compute the predicted and actual reduction */ 150 if (bnk->active_idx) { 151 PetscCall(VecGetSubVector(bnk->W, bnk->inactive_idx, &bnk->X_inactive)); 152 PetscCall(VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work)); 153 } else { 154 bnk->X_inactive = bnk->W; 155 bnk->inactive_work = bnk->Xwork; 156 } 157 PetscCall(MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work)); 158 PetscCall(VecDot(bnk->X_inactive, bnk->inactive_work, &prered)); 159 if (bnk->active_idx) { 160 PetscCall(VecRestoreSubVector(bnk->W, bnk->inactive_idx, &bnk->X_inactive)); 161 PetscCall(VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work)); 162 } 163 prered = tao->trust * (bnk->gnorm - 0.5 * tao->trust * prered / (bnk->gnorm * bnk->gnorm)); 164 actred = bnk->f - ftrial; 165 if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) { 166 kappa = 1.0; 167 } else { 168 kappa = actred / prered; 169 } 170 171 tau_1 = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust + (1.0 - bnk->theta_i) * prered - actred); 172 tau_2 = bnk->theta_i * bnk->gnorm * tao->trust / (bnk->theta_i * bnk->gnorm * tao->trust - (1.0 + bnk->theta_i) * prered + actred); 173 tau_min = PetscMin(tau_1, tau_2); 174 tau_max = PetscMax(tau_1, tau_2); 175 176 if (PetscAbsScalar(kappa - (PetscReal)1.0) <= bnk->mu1_i) { 177 /* Great agreement */ 178 max_radius = PetscMax(max_radius, tao->trust); 179 180 if (tau_max < 1.0) { 181 tau = bnk->gamma3_i; 182 } else if (tau_max > bnk->gamma4_i) { 183 tau = bnk->gamma4_i; 184 } else { 185 tau = tau_max; 186 } 187 } else if (PetscAbsScalar(kappa - (PetscReal)1.0) <= bnk->mu2_i) { 188 /* Good agreement */ 189 max_radius = PetscMax(max_radius, tao->trust); 190 191 if (tau_max < bnk->gamma2_i) { 192 tau = bnk->gamma2_i; 193 } else if (tau_max > bnk->gamma3_i) { 194 tau = bnk->gamma3_i; 195 } else { 196 tau = tau_max; 197 } 198 } else { 199 /* Not good agreement */ 200 if (tau_min > 1.0) { 201 tau = bnk->gamma2_i; 202 } else if (tau_max < bnk->gamma1_i) { 203 tau = bnk->gamma1_i; 204 } else if ((tau_min < bnk->gamma1_i) && (tau_max >= 1.0)) { 205 tau = bnk->gamma1_i; 206 } else if ((tau_1 >= bnk->gamma1_i) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1_i) || (tau_2 >= 1.0))) { 207 tau = tau_1; 208 } else if ((tau_2 >= bnk->gamma1_i) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1_i) || (tau_2 >= 1.0))) { 209 tau = tau_2; 210 } else { 211 tau = tau_max; 212 } 213 } 214 } 215 tao->trust = tau * tao->trust; 216 } 217 218 if (f_min < bnk->f) { 219 /* We accidentally found a solution better than the initial, so accept it */ 220 bnk->f = f_min; 221 PetscCall(VecCopy(tao->solution, bnk->Xold)); 222 PetscCall(VecAXPY(tao->solution,sigma,tao->gradient)); 223 PetscCall(TaoBoundSolution(tao->solution, tao->XL,tao->XU, 0.0, &nDiff, tao->solution)); 224 PetscCall(VecCopy(tao->solution, tao->stepdirection)); 225 PetscCall(VecAXPY(tao->stepdirection, -1.0, bnk->Xold)); 226 PetscCall(TaoComputeGradient(tao,tao->solution,bnk->unprojected_gradient)); 227 PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type)); 228 PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient)); 229 PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0)); 230 /* Compute gradient at the new iterate and flip switch to compute the Hessian later */ 231 PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm)); 232 *needH = PETSC_TRUE; 233 /* Test the new step for convergence */ 234 PetscCall(VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W)); 235 PetscCall(VecNorm(bnk->W, NORM_2, &resnorm)); 236 PetscCheck(!PetscIsInfOrNanReal(resnorm),PetscObjectComm((PetscObject)tao),PETSC_ERR_USER, "User provided compute function generated Inf or NaN"); 237 PetscCall(TaoLogConvergenceHistory(tao,bnk->f,resnorm,0.0,tao->ksp_its)); 238 PetscCall(TaoMonitor(tao,tao->niter,bnk->f,resnorm,0.0,1.0)); 239 PetscCall((*tao->ops->convergencetest)(tao,tao->cnvP)); 240 if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0); 241 /* active BNCG recycling early because we have a stepdirection computed */ 242 PetscCall(TaoSetRecycleHistory(bnk->bncg, PETSC_TRUE)); 243 } 244 } 245 tao->trust = PetscMax(tao->trust, max_radius); 246 247 /* Ensure that the trust radius is within the limits */ 248 tao->trust = PetscMax(tao->trust, bnk->min_radius); 249 tao->trust = PetscMin(tao->trust, bnk->max_radius); 250 break; 251 252 default: 253 /* Norm of the first direction will initialize radius */ 254 tao->trust = 0.0; 255 break; 256 } 257 } 258 PetscFunctionReturn(0); 259 } 260 261 /*------------------------------------------------------------*/ 262 263 /* Routine for computing the exact Hessian and preparing the preconditioner at the new iterate */ 264 265 PetscErrorCode TaoBNKComputeHessian(Tao tao) 266 { 267 TAO_BNK *bnk = (TAO_BNK *)tao->data; 268 269 PetscFunctionBegin; 270 /* Compute the Hessian */ 271 PetscCall(TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre)); 272 /* Add a correction to the BFGS preconditioner */ 273 if (bnk->M) { 274 PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient)); 275 } 276 /* Prepare the reduced sub-matrices for the inactive set */ 277 PetscCall(MatDestroy(&bnk->Hpre_inactive)); 278 PetscCall(MatDestroy(&bnk->H_inactive)); 279 if (bnk->active_idx) { 280 PetscCall(MatCreateSubMatrix(tao->hessian, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->H_inactive)); 281 if (tao->hessian == tao->hessian_pre) { 282 PetscCall(PetscObjectReference((PetscObject)bnk->H_inactive)); 283 bnk->Hpre_inactive = bnk->H_inactive; 284 } else { 285 PetscCall(MatCreateSubMatrix(tao->hessian_pre, bnk->inactive_idx, bnk->inactive_idx, MAT_INITIAL_MATRIX, &bnk->Hpre_inactive)); 286 } 287 if (bnk->bfgs_pre) { 288 PetscCall(PCLMVMSetIS(bnk->bfgs_pre, bnk->inactive_idx)); 289 } 290 } else { 291 PetscCall(PetscObjectReference((PetscObject)tao->hessian)); 292 bnk->H_inactive = tao->hessian; 293 if (tao->hessian == tao->hessian_pre) { 294 PetscCall(PetscObjectReference((PetscObject)bnk->H_inactive)); 295 bnk->Hpre_inactive = bnk->H_inactive; 296 } else { 297 PetscCall(PetscObjectReference((PetscObject)tao->hessian_pre)); 298 bnk->Hpre_inactive = tao->hessian_pre; 299 } 300 if (bnk->bfgs_pre) { 301 PetscCall(PCLMVMClearIS(bnk->bfgs_pre)); 302 } 303 } 304 PetscFunctionReturn(0); 305 } 306 307 /*------------------------------------------------------------*/ 308 309 /* Routine for estimating the active set */ 310 311 PetscErrorCode TaoBNKEstimateActiveSet(Tao tao, PetscInt asType) 312 { 313 TAO_BNK *bnk = (TAO_BNK *)tao->data; 314 PetscBool hessComputed, diagExists; 315 316 PetscFunctionBegin; 317 switch (asType) { 318 case BNK_AS_NONE: 319 PetscCall(ISDestroy(&bnk->inactive_idx)); 320 PetscCall(VecWhichInactive(tao->XL, tao->solution, bnk->unprojected_gradient, tao->XU, PETSC_TRUE, &bnk->inactive_idx)); 321 PetscCall(ISDestroy(&bnk->active_idx)); 322 PetscCall(ISComplementVec(bnk->inactive_idx, tao->solution, &bnk->active_idx)); 323 break; 324 325 case BNK_AS_BERTSEKAS: 326 /* Compute the trial step vector with which we will estimate the active set at the next iteration */ 327 if (bnk->M) { 328 /* If the BFGS preconditioner matrix is available, we will construct a trial step with it */ 329 PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, bnk->W)); 330 } else { 331 hessComputed = diagExists = PETSC_FALSE; 332 if (tao->hessian) { 333 PetscCall(MatAssembled(tao->hessian, &hessComputed)); 334 } 335 if (hessComputed) { 336 PetscCall(MatHasOperation(tao->hessian, MATOP_GET_DIAGONAL, &diagExists)); 337 } 338 if (diagExists) { 339 /* BFGS preconditioner doesn't exist so let's invert the absolute diagonal of the Hessian instead onto the gradient */ 340 PetscCall(MatGetDiagonal(tao->hessian, bnk->Xwork)); 341 PetscCall(VecAbs(bnk->Xwork)); 342 PetscCall(VecMedian(bnk->Diag_min, bnk->Xwork, bnk->Diag_max, bnk->Xwork)); 343 PetscCall(VecReciprocal(bnk->Xwork)); 344 PetscCall(VecPointwiseMult(bnk->W, bnk->Xwork, bnk->unprojected_gradient)); 345 } else { 346 /* If the Hessian or its diagonal does not exist, we will simply use gradient step */ 347 PetscCall(VecCopy(bnk->unprojected_gradient, bnk->W)); 348 } 349 } 350 PetscCall(VecScale(bnk->W, -1.0)); 351 PetscCall(TaoEstimateActiveBounds(tao->solution, tao->XL, tao->XU, bnk->unprojected_gradient, bnk->W, bnk->Xwork, bnk->as_step, &bnk->as_tol, 352 &bnk->active_lower, &bnk->active_upper, &bnk->active_fixed, &bnk->active_idx, &bnk->inactive_idx)); 353 break; 354 355 default: 356 break; 357 } 358 PetscFunctionReturn(0); 359 } 360 361 /*------------------------------------------------------------*/ 362 363 /* Routine for bounding the step direction */ 364 365 PetscErrorCode TaoBNKBoundStep(Tao tao, PetscInt asType, Vec step) 366 { 367 TAO_BNK *bnk = (TAO_BNK *)tao->data; 368 369 PetscFunctionBegin; 370 switch (asType) { 371 case BNK_AS_NONE: 372 PetscCall(VecISSet(step, bnk->active_idx, 0.0)); 373 break; 374 375 case BNK_AS_BERTSEKAS: 376 PetscCall(TaoBoundStep(tao->solution, tao->XL, tao->XU, bnk->active_lower, bnk->active_upper, bnk->active_fixed, 1.0, step)); 377 break; 378 379 default: 380 break; 381 } 382 PetscFunctionReturn(0); 383 } 384 385 /*------------------------------------------------------------*/ 386 387 /* Routine for taking a finite number of BNCG iterations to 388 accelerate Newton convergence. 389 390 In practice, this approach simply trades off Hessian evaluations 391 for more gradient evaluations. 392 */ 393 394 PetscErrorCode TaoBNKTakeCGSteps(Tao tao, PetscBool *terminate) 395 { 396 TAO_BNK *bnk = (TAO_BNK *)tao->data; 397 398 PetscFunctionBegin; 399 *terminate = PETSC_FALSE; 400 if (bnk->max_cg_its > 0) { 401 /* Copy the current function value (important vectors are already shared) */ 402 bnk->bncg_ctx->f = bnk->f; 403 /* Take some small finite number of BNCG iterations */ 404 PetscCall(TaoSolve(bnk->bncg)); 405 /* Add the number of gradient and function evaluations to the total */ 406 tao->nfuncs += bnk->bncg->nfuncs; 407 tao->nfuncgrads += bnk->bncg->nfuncgrads; 408 tao->ngrads += bnk->bncg->ngrads; 409 tao->nhess += bnk->bncg->nhess; 410 bnk->tot_cg_its += bnk->bncg->niter; 411 /* Extract the BNCG function value out and save it into BNK */ 412 bnk->f = bnk->bncg_ctx->f; 413 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) { 414 *terminate = PETSC_TRUE; 415 } else { 416 PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type)); 417 } 418 } 419 PetscFunctionReturn(0); 420 } 421 422 /*------------------------------------------------------------*/ 423 424 /* Routine for computing the Newton step. */ 425 426 PetscErrorCode TaoBNKComputeStep(Tao tao, PetscBool shift, KSPConvergedReason *ksp_reason, PetscInt *step_type) 427 { 428 TAO_BNK *bnk = (TAO_BNK *)tao->data; 429 PetscInt bfgsUpdates = 0; 430 PetscInt kspits; 431 PetscBool is_lmvm; 432 PetscVoidFunction kspTR; 433 434 PetscFunctionBegin; 435 /* If there are no inactive variables left, save some computation and return an adjusted zero step 436 that has (l-x) and (u-x) for lower and upper bounded variables. */ 437 if (!bnk->inactive_idx) { 438 PetscCall(VecSet(tao->stepdirection, 0.0)); 439 PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection)); 440 PetscFunctionReturn(0); 441 } 442 443 /* Shift the reduced Hessian matrix */ 444 if (shift && bnk->pert > 0) { 445 PetscCall(PetscObjectTypeCompare((PetscObject)tao->hessian, MATLMVM, &is_lmvm)); 446 if (is_lmvm) { 447 PetscCall(MatShift(tao->hessian, bnk->pert)); 448 } else { 449 PetscCall(MatShift(bnk->H_inactive, bnk->pert)); 450 if (bnk->H_inactive != bnk->Hpre_inactive) { 451 PetscCall(MatShift(bnk->Hpre_inactive, bnk->pert)); 452 } 453 } 454 } 455 456 /* Solve the Newton system of equations */ 457 tao->ksp_its = 0; 458 PetscCall(VecSet(tao->stepdirection, 0.0)); 459 PetscCall(KSPReset(tao->ksp)); 460 PetscCall(KSPResetFromOptions(tao->ksp)); 461 PetscCall(KSPSetOperators(tao->ksp,bnk->H_inactive,bnk->Hpre_inactive)); 462 PetscCall(VecCopy(bnk->unprojected_gradient, bnk->Gwork)); 463 if (bnk->active_idx) { 464 PetscCall(VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive)); 465 PetscCall(VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive)); 466 } else { 467 bnk->G_inactive = bnk->unprojected_gradient; 468 bnk->X_inactive = tao->stepdirection; 469 } 470 PetscCall(PetscObjectQueryFunction((PetscObject)tao->ksp,"KSPCGSetRadius_C",&kspTR)); 471 if (kspTR) { 472 PetscCall(KSPCGSetRadius(tao->ksp,tao->trust)); 473 PetscCall(KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive)); 474 PetscCall(KSPGetIterationNumber(tao->ksp,&kspits)); 475 tao->ksp_its += kspits; 476 tao->ksp_tot_its += kspits; 477 PetscCall(KSPCGGetNormD(tao->ksp,&bnk->dnorm)); 478 479 if (0.0 == tao->trust) { 480 /* Radius was uninitialized; use the norm of the direction */ 481 if (bnk->dnorm > 0.0) { 482 tao->trust = bnk->dnorm; 483 484 /* Modify the radius if it is too large or small */ 485 tao->trust = PetscMax(tao->trust, bnk->min_radius); 486 tao->trust = PetscMin(tao->trust, bnk->max_radius); 487 } else { 488 /* The direction was bad; set radius to default value and re-solve 489 the trust-region subproblem to get a direction */ 490 tao->trust = tao->trust0; 491 492 /* Modify the radius if it is too large or small */ 493 tao->trust = PetscMax(tao->trust, bnk->min_radius); 494 tao->trust = PetscMin(tao->trust, bnk->max_radius); 495 496 PetscCall(KSPCGSetRadius(tao->ksp,tao->trust)); 497 PetscCall(KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive)); 498 PetscCall(KSPGetIterationNumber(tao->ksp,&kspits)); 499 tao->ksp_its += kspits; 500 tao->ksp_tot_its += kspits; 501 PetscCall(KSPCGGetNormD(tao->ksp,&bnk->dnorm)); 502 503 PetscCheck(bnk->dnorm != 0.0,PetscObjectComm((PetscObject)tao),PETSC_ERR_PLIB, "Initial direction zero"); 504 } 505 } 506 } else { 507 PetscCall(KSPSolve(tao->ksp, bnk->G_inactive, bnk->X_inactive)); 508 PetscCall(KSPGetIterationNumber(tao->ksp, &kspits)); 509 tao->ksp_its += kspits; 510 tao->ksp_tot_its += kspits; 511 } 512 /* Restore sub vectors back */ 513 if (bnk->active_idx) { 514 PetscCall(VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive)); 515 PetscCall(VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive)); 516 } 517 /* Make sure the safeguarded fall-back step is zero for actively bounded variables */ 518 PetscCall(VecScale(tao->stepdirection, -1.0)); 519 PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection)); 520 521 /* Record convergence reasons */ 522 PetscCall(KSPGetConvergedReason(tao->ksp, ksp_reason)); 523 if (KSP_CONVERGED_ATOL == *ksp_reason) { 524 ++bnk->ksp_atol; 525 } else if (KSP_CONVERGED_RTOL == *ksp_reason) { 526 ++bnk->ksp_rtol; 527 } else if (KSP_CONVERGED_CG_CONSTRAINED == *ksp_reason) { 528 ++bnk->ksp_ctol; 529 } else if (KSP_CONVERGED_CG_NEG_CURVE == *ksp_reason) { 530 ++bnk->ksp_negc; 531 } else if (KSP_DIVERGED_DTOL == *ksp_reason) { 532 ++bnk->ksp_dtol; 533 } else if (KSP_DIVERGED_ITS == *ksp_reason) { 534 ++bnk->ksp_iter; 535 } else { 536 ++bnk->ksp_othr; 537 } 538 539 /* Make sure the BFGS preconditioner is healthy */ 540 if (bnk->M) { 541 PetscCall(MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates)); 542 if ((KSP_DIVERGED_INDEFINITE_PC == *ksp_reason) && (bfgsUpdates > 0)) { 543 /* Preconditioner is numerically indefinite; reset the approximation. */ 544 PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE)); 545 PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient)); 546 } 547 } 548 *step_type = BNK_NEWTON; 549 PetscFunctionReturn(0); 550 } 551 552 /*------------------------------------------------------------*/ 553 554 /* Routine for recomputing the predicted reduction for a given step vector */ 555 556 PetscErrorCode TaoBNKRecomputePred(Tao tao, Vec S, PetscReal *prered) 557 { 558 TAO_BNK *bnk = (TAO_BNK *)tao->data; 559 560 PetscFunctionBegin; 561 /* Extract subvectors associated with the inactive set */ 562 if (bnk->active_idx) { 563 PetscCall(VecGetSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive)); 564 PetscCall(VecGetSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work)); 565 PetscCall(VecGetSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive)); 566 } else { 567 bnk->X_inactive = tao->stepdirection; 568 bnk->inactive_work = bnk->Xwork; 569 bnk->G_inactive = bnk->Gwork; 570 } 571 /* Recompute the predicted decrease based on the quadratic model */ 572 PetscCall(MatMult(bnk->H_inactive, bnk->X_inactive, bnk->inactive_work)); 573 PetscCall(VecAYPX(bnk->inactive_work, -0.5, bnk->G_inactive)); 574 PetscCall(VecDot(bnk->inactive_work, bnk->X_inactive, prered)); 575 /* Restore the sub vectors */ 576 if (bnk->active_idx) { 577 PetscCall(VecRestoreSubVector(tao->stepdirection, bnk->inactive_idx, &bnk->X_inactive)); 578 PetscCall(VecRestoreSubVector(bnk->Xwork, bnk->inactive_idx, &bnk->inactive_work)); 579 PetscCall(VecRestoreSubVector(bnk->Gwork, bnk->inactive_idx, &bnk->G_inactive)); 580 } 581 PetscFunctionReturn(0); 582 } 583 584 /*------------------------------------------------------------*/ 585 586 /* Routine for ensuring that the Newton step is a descent direction. 587 588 The step direction falls back onto BFGS, scaled gradient and gradient steps 589 in the event that the Newton step fails the test. 590 */ 591 592 PetscErrorCode TaoBNKSafeguardStep(Tao tao, KSPConvergedReason ksp_reason, PetscInt *stepType) 593 { 594 TAO_BNK *bnk = (TAO_BNK *)tao->data; 595 PetscReal gdx, e_min; 596 PetscInt bfgsUpdates; 597 598 PetscFunctionBegin; 599 switch (*stepType) { 600 case BNK_NEWTON: 601 PetscCall(VecDot(tao->stepdirection, tao->gradient, &gdx)); 602 if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) { 603 /* Newton step is not descent or direction produced Inf or NaN 604 Update the perturbation for next time */ 605 if (bnk->pert <= 0.0) { 606 PetscBool is_gltr; 607 608 /* Initialize the perturbation */ 609 bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm)); 610 PetscCall(PetscObjectTypeCompare((PetscObject)(tao->ksp),KSPGLTR,&is_gltr)); 611 if (is_gltr) { 612 PetscCall(KSPGLTRGetMinEig(tao->ksp,&e_min)); 613 bnk->pert = PetscMax(bnk->pert, -e_min); 614 } 615 } else { 616 /* Increase the perturbation */ 617 bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm)); 618 } 619 620 if (!bnk->M) { 621 /* We don't have the bfgs matrix around and updated 622 Must use gradient direction in this case */ 623 PetscCall(VecCopy(tao->gradient, tao->stepdirection)); 624 *stepType = BNK_GRADIENT; 625 } else { 626 /* Attempt to use the BFGS direction */ 627 PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection)); 628 629 /* Check for success (descent direction) 630 NOTE: Negative gdx here means not a descent direction because 631 the fall-back step is missing a negative sign. */ 632 PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx)); 633 if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) { 634 /* BFGS direction is not descent or direction produced not a number 635 We can assert bfgsUpdates > 1 in this case because 636 the first solve produces the scaled gradient direction, 637 which is guaranteed to be descent */ 638 639 /* Use steepest descent direction (scaled) */ 640 PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE)); 641 PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient)); 642 PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection)); 643 644 *stepType = BNK_SCALED_GRADIENT; 645 } else { 646 PetscCall(MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates)); 647 if (1 == bfgsUpdates) { 648 /* The first BFGS direction is always the scaled gradient */ 649 *stepType = BNK_SCALED_GRADIENT; 650 } else { 651 *stepType = BNK_BFGS; 652 } 653 } 654 } 655 /* Make sure the safeguarded fall-back step is zero for actively bounded variables */ 656 PetscCall(VecScale(tao->stepdirection, -1.0)); 657 PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection)); 658 } else { 659 /* Computed Newton step is descent */ 660 switch (ksp_reason) { 661 case KSP_DIVERGED_NANORINF: 662 case KSP_DIVERGED_BREAKDOWN: 663 case KSP_DIVERGED_INDEFINITE_MAT: 664 case KSP_DIVERGED_INDEFINITE_PC: 665 case KSP_CONVERGED_CG_NEG_CURVE: 666 /* Matrix or preconditioner is indefinite; increase perturbation */ 667 if (bnk->pert <= 0.0) { 668 PetscBool is_gltr; 669 670 /* Initialize the perturbation */ 671 bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm)); 672 PetscCall(PetscObjectTypeCompare((PetscObject)(tao->ksp),KSPGLTR,&is_gltr)); 673 if (is_gltr) { 674 PetscCall(KSPGLTRGetMinEig(tao->ksp, &e_min)); 675 bnk->pert = PetscMax(bnk->pert, -e_min); 676 } 677 } else { 678 /* Increase the perturbation */ 679 bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm)); 680 } 681 break; 682 683 default: 684 /* Newton step computation is good; decrease perturbation */ 685 bnk->pert = PetscMin(bnk->psfac * bnk->pert, bnk->pmsfac * bnk->gnorm); 686 if (bnk->pert < bnk->pmin) { 687 bnk->pert = 0.0; 688 } 689 break; 690 } 691 *stepType = BNK_NEWTON; 692 } 693 break; 694 695 case BNK_BFGS: 696 /* Check for success (descent direction) */ 697 PetscCall(VecDot(tao->stepdirection, tao->gradient, &gdx)); 698 if (gdx >= 0 || PetscIsInfOrNanReal(gdx)) { 699 /* Step is not descent or solve was not successful 700 Use steepest descent direction (scaled) */ 701 PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE)); 702 PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient)); 703 PetscCall(MatSolve(bnk->M, tao->gradient, tao->stepdirection)); 704 PetscCall(VecScale(tao->stepdirection,-1.0)); 705 PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection)); 706 *stepType = BNK_SCALED_GRADIENT; 707 } else { 708 *stepType = BNK_BFGS; 709 } 710 break; 711 712 case BNK_SCALED_GRADIENT: 713 break; 714 715 default: 716 break; 717 } 718 719 PetscFunctionReturn(0); 720 } 721 722 /*------------------------------------------------------------*/ 723 724 /* Routine for performing a bound-projected More-Thuente line search. 725 726 Includes fallbacks to BFGS, scaled gradient, and unscaled gradient steps if the 727 Newton step does not produce a valid step length. 728 */ 729 730 PetscErrorCode TaoBNKPerformLineSearch(Tao tao, PetscInt *stepType, PetscReal *steplen, TaoLineSearchConvergedReason *reason) 731 { 732 TAO_BNK *bnk = (TAO_BNK *)tao->data; 733 TaoLineSearchConvergedReason ls_reason; 734 PetscReal e_min, gdx; 735 PetscInt bfgsUpdates; 736 737 PetscFunctionBegin; 738 /* Perform the linesearch */ 739 PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason)); 740 PetscCall(TaoAddLineSearchCounts(tao)); 741 742 while (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER && *stepType != BNK_SCALED_GRADIENT && *stepType != BNK_GRADIENT) { 743 /* Linesearch failed, revert solution */ 744 bnk->f = bnk->fold; 745 PetscCall(VecCopy(bnk->Xold, tao->solution)); 746 PetscCall(VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient)); 747 748 switch(*stepType) { 749 case BNK_NEWTON: 750 /* Failed to obtain acceptable iterate with Newton step 751 Update the perturbation for next time */ 752 if (bnk->pert <= 0.0) { 753 PetscBool is_gltr; 754 755 /* Initialize the perturbation */ 756 bnk->pert = PetscMin(bnk->imax, PetscMax(bnk->imin, bnk->imfac * bnk->gnorm)); 757 PetscCall(PetscObjectTypeCompare((PetscObject)(tao->ksp),KSPGLTR,&is_gltr)); 758 if (is_gltr) { 759 PetscCall(KSPGLTRGetMinEig(tao->ksp,&e_min)); 760 bnk->pert = PetscMax(bnk->pert, -e_min); 761 } 762 } else { 763 /* Increase the perturbation */ 764 bnk->pert = PetscMin(bnk->pmax, PetscMax(bnk->pgfac * bnk->pert, bnk->pmgfac * bnk->gnorm)); 765 } 766 767 if (!bnk->M) { 768 /* We don't have the bfgs matrix around and being updated 769 Must use gradient direction in this case */ 770 PetscCall(VecCopy(bnk->unprojected_gradient, tao->stepdirection)); 771 *stepType = BNK_GRADIENT; 772 } else { 773 /* Attempt to use the BFGS direction */ 774 PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection)); 775 /* Check for success (descent direction) 776 NOTE: Negative gdx means not a descent direction because the step here is missing a negative sign. */ 777 PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx)); 778 if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) { 779 /* BFGS direction is not descent or direction produced not a number 780 We can assert bfgsUpdates > 1 in this case 781 Use steepest descent direction (scaled) */ 782 PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE)); 783 PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient)); 784 PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection)); 785 786 bfgsUpdates = 1; 787 *stepType = BNK_SCALED_GRADIENT; 788 } else { 789 PetscCall(MatLMVMGetUpdateCount(bnk->M, &bfgsUpdates)); 790 if (1 == bfgsUpdates) { 791 /* The first BFGS direction is always the scaled gradient */ 792 *stepType = BNK_SCALED_GRADIENT; 793 } else { 794 *stepType = BNK_BFGS; 795 } 796 } 797 } 798 break; 799 800 case BNK_BFGS: 801 /* Can only enter if pc_type == BNK_PC_BFGS 802 Failed to obtain acceptable iterate with BFGS step 803 Attempt to use the scaled gradient direction */ 804 PetscCall(MatLMVMReset(bnk->M, PETSC_FALSE)); 805 PetscCall(MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient)); 806 PetscCall(MatSolve(bnk->M, bnk->unprojected_gradient, tao->stepdirection)); 807 808 bfgsUpdates = 1; 809 *stepType = BNK_SCALED_GRADIENT; 810 break; 811 } 812 /* Make sure the safeguarded fall-back step is zero for actively bounded variables */ 813 PetscCall(VecScale(tao->stepdirection, -1.0)); 814 PetscCall(TaoBNKBoundStep(tao, bnk->as_type, tao->stepdirection)); 815 816 /* Perform one last line search with the fall-back step */ 817 PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &bnk->f, bnk->unprojected_gradient, tao->stepdirection, steplen, &ls_reason)); 818 PetscCall(TaoAddLineSearchCounts(tao)); 819 } 820 *reason = ls_reason; 821 PetscFunctionReturn(0); 822 } 823 824 /*------------------------------------------------------------*/ 825 826 /* Routine for updating the trust radius. 827 828 Function features three different update methods: 829 1) Line-search step length based 830 2) Predicted decrease on the CG quadratic model 831 3) Interpolation 832 */ 833 834 PetscErrorCode TaoBNKUpdateTrustRadius(Tao tao, PetscReal prered, PetscReal actred, PetscInt updateType, PetscInt stepType, PetscBool *accept) 835 { 836 TAO_BNK *bnk = (TAO_BNK *)tao->data; 837 838 PetscReal step, kappa; 839 PetscReal gdx, tau_1, tau_2, tau_min, tau_max; 840 841 PetscFunctionBegin; 842 /* Update trust region radius */ 843 *accept = PETSC_FALSE; 844 switch(updateType) { 845 case BNK_UPDATE_STEP: 846 *accept = PETSC_TRUE; /* always accept here because line search succeeded */ 847 if (stepType == BNK_NEWTON) { 848 PetscCall(TaoLineSearchGetStepLength(tao->linesearch, &step)); 849 if (step < bnk->nu1) { 850 /* Very bad step taken; reduce radius */ 851 tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust); 852 } else if (step < bnk->nu2) { 853 /* Reasonably bad step taken; reduce radius */ 854 tao->trust = bnk->omega2 * PetscMin(bnk->dnorm, tao->trust); 855 } else if (step < bnk->nu3) { 856 /* Reasonable step was taken; leave radius alone */ 857 if (bnk->omega3 < 1.0) { 858 tao->trust = bnk->omega3 * PetscMin(bnk->dnorm, tao->trust); 859 } else if (bnk->omega3 > 1.0) { 860 tao->trust = PetscMax(bnk->omega3 * bnk->dnorm, tao->trust); 861 } 862 } else if (step < bnk->nu4) { 863 /* Full step taken; increase the radius */ 864 tao->trust = PetscMax(bnk->omega4 * bnk->dnorm, tao->trust); 865 } else { 866 /* More than full step taken; increase the radius */ 867 tao->trust = PetscMax(bnk->omega5 * bnk->dnorm, tao->trust); 868 } 869 } else { 870 /* Newton step was not good; reduce the radius */ 871 tao->trust = bnk->omega1 * PetscMin(bnk->dnorm, tao->trust); 872 } 873 break; 874 875 case BNK_UPDATE_REDUCTION: 876 if (stepType == BNK_NEWTON) { 877 if ((prered < 0.0) || PetscIsInfOrNanReal(prered)) { 878 /* The predicted reduction has the wrong sign. This cannot 879 happen in infinite precision arithmetic. Step should 880 be rejected! */ 881 tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm); 882 } else { 883 if (PetscIsInfOrNanReal(actred)) { 884 tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm); 885 } else { 886 if ((PetscAbsScalar(actred) <= PetscMax(1.0, PetscAbsScalar(bnk->f))*bnk->epsilon) && (PetscAbsScalar(prered) <= PetscMax(1.0, PetscAbsScalar(bnk->f))*bnk->epsilon)) { 887 kappa = 1.0; 888 } else { 889 kappa = actred / prered; 890 } 891 /* Accept or reject the step and update radius */ 892 if (kappa < bnk->eta1) { 893 /* Reject the step */ 894 tao->trust = bnk->alpha1 * PetscMin(tao->trust, bnk->dnorm); 895 } else { 896 /* Accept the step */ 897 *accept = PETSC_TRUE; 898 /* Update the trust region radius only if the computed step is at the trust radius boundary */ 899 if (bnk->dnorm == tao->trust) { 900 if (kappa < bnk->eta2) { 901 /* Marginal bad step */ 902 tao->trust = bnk->alpha2 * tao->trust; 903 } else if (kappa < bnk->eta3) { 904 /* Reasonable step */ 905 tao->trust = bnk->alpha3 * tao->trust; 906 } else if (kappa < bnk->eta4) { 907 /* Good step */ 908 tao->trust = bnk->alpha4 * tao->trust; 909 } else { 910 /* Very good step */ 911 tao->trust = bnk->alpha5 * tao->trust; 912 } 913 } 914 } 915 } 916 } 917 } else { 918 /* Newton step was not good; reduce the radius */ 919 tao->trust = bnk->alpha1 * PetscMin(bnk->dnorm, tao->trust); 920 } 921 break; 922 923 default: 924 if (stepType == BNK_NEWTON) { 925 if (prered < 0.0) { 926 /* The predicted reduction has the wrong sign. This cannot */ 927 /* happen in infinite precision arithmetic. Step should */ 928 /* be rejected! */ 929 tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm); 930 } else { 931 if (PetscIsInfOrNanReal(actred)) { 932 tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm); 933 } else { 934 if ((PetscAbsScalar(actred) <= bnk->epsilon) && (PetscAbsScalar(prered) <= bnk->epsilon)) { 935 kappa = 1.0; 936 } else { 937 kappa = actred / prered; 938 } 939 940 PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx)); 941 tau_1 = bnk->theta * gdx / (bnk->theta * gdx - (1.0 - bnk->theta) * prered + actred); 942 tau_2 = bnk->theta * gdx / (bnk->theta * gdx + (1.0 + bnk->theta) * prered - actred); 943 tau_min = PetscMin(tau_1, tau_2); 944 tau_max = PetscMax(tau_1, tau_2); 945 946 if (kappa >= 1.0 - bnk->mu1) { 947 /* Great agreement */ 948 *accept = PETSC_TRUE; 949 if (tau_max < 1.0) { 950 tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm); 951 } else if (tau_max > bnk->gamma4) { 952 tao->trust = PetscMax(tao->trust, bnk->gamma4 * bnk->dnorm); 953 } else { 954 tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm); 955 } 956 } else if (kappa >= 1.0 - bnk->mu2) { 957 /* Good agreement */ 958 *accept = PETSC_TRUE; 959 if (tau_max < bnk->gamma2) { 960 tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm); 961 } else if (tau_max > bnk->gamma3) { 962 tao->trust = PetscMax(tao->trust, bnk->gamma3 * bnk->dnorm); 963 } else if (tau_max < 1.0) { 964 tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm); 965 } else { 966 tao->trust = PetscMax(tao->trust, tau_max * bnk->dnorm); 967 } 968 } else { 969 /* Not good agreement */ 970 if (tau_min > 1.0) { 971 tao->trust = bnk->gamma2 * PetscMin(tao->trust, bnk->dnorm); 972 } else if (tau_max < bnk->gamma1) { 973 tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm); 974 } else if ((tau_min < bnk->gamma1) && (tau_max >= 1.0)) { 975 tao->trust = bnk->gamma1 * PetscMin(tao->trust, bnk->dnorm); 976 } else if ((tau_1 >= bnk->gamma1) && (tau_1 < 1.0) && ((tau_2 < bnk->gamma1) || (tau_2 >= 1.0))) { 977 tao->trust = tau_1 * PetscMin(tao->trust, bnk->dnorm); 978 } else if ((tau_2 >= bnk->gamma1) && (tau_2 < 1.0) && ((tau_1 < bnk->gamma1) || (tau_2 >= 1.0))) { 979 tao->trust = tau_2 * PetscMin(tao->trust, bnk->dnorm); 980 } else { 981 tao->trust = tau_max * PetscMin(tao->trust, bnk->dnorm); 982 } 983 } 984 } 985 } 986 } else { 987 /* Newton step was not good; reduce the radius */ 988 tao->trust = bnk->gamma1 * PetscMin(bnk->dnorm, tao->trust); 989 } 990 break; 991 } 992 /* Make sure the radius does not violate min and max settings */ 993 tao->trust = PetscMin(tao->trust, bnk->max_radius); 994 tao->trust = PetscMax(tao->trust, bnk->min_radius); 995 PetscFunctionReturn(0); 996 } 997 998 /* ---------------------------------------------------------- */ 999 1000 PetscErrorCode TaoBNKAddStepCounts(Tao tao, PetscInt stepType) 1001 { 1002 TAO_BNK *bnk = (TAO_BNK *)tao->data; 1003 1004 PetscFunctionBegin; 1005 switch (stepType) { 1006 case BNK_NEWTON: 1007 ++bnk->newt; 1008 break; 1009 case BNK_BFGS: 1010 ++bnk->bfgs; 1011 break; 1012 case BNK_SCALED_GRADIENT: 1013 ++bnk->sgrad; 1014 break; 1015 case BNK_GRADIENT: 1016 ++bnk->grad; 1017 break; 1018 default: 1019 break; 1020 } 1021 PetscFunctionReturn(0); 1022 } 1023 1024 /* ---------------------------------------------------------- */ 1025 1026 PetscErrorCode TaoSetUp_BNK(Tao tao) 1027 { 1028 TAO_BNK *bnk = (TAO_BNK *)tao->data; 1029 PetscInt i; 1030 1031 PetscFunctionBegin; 1032 if (!tao->gradient) { 1033 PetscCall(VecDuplicate(tao->solution,&tao->gradient)); 1034 } 1035 if (!tao->stepdirection) { 1036 PetscCall(VecDuplicate(tao->solution,&tao->stepdirection)); 1037 } 1038 if (!bnk->W) { 1039 PetscCall(VecDuplicate(tao->solution,&bnk->W)); 1040 } 1041 if (!bnk->Xold) { 1042 PetscCall(VecDuplicate(tao->solution,&bnk->Xold)); 1043 } 1044 if (!bnk->Gold) { 1045 PetscCall(VecDuplicate(tao->solution,&bnk->Gold)); 1046 } 1047 if (!bnk->Xwork) { 1048 PetscCall(VecDuplicate(tao->solution,&bnk->Xwork)); 1049 } 1050 if (!bnk->Gwork) { 1051 PetscCall(VecDuplicate(tao->solution,&bnk->Gwork)); 1052 } 1053 if (!bnk->unprojected_gradient) { 1054 PetscCall(VecDuplicate(tao->solution,&bnk->unprojected_gradient)); 1055 } 1056 if (!bnk->unprojected_gradient_old) { 1057 PetscCall(VecDuplicate(tao->solution,&bnk->unprojected_gradient_old)); 1058 } 1059 if (!bnk->Diag_min) { 1060 PetscCall(VecDuplicate(tao->solution,&bnk->Diag_min)); 1061 } 1062 if (!bnk->Diag_max) { 1063 PetscCall(VecDuplicate(tao->solution,&bnk->Diag_max)); 1064 } 1065 if (bnk->max_cg_its > 0) { 1066 /* Ensure that the important common vectors are shared between BNK and embedded BNCG */ 1067 bnk->bncg_ctx = (TAO_BNCG *)bnk->bncg->data; 1068 PetscCall(PetscObjectReference((PetscObject)(bnk->unprojected_gradient_old))); 1069 PetscCall(VecDestroy(&bnk->bncg_ctx->unprojected_gradient_old)); 1070 bnk->bncg_ctx->unprojected_gradient_old = bnk->unprojected_gradient_old; 1071 PetscCall(PetscObjectReference((PetscObject)(bnk->unprojected_gradient))); 1072 PetscCall(VecDestroy(&bnk->bncg_ctx->unprojected_gradient)); 1073 bnk->bncg_ctx->unprojected_gradient = bnk->unprojected_gradient; 1074 PetscCall(PetscObjectReference((PetscObject)(bnk->Gold))); 1075 PetscCall(VecDestroy(&bnk->bncg_ctx->G_old)); 1076 bnk->bncg_ctx->G_old = bnk->Gold; 1077 PetscCall(PetscObjectReference((PetscObject)(tao->gradient))); 1078 PetscCall(VecDestroy(&bnk->bncg->gradient)); 1079 bnk->bncg->gradient = tao->gradient; 1080 PetscCall(PetscObjectReference((PetscObject)(tao->stepdirection))); 1081 PetscCall(VecDestroy(&bnk->bncg->stepdirection)); 1082 bnk->bncg->stepdirection = tao->stepdirection; 1083 PetscCall(TaoSetSolution(bnk->bncg, tao->solution)); 1084 /* Copy over some settings from BNK into BNCG */ 1085 PetscCall(TaoSetMaximumIterations(bnk->bncg, bnk->max_cg_its)); 1086 PetscCall(TaoSetTolerances(bnk->bncg, tao->gatol, tao->grtol, tao->gttol)); 1087 PetscCall(TaoSetFunctionLowerBound(bnk->bncg, tao->fmin)); 1088 PetscCall(TaoSetConvergenceTest(bnk->bncg, tao->ops->convergencetest, tao->cnvP)); 1089 PetscCall(TaoSetObjective(bnk->bncg, tao->ops->computeobjective, tao->user_objP)); 1090 PetscCall(TaoSetGradient(bnk->bncg, NULL, tao->ops->computegradient, tao->user_gradP)); 1091 PetscCall(TaoSetObjectiveAndGradient(bnk->bncg, NULL, tao->ops->computeobjectiveandgradient, tao->user_objgradP)); 1092 PetscCall(PetscObjectCopyFortranFunctionPointers((PetscObject)tao, (PetscObject)(bnk->bncg))); 1093 for (i=0; i<tao->numbermonitors; ++i) { 1094 PetscCall(TaoSetMonitor(bnk->bncg, tao->monitor[i], tao->monitorcontext[i], tao->monitordestroy[i])); 1095 PetscCall(PetscObjectReference((PetscObject)(tao->monitorcontext[i]))); 1096 } 1097 } 1098 bnk->X_inactive = NULL; 1099 bnk->G_inactive = NULL; 1100 bnk->inactive_work = NULL; 1101 bnk->active_work = NULL; 1102 bnk->inactive_idx = NULL; 1103 bnk->active_idx = NULL; 1104 bnk->active_lower = NULL; 1105 bnk->active_upper = NULL; 1106 bnk->active_fixed = NULL; 1107 bnk->M = NULL; 1108 bnk->H_inactive = NULL; 1109 bnk->Hpre_inactive = NULL; 1110 PetscFunctionReturn(0); 1111 } 1112 1113 /*------------------------------------------------------------*/ 1114 1115 PetscErrorCode TaoDestroy_BNK(Tao tao) 1116 { 1117 TAO_BNK *bnk = (TAO_BNK *)tao->data; 1118 1119 PetscFunctionBegin; 1120 if (tao->setupcalled) { 1121 PetscCall(VecDestroy(&bnk->W)); 1122 PetscCall(VecDestroy(&bnk->Xold)); 1123 PetscCall(VecDestroy(&bnk->Gold)); 1124 PetscCall(VecDestroy(&bnk->Xwork)); 1125 PetscCall(VecDestroy(&bnk->Gwork)); 1126 PetscCall(VecDestroy(&bnk->unprojected_gradient)); 1127 PetscCall(VecDestroy(&bnk->unprojected_gradient_old)); 1128 PetscCall(VecDestroy(&bnk->Diag_min)); 1129 PetscCall(VecDestroy(&bnk->Diag_max)); 1130 } 1131 PetscCall(ISDestroy(&bnk->active_lower)); 1132 PetscCall(ISDestroy(&bnk->active_upper)); 1133 PetscCall(ISDestroy(&bnk->active_fixed)); 1134 PetscCall(ISDestroy(&bnk->active_idx)); 1135 PetscCall(ISDestroy(&bnk->inactive_idx)); 1136 PetscCall(MatDestroy(&bnk->Hpre_inactive)); 1137 PetscCall(MatDestroy(&bnk->H_inactive)); 1138 PetscCall(TaoDestroy(&bnk->bncg)); 1139 PetscCall(PetscFree(tao->data)); 1140 PetscFunctionReturn(0); 1141 } 1142 1143 /*------------------------------------------------------------*/ 1144 1145 PetscErrorCode TaoSetFromOptions_BNK(PetscOptionItems *PetscOptionsObject,Tao tao) 1146 { 1147 TAO_BNK *bnk = (TAO_BNK *)tao->data; 1148 1149 PetscFunctionBegin; 1150 PetscOptionsHeadBegin(PetscOptionsObject,"Newton-Krylov method for bound constrained optimization"); 1151 PetscCall(PetscOptionsEList("-tao_bnk_init_type", "radius initialization type", "", BNK_INIT, BNK_INIT_TYPES, BNK_INIT[bnk->init_type], &bnk->init_type, NULL)); 1152 PetscCall(PetscOptionsEList("-tao_bnk_update_type", "radius update type", "", BNK_UPDATE, BNK_UPDATE_TYPES, BNK_UPDATE[bnk->update_type], &bnk->update_type, NULL)); 1153 PetscCall(PetscOptionsEList("-tao_bnk_as_type", "active set estimation method", "", BNK_AS, BNK_AS_TYPES, BNK_AS[bnk->as_type], &bnk->as_type, NULL)); 1154 PetscCall(PetscOptionsReal("-tao_bnk_sval", "(developer) Hessian perturbation starting value", "", bnk->sval, &bnk->sval,NULL)); 1155 PetscCall(PetscOptionsReal("-tao_bnk_imin", "(developer) minimum initial Hessian perturbation", "", bnk->imin, &bnk->imin,NULL)); 1156 PetscCall(PetscOptionsReal("-tao_bnk_imax", "(developer) maximum initial Hessian perturbation", "", bnk->imax, &bnk->imax,NULL)); 1157 PetscCall(PetscOptionsReal("-tao_bnk_imfac", "(developer) initial merit factor for Hessian perturbation", "", bnk->imfac, &bnk->imfac,NULL)); 1158 PetscCall(PetscOptionsReal("-tao_bnk_pmin", "(developer) minimum Hessian perturbation", "", bnk->pmin, &bnk->pmin,NULL)); 1159 PetscCall(PetscOptionsReal("-tao_bnk_pmax", "(developer) maximum Hessian perturbation", "", bnk->pmax, &bnk->pmax,NULL)); 1160 PetscCall(PetscOptionsReal("-tao_bnk_pgfac", "(developer) Hessian perturbation growth factor", "", bnk->pgfac, &bnk->pgfac,NULL)); 1161 PetscCall(PetscOptionsReal("-tao_bnk_psfac", "(developer) Hessian perturbation shrink factor", "", bnk->psfac, &bnk->psfac,NULL)); 1162 PetscCall(PetscOptionsReal("-tao_bnk_pmgfac", "(developer) merit growth factor for Hessian perturbation", "", bnk->pmgfac, &bnk->pmgfac,NULL)); 1163 PetscCall(PetscOptionsReal("-tao_bnk_pmsfac", "(developer) merit shrink factor for Hessian perturbation", "", bnk->pmsfac, &bnk->pmsfac,NULL)); 1164 PetscCall(PetscOptionsReal("-tao_bnk_eta1", "(developer) threshold for rejecting step (-tao_bnk_update_type reduction)", "", bnk->eta1, &bnk->eta1,NULL)); 1165 PetscCall(PetscOptionsReal("-tao_bnk_eta2", "(developer) threshold for accepting marginal step (-tao_bnk_update_type reduction)", "", bnk->eta2, &bnk->eta2,NULL)); 1166 PetscCall(PetscOptionsReal("-tao_bnk_eta3", "(developer) threshold for accepting reasonable step (-tao_bnk_update_type reduction)", "", bnk->eta3, &bnk->eta3,NULL)); 1167 PetscCall(PetscOptionsReal("-tao_bnk_eta4", "(developer) threshold for accepting good step (-tao_bnk_update_type reduction)", "", bnk->eta4, &bnk->eta4,NULL)); 1168 PetscCall(PetscOptionsReal("-tao_bnk_alpha1", "(developer) radius reduction factor for rejected step (-tao_bnk_update_type reduction)", "", bnk->alpha1, &bnk->alpha1,NULL)); 1169 PetscCall(PetscOptionsReal("-tao_bnk_alpha2", "(developer) radius reduction factor for marginally accepted bad step (-tao_bnk_update_type reduction)", "", bnk->alpha2, &bnk->alpha2,NULL)); 1170 PetscCall(PetscOptionsReal("-tao_bnk_alpha3", "(developer) radius increase factor for reasonable accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha3, &bnk->alpha3,NULL)); 1171 PetscCall(PetscOptionsReal("-tao_bnk_alpha4", "(developer) radius increase factor for good accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha4, &bnk->alpha4,NULL)); 1172 PetscCall(PetscOptionsReal("-tao_bnk_alpha5", "(developer) radius increase factor for very good accepted step (-tao_bnk_update_type reduction)", "", bnk->alpha5, &bnk->alpha5,NULL)); 1173 PetscCall(PetscOptionsReal("-tao_bnk_nu1", "(developer) threshold for small line-search step length (-tao_bnk_update_type step)", "", bnk->nu1, &bnk->nu1,NULL)); 1174 PetscCall(PetscOptionsReal("-tao_bnk_nu2", "(developer) threshold for reasonable line-search step length (-tao_bnk_update_type step)", "", bnk->nu2, &bnk->nu2,NULL)); 1175 PetscCall(PetscOptionsReal("-tao_bnk_nu3", "(developer) threshold for large line-search step length (-tao_bnk_update_type step)", "", bnk->nu3, &bnk->nu3,NULL)); 1176 PetscCall(PetscOptionsReal("-tao_bnk_nu4", "(developer) threshold for very large line-search step length (-tao_bnk_update_type step)", "", bnk->nu4, &bnk->nu4,NULL)); 1177 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)); 1178 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)); 1179 PetscCall(PetscOptionsReal("-tao_bnk_omega3", "(developer) radius factor for decent line-search step length (-tao_bnk_update_type step)", "", bnk->omega3, &bnk->omega3,NULL)); 1180 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)); 1181 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)); 1182 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)); 1183 PetscCall(PetscOptionsReal("-tao_bnk_mu2_i", "(developer) threshold for accepting good step (-tao_bnk_init_type interpolation)", "", bnk->mu2_i, &bnk->mu2_i,NULL)); 1184 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)); 1185 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)); 1186 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)); 1187 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)); 1188 PetscCall(PetscOptionsReal("-tao_bnk_theta_i", "(developer) trust region interpolation factor (-tao_bnk_init_type interpolation)", "", bnk->theta_i, &bnk->theta_i,NULL)); 1189 PetscCall(PetscOptionsReal("-tao_bnk_mu1", "(developer) threshold for accepting very good step (-tao_bnk_update_type interpolation)", "", bnk->mu1, &bnk->mu1,NULL)); 1190 PetscCall(PetscOptionsReal("-tao_bnk_mu2", "(developer) threshold for accepting good step (-tao_bnk_update_type interpolation)", "", bnk->mu2, &bnk->mu2,NULL)); 1191 PetscCall(PetscOptionsReal("-tao_bnk_gamma1", "(developer) radius reduction factor for rejected very bad step (-tao_bnk_update_type interpolation)", "", bnk->gamma1, &bnk->gamma1,NULL)); 1192 PetscCall(PetscOptionsReal("-tao_bnk_gamma2", "(developer) radius reduction factor for rejected bad step (-tao_bnk_update_type interpolation)", "", bnk->gamma2, &bnk->gamma2,NULL)); 1193 PetscCall(PetscOptionsReal("-tao_bnk_gamma3", "(developer) radius increase factor for accepted good step (-tao_bnk_update_type interpolation)", "", bnk->gamma3, &bnk->gamma3,NULL)); 1194 PetscCall(PetscOptionsReal("-tao_bnk_gamma4", "(developer) radius increase factor for accepted very good step (-tao_bnk_update_type interpolation)", "", bnk->gamma4, &bnk->gamma4,NULL)); 1195 PetscCall(PetscOptionsReal("-tao_bnk_theta", "(developer) trust region interpolation factor (-tao_bnk_update_type interpolation)", "", bnk->theta, &bnk->theta,NULL)); 1196 PetscCall(PetscOptionsReal("-tao_bnk_min_radius", "(developer) lower bound on initial radius", "", bnk->min_radius, &bnk->min_radius,NULL)); 1197 PetscCall(PetscOptionsReal("-tao_bnk_max_radius", "(developer) upper bound on radius", "", bnk->max_radius, &bnk->max_radius,NULL)); 1198 PetscCall(PetscOptionsReal("-tao_bnk_epsilon", "(developer) tolerance used when computing actual and predicted reduction", "", bnk->epsilon, &bnk->epsilon,NULL)); 1199 PetscCall(PetscOptionsReal("-tao_bnk_as_tol", "(developer) initial tolerance used when estimating actively bounded variables", "", bnk->as_tol, &bnk->as_tol,NULL)); 1200 PetscCall(PetscOptionsReal("-tao_bnk_as_step", "(developer) step length used when estimating actively bounded variables", "", bnk->as_step, &bnk->as_step,NULL)); 1201 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)); 1202 PetscOptionsHeadEnd(); 1203 1204 PetscCall(TaoSetOptionsPrefix(bnk->bncg,((PetscObject)(tao))->prefix)); 1205 PetscCall(TaoAppendOptionsPrefix(bnk->bncg,"tao_bnk_cg_")); 1206 PetscCall(TaoSetFromOptions(bnk->bncg)); 1207 1208 PetscCall(KSPSetOptionsPrefix(tao->ksp,((PetscObject)(tao))->prefix)); 1209 PetscCall(KSPAppendOptionsPrefix(tao->ksp,"tao_bnk_")); 1210 PetscCall(KSPSetFromOptions(tao->ksp)); 1211 PetscFunctionReturn(0); 1212 } 1213 1214 /*------------------------------------------------------------*/ 1215 1216 PetscErrorCode TaoView_BNK(Tao tao, PetscViewer viewer) 1217 { 1218 TAO_BNK *bnk = (TAO_BNK *)tao->data; 1219 PetscInt nrejects; 1220 PetscBool isascii; 1221 1222 PetscFunctionBegin; 1223 PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii)); 1224 if (isascii) { 1225 PetscCall(PetscViewerASCIIPushTab(viewer)); 1226 if (bnk->M) { 1227 PetscCall(MatLMVMGetRejectCount(bnk->M,&nrejects)); 1228 PetscCall(PetscViewerASCIIPrintf(viewer, "Rejected BFGS updates: %" PetscInt_FMT "\n",nrejects)); 1229 } 1230 PetscCall(PetscViewerASCIIPrintf(viewer, "CG steps: %" PetscInt_FMT "\n", bnk->tot_cg_its)); 1231 PetscCall(PetscViewerASCIIPrintf(viewer, "Newton steps: %" PetscInt_FMT "\n", bnk->newt)); 1232 if (bnk->M) { 1233 PetscCall(PetscViewerASCIIPrintf(viewer, "BFGS steps: %" PetscInt_FMT "\n", bnk->bfgs)); 1234 } 1235 PetscCall(PetscViewerASCIIPrintf(viewer, "Scaled gradient steps: %" PetscInt_FMT "\n", bnk->sgrad)); 1236 PetscCall(PetscViewerASCIIPrintf(viewer, "Gradient steps: %" PetscInt_FMT "\n", bnk->grad)); 1237 PetscCall(PetscViewerASCIIPrintf(viewer, "KSP termination reasons:\n")); 1238 PetscCall(PetscViewerASCIIPrintf(viewer, " atol: %" PetscInt_FMT "\n", bnk->ksp_atol)); 1239 PetscCall(PetscViewerASCIIPrintf(viewer, " rtol: %" PetscInt_FMT "\n", bnk->ksp_rtol)); 1240 PetscCall(PetscViewerASCIIPrintf(viewer, " ctol: %" PetscInt_FMT "\n", bnk->ksp_ctol)); 1241 PetscCall(PetscViewerASCIIPrintf(viewer, " negc: %" PetscInt_FMT "\n", bnk->ksp_negc)); 1242 PetscCall(PetscViewerASCIIPrintf(viewer, " dtol: %" PetscInt_FMT "\n", bnk->ksp_dtol)); 1243 PetscCall(PetscViewerASCIIPrintf(viewer, " iter: %" PetscInt_FMT "\n", bnk->ksp_iter)); 1244 PetscCall(PetscViewerASCIIPrintf(viewer, " othr: %" PetscInt_FMT "\n", bnk->ksp_othr)); 1245 PetscCall(PetscViewerASCIIPopTab(viewer)); 1246 } 1247 PetscFunctionReturn(0); 1248 } 1249 1250 /* ---------------------------------------------------------- */ 1251 1252 /*MC 1253 TAOBNK - Shared base-type for Bounded Newton-Krylov type algorithms. 1254 At each iteration, the BNK methods solve the symmetric 1255 system of equations to obtain the step diretion dk: 1256 Hk dk = -gk 1257 for free variables only. The step can be globalized either through 1258 trust-region methods, or a line search, or a heuristic mixture of both. 1259 1260 Options Database Keys: 1261 + -tao_bnk_max_cg_its - maximum number of bounded conjugate-gradient iterations taken in each Newton loop 1262 . -tao_bnk_init_type - trust radius initialization method ("constant", "direction", "interpolation") 1263 . -tao_bnk_update_type - trust radius update method ("step", "direction", "interpolation") 1264 . -tao_bnk_as_type - active-set estimation method ("none", "bertsekas") 1265 . -tao_bnk_as_tol - (developer) initial tolerance used in estimating bounded active variables (-as_type bertsekas) 1266 . -tao_bnk_as_step - (developer) trial step length used in estimating bounded active variables (-as_type bertsekas) 1267 . -tao_bnk_sval - (developer) Hessian perturbation starting value 1268 . -tao_bnk_imin - (developer) minimum initial Hessian perturbation 1269 . -tao_bnk_imax - (developer) maximum initial Hessian perturbation 1270 . -tao_bnk_pmin - (developer) minimum Hessian perturbation 1271 . -tao_bnk_pmax - (developer) aximum Hessian perturbation 1272 . -tao_bnk_pgfac - (developer) Hessian perturbation growth factor 1273 . -tao_bnk_psfac - (developer) Hessian perturbation shrink factor 1274 . -tao_bnk_imfac - (developer) initial merit factor for Hessian perturbation 1275 . -tao_bnk_pmgfac - (developer) merit growth factor for Hessian perturbation 1276 . -tao_bnk_pmsfac - (developer) merit shrink factor for Hessian perturbation 1277 . -tao_bnk_eta1 - (developer) threshold for rejecting step (-update_type reduction) 1278 . -tao_bnk_eta2 - (developer) threshold for accepting marginal step (-update_type reduction) 1279 . -tao_bnk_eta3 - (developer) threshold for accepting reasonable step (-update_type reduction) 1280 . -tao_bnk_eta4 - (developer) threshold for accepting good step (-update_type reduction) 1281 . -tao_bnk_alpha1 - (developer) radius reduction factor for rejected step (-update_type reduction) 1282 . -tao_bnk_alpha2 - (developer) radius reduction factor for marginally accepted bad step (-update_type reduction) 1283 . -tao_bnk_alpha3 - (developer) radius increase factor for reasonable accepted step (-update_type reduction) 1284 . -tao_bnk_alpha4 - (developer) radius increase factor for good accepted step (-update_type reduction) 1285 . -tao_bnk_alpha5 - (developer) radius increase factor for very good accepted step (-update_type reduction) 1286 . -tao_bnk_epsilon - (developer) tolerance for small pred/actual ratios that trigger automatic step acceptance (-update_type reduction) 1287 . -tao_bnk_mu1 - (developer) threshold for accepting very good step (-update_type interpolation) 1288 . -tao_bnk_mu2 - (developer) threshold for accepting good step (-update_type interpolation) 1289 . -tao_bnk_gamma1 - (developer) radius reduction factor for rejected very bad step (-update_type interpolation) 1290 . -tao_bnk_gamma2 - (developer) radius reduction factor for rejected bad step (-update_type interpolation) 1291 . -tao_bnk_gamma3 - (developer) radius increase factor for accepted good step (-update_type interpolation) 1292 . -tao_bnk_gamma4 - (developer) radius increase factor for accepted very good step (-update_type interpolation) 1293 . -tao_bnk_theta - (developer) trust region interpolation factor (-update_type interpolation) 1294 . -tao_bnk_nu1 - (developer) threshold for small line-search step length (-update_type step) 1295 . -tao_bnk_nu2 - (developer) threshold for reasonable line-search step length (-update_type step) 1296 . -tao_bnk_nu3 - (developer) threshold for large line-search step length (-update_type step) 1297 . -tao_bnk_nu4 - (developer) threshold for very large line-search step length (-update_type step) 1298 . -tao_bnk_omega1 - (developer) radius reduction factor for very small line-search step length (-update_type step) 1299 . -tao_bnk_omega2 - (developer) radius reduction factor for small line-search step length (-update_type step) 1300 . -tao_bnk_omega3 - (developer) radius factor for decent line-search step length (-update_type step) 1301 . -tao_bnk_omega4 - (developer) radius increase factor for large line-search step length (-update_type step) 1302 . -tao_bnk_omega5 - (developer) radius increase factor for very large line-search step length (-update_type step) 1303 . -tao_bnk_mu1_i - (developer) threshold for accepting very good step (-init_type interpolation) 1304 . -tao_bnk_mu2_i - (developer) threshold for accepting good step (-init_type interpolation) 1305 . -tao_bnk_gamma1_i - (developer) radius reduction factor for rejected very bad step (-init_type interpolation) 1306 . -tao_bnk_gamma2_i - (developer) radius reduction factor for rejected bad step (-init_type interpolation) 1307 . -tao_bnk_gamma3_i - (developer) radius increase factor for accepted good step (-init_type interpolation) 1308 . -tao_bnk_gamma4_i - (developer) radius increase factor for accepted very good step (-init_type interpolation) 1309 - -tao_bnk_theta_i - (developer) trust region interpolation factor (-init_type interpolation) 1310 1311 Level: beginner 1312 M*/ 1313 1314 PetscErrorCode TaoCreate_BNK(Tao tao) 1315 { 1316 TAO_BNK *bnk; 1317 const char *morethuente_type = TAOLINESEARCHMT; 1318 PC pc; 1319 1320 PetscFunctionBegin; 1321 PetscCall(PetscNewLog(tao,&bnk)); 1322 1323 tao->ops->setup = TaoSetUp_BNK; 1324 tao->ops->view = TaoView_BNK; 1325 tao->ops->setfromoptions = TaoSetFromOptions_BNK; 1326 tao->ops->destroy = TaoDestroy_BNK; 1327 1328 /* Override default settings (unless already changed) */ 1329 if (!tao->max_it_changed) tao->max_it = 50; 1330 if (!tao->trust0_changed) tao->trust0 = 100.0; 1331 1332 tao->data = (void*)bnk; 1333 1334 /* Hessian shifting parameters */ 1335 bnk->computehessian = TaoBNKComputeHessian; 1336 bnk->computestep = TaoBNKComputeStep; 1337 1338 bnk->sval = 0.0; 1339 bnk->imin = 1.0e-4; 1340 bnk->imax = 1.0e+2; 1341 bnk->imfac = 1.0e-1; 1342 1343 bnk->pmin = 1.0e-12; 1344 bnk->pmax = 1.0e+2; 1345 bnk->pgfac = 1.0e+1; 1346 bnk->psfac = 4.0e-1; 1347 bnk->pmgfac = 1.0e-1; 1348 bnk->pmsfac = 1.0e-1; 1349 1350 /* Default values for trust-region radius update based on steplength */ 1351 bnk->nu1 = 0.25; 1352 bnk->nu2 = 0.50; 1353 bnk->nu3 = 1.00; 1354 bnk->nu4 = 1.25; 1355 1356 bnk->omega1 = 0.25; 1357 bnk->omega2 = 0.50; 1358 bnk->omega3 = 1.00; 1359 bnk->omega4 = 2.00; 1360 bnk->omega5 = 4.00; 1361 1362 /* Default values for trust-region radius update based on reduction */ 1363 bnk->eta1 = 1.0e-4; 1364 bnk->eta2 = 0.25; 1365 bnk->eta3 = 0.50; 1366 bnk->eta4 = 0.90; 1367 1368 bnk->alpha1 = 0.25; 1369 bnk->alpha2 = 0.50; 1370 bnk->alpha3 = 1.00; 1371 bnk->alpha4 = 2.00; 1372 bnk->alpha5 = 4.00; 1373 1374 /* Default values for trust-region radius update based on interpolation */ 1375 bnk->mu1 = 0.10; 1376 bnk->mu2 = 0.50; 1377 1378 bnk->gamma1 = 0.25; 1379 bnk->gamma2 = 0.50; 1380 bnk->gamma3 = 2.00; 1381 bnk->gamma4 = 4.00; 1382 1383 bnk->theta = 0.05; 1384 1385 /* Default values for trust region initialization based on interpolation */ 1386 bnk->mu1_i = 0.35; 1387 bnk->mu2_i = 0.50; 1388 1389 bnk->gamma1_i = 0.0625; 1390 bnk->gamma2_i = 0.5; 1391 bnk->gamma3_i = 2.0; 1392 bnk->gamma4_i = 5.0; 1393 1394 bnk->theta_i = 0.25; 1395 1396 /* Remaining parameters */ 1397 bnk->max_cg_its = 0; 1398 bnk->min_radius = 1.0e-10; 1399 bnk->max_radius = 1.0e10; 1400 bnk->epsilon = PetscPowReal(PETSC_MACHINE_EPSILON, 2.0/3.0); 1401 bnk->as_tol = 1.0e-3; 1402 bnk->as_step = 1.0e-3; 1403 bnk->dmin = 1.0e-6; 1404 bnk->dmax = 1.0e6; 1405 1406 bnk->M = NULL; 1407 bnk->bfgs_pre = NULL; 1408 bnk->init_type = BNK_INIT_INTERPOLATION; 1409 bnk->update_type = BNK_UPDATE_REDUCTION; 1410 bnk->as_type = BNK_AS_BERTSEKAS; 1411 1412 /* Create the embedded BNCG solver */ 1413 PetscCall(TaoCreate(PetscObjectComm((PetscObject)tao), &bnk->bncg)); 1414 PetscCall(PetscObjectIncrementTabLevel((PetscObject)bnk->bncg, (PetscObject)tao, 1)); 1415 PetscCall(TaoSetType(bnk->bncg, TAOBNCG)); 1416 1417 /* Create the line search */ 1418 PetscCall(TaoLineSearchCreate(((PetscObject)tao)->comm,&tao->linesearch)); 1419 PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1)); 1420 PetscCall(TaoLineSearchSetType(tao->linesearch,morethuente_type)); 1421 PetscCall(TaoLineSearchUseTaoRoutines(tao->linesearch,tao)); 1422 1423 /* Set linear solver to default for symmetric matrices */ 1424 PetscCall(KSPCreate(((PetscObject)tao)->comm,&tao->ksp)); 1425 PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1)); 1426 PetscCall(KSPSetType(tao->ksp,KSPSTCG)); 1427 PetscCall(KSPGetPC(tao->ksp, &pc)); 1428 PetscCall(PCSetType(pc, PCLMVM)); 1429 PetscFunctionReturn(0); 1430 } 1431