1 #include <../src/tao/unconstrained/impls/ntl/ntlimpl.h> 2 3 #include <petscksp.h> 4 5 #define NTL_INIT_CONSTANT 0 6 #define NTL_INIT_DIRECTION 1 7 #define NTL_INIT_INTERPOLATION 2 8 #define NTL_INIT_TYPES 3 9 10 #define NTL_UPDATE_REDUCTION 0 11 #define NTL_UPDATE_INTERPOLATION 1 12 #define NTL_UPDATE_TYPES 2 13 14 static const char *NTL_INIT[64] = {"constant","direction","interpolation"}; 15 16 static const char *NTL_UPDATE[64] = {"reduction","interpolation"}; 17 18 /* Implements Newton's Method with a trust-region, line-search approach for 19 solving unconstrained minimization problems. A More'-Thuente line search 20 is used to guarantee that the bfgs preconditioner remains positive 21 definite. */ 22 23 #define NTL_NEWTON 0 24 #define NTL_BFGS 1 25 #define NTL_SCALED_GRADIENT 2 26 #define NTL_GRADIENT 3 27 28 static PetscErrorCode TaoSolve_NTL(Tao tao) 29 { 30 TAO_NTL *tl = (TAO_NTL *)tao->data; 31 KSPType ksp_type; 32 PetscBool is_nash,is_stcg,is_gltr,is_bfgs,is_jacobi,is_symmetric,sym_set; 33 KSPConvergedReason ksp_reason; 34 PC pc; 35 TaoLineSearchConvergedReason ls_reason; 36 37 PetscReal fmin, ftrial, prered, actred, kappa, sigma; 38 PetscReal tau, tau_1, tau_2, tau_max, tau_min, max_radius; 39 PetscReal f, fold, gdx, gnorm; 40 PetscReal step = 1.0; 41 42 PetscReal norm_d = 0.0; 43 PetscErrorCode ierr; 44 PetscInt stepType; 45 PetscInt its; 46 47 PetscInt bfgsUpdates = 0; 48 PetscInt needH; 49 50 PetscInt i_max = 5; 51 PetscInt j_max = 1; 52 PetscInt i, j, n, N; 53 54 PetscInt tr_reject; 55 56 PetscFunctionBegin; 57 if (tao->XL || tao->XU || tao->ops->computebounds) { 58 ierr = PetscPrintf(((PetscObject)tao)->comm,"WARNING: Variable bounds have been set but will be ignored by ntl algorithm\n");CHKERRQ(ierr); 59 } 60 61 ierr = KSPGetType(tao->ksp,&ksp_type);CHKERRQ(ierr); 62 ierr = PetscStrcmp(ksp_type,KSPCGNASH,&is_nash);CHKERRQ(ierr); 63 ierr = PetscStrcmp(ksp_type,KSPCGSTCG,&is_stcg);CHKERRQ(ierr); 64 ierr = PetscStrcmp(ksp_type,KSPCGGLTR,&is_gltr);CHKERRQ(ierr); 65 if (!is_nash && !is_stcg && !is_gltr) { 66 SETERRQ(PETSC_COMM_SELF,1,"TAO_NTR requires nash, stcg, or gltr for the KSP"); 67 } 68 69 /* Initialize the radius and modify if it is too large or small */ 70 tao->trust = tao->trust0; 71 tao->trust = PetscMax(tao->trust, tl->min_radius); 72 tao->trust = PetscMin(tao->trust, tl->max_radius); 73 74 /* Allocate the vectors needed for the BFGS approximation */ 75 ierr = KSPGetPC(tao->ksp, &pc);CHKERRQ(ierr); 76 ierr = PetscObjectTypeCompare((PetscObject)pc, PCLMVM, &is_bfgs);CHKERRQ(ierr); 77 ierr = PetscObjectTypeCompare((PetscObject)pc, PCJACOBI, &is_jacobi);CHKERRQ(ierr); 78 if (is_bfgs) { 79 tl->bfgs_pre = pc; 80 ierr = PCLMVMGetMatLMVM(tl->bfgs_pre, &tl->M);CHKERRQ(ierr); 81 ierr = VecGetLocalSize(tao->solution, &n);CHKERRQ(ierr); 82 ierr = VecGetSize(tao->solution, &N);CHKERRQ(ierr); 83 ierr = MatSetSizes(tl->M, n, n, N, N);CHKERRQ(ierr); 84 ierr = MatLMVMAllocate(tl->M, tao->solution, tao->gradient);CHKERRQ(ierr); 85 ierr = MatIsSymmetricKnown(tl->M, &sym_set, &is_symmetric);CHKERRQ(ierr); 86 if (!sym_set || !is_symmetric) SETERRQ(PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_INCOMP, "LMVM matrix in the LMVM preconditioner must be symmetric."); 87 } else if (is_jacobi) { 88 ierr = PCJacobiSetUseAbs(pc,PETSC_TRUE);CHKERRQ(ierr); 89 } 90 91 /* Check convergence criteria */ 92 ierr = TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient);CHKERRQ(ierr); 93 ierr = VecNorm(tao->gradient, NORM_2, &gnorm);CHKERRQ(ierr); 94 if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN"); 95 needH = 1; 96 97 tao->reason = TAO_CONTINUE_ITERATING; 98 ierr = TaoLogConvergenceHistory(tao,f,gnorm,0.0,tao->ksp_its);CHKERRQ(ierr); 99 ierr = TaoMonitor(tao,tao->niter,f,gnorm,0.0,step);CHKERRQ(ierr); 100 ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr); 101 if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0); 102 103 /* Initialize trust-region radius */ 104 switch(tl->init_type) { 105 case NTL_INIT_CONSTANT: 106 /* Use the initial radius specified */ 107 break; 108 109 case NTL_INIT_INTERPOLATION: 110 /* Use the initial radius specified */ 111 max_radius = 0.0; 112 113 for (j = 0; j < j_max; ++j) { 114 fmin = f; 115 sigma = 0.0; 116 117 if (needH) { 118 ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr); 119 needH = 0; 120 } 121 122 for (i = 0; i < i_max; ++i) { 123 ierr = VecCopy(tao->solution, tl->W);CHKERRQ(ierr); 124 ierr = VecAXPY(tl->W, -tao->trust/gnorm, tao->gradient);CHKERRQ(ierr); 125 126 ierr = TaoComputeObjective(tao, tl->W, &ftrial);CHKERRQ(ierr); 127 if (PetscIsInfOrNanReal(ftrial)) { 128 tau = tl->gamma1_i; 129 } else { 130 if (ftrial < fmin) { 131 fmin = ftrial; 132 sigma = -tao->trust / gnorm; 133 } 134 135 ierr = MatMult(tao->hessian, tao->gradient, tao->stepdirection);CHKERRQ(ierr); 136 ierr = VecDot(tao->gradient, tao->stepdirection, &prered);CHKERRQ(ierr); 137 138 prered = tao->trust * (gnorm - 0.5 * tao->trust * prered / (gnorm * gnorm)); 139 actred = f - ftrial; 140 if ((PetscAbsScalar(actred) <= tl->epsilon) && (PetscAbsScalar(prered) <= tl->epsilon)) { 141 kappa = 1.0; 142 } else { 143 kappa = actred / prered; 144 } 145 146 tau_1 = tl->theta_i * gnorm * tao->trust / (tl->theta_i * gnorm * tao->trust + (1.0 - tl->theta_i) * prered - actred); 147 tau_2 = tl->theta_i * gnorm * tao->trust / (tl->theta_i * gnorm * tao->trust - (1.0 + tl->theta_i) * prered + actred); 148 tau_min = PetscMin(tau_1, tau_2); 149 tau_max = PetscMax(tau_1, tau_2); 150 151 if (PetscAbsScalar(kappa - 1.0) <= tl->mu1_i) { 152 /* Great agreement */ 153 max_radius = PetscMax(max_radius, tao->trust); 154 155 if (tau_max < 1.0) { 156 tau = tl->gamma3_i; 157 } else if (tau_max > tl->gamma4_i) { 158 tau = tl->gamma4_i; 159 } else if (tau_1 >= 1.0 && tau_1 <= tl->gamma4_i && tau_2 < 1.0) { 160 tau = tau_1; 161 } else if (tau_2 >= 1.0 && tau_2 <= tl->gamma4_i && tau_1 < 1.0) { 162 tau = tau_2; 163 } else { 164 tau = tau_max; 165 } 166 } else if (PetscAbsScalar(kappa - 1.0) <= tl->mu2_i) { 167 /* Good agreement */ 168 max_radius = PetscMax(max_radius, tao->trust); 169 170 if (tau_max < tl->gamma2_i) { 171 tau = tl->gamma2_i; 172 } else if (tau_max > tl->gamma3_i) { 173 tau = tl->gamma3_i; 174 } else { 175 tau = tau_max; 176 } 177 } else { 178 /* Not good agreement */ 179 if (tau_min > 1.0) { 180 tau = tl->gamma2_i; 181 } else if (tau_max < tl->gamma1_i) { 182 tau = tl->gamma1_i; 183 } else if ((tau_min < tl->gamma1_i) && (tau_max >= 1.0)) { 184 tau = tl->gamma1_i; 185 } else if ((tau_1 >= tl->gamma1_i) && (tau_1 < 1.0) && ((tau_2 < tl->gamma1_i) || (tau_2 >= 1.0))) { 186 tau = tau_1; 187 } else if ((tau_2 >= tl->gamma1_i) && (tau_2 < 1.0) && ((tau_1 < tl->gamma1_i) || (tau_2 >= 1.0))) { 188 tau = tau_2; 189 } else { 190 tau = tau_max; 191 } 192 } 193 } 194 tao->trust = tau * tao->trust; 195 } 196 197 if (fmin < f) { 198 f = fmin; 199 ierr = VecAXPY(tao->solution, sigma, tao->gradient);CHKERRQ(ierr); 200 ierr = TaoComputeGradient(tao, tao->solution, tao->gradient);CHKERRQ(ierr); 201 202 ierr = VecNorm(tao->gradient, NORM_2, &gnorm);CHKERRQ(ierr); 203 if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN"); 204 needH = 1; 205 206 ierr = TaoLogConvergenceHistory(tao,f,gnorm,0.0,tao->ksp_its);CHKERRQ(ierr); 207 ierr = TaoMonitor(tao,tao->niter,f,gnorm,0.0,step);CHKERRQ(ierr); 208 ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr); 209 if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0); 210 } 211 } 212 tao->trust = PetscMax(tao->trust, max_radius); 213 214 /* Modify the radius if it is too large or small */ 215 tao->trust = PetscMax(tao->trust, tl->min_radius); 216 tao->trust = PetscMin(tao->trust, tl->max_radius); 217 break; 218 219 default: 220 /* Norm of the first direction will initialize radius */ 221 tao->trust = 0.0; 222 break; 223 } 224 225 /* Set counter for gradient/reset steps */ 226 tl->ntrust = 0; 227 tl->newt = 0; 228 tl->bfgs = 0; 229 tl->grad = 0; 230 231 /* Have not converged; continue with Newton method */ 232 while (tao->reason == TAO_CONTINUE_ITERATING) { 233 ++tao->niter; 234 tao->ksp_its=0; 235 /* Compute the Hessian */ 236 if (needH) { 237 ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr); 238 } 239 240 if (tl->bfgs_pre) { 241 /* Update the limited memory preconditioner */ 242 ierr = MatLMVMUpdate(tl->M,tao->solution, tao->gradient);CHKERRQ(ierr); 243 ++bfgsUpdates; 244 } 245 ierr = KSPSetOperators(tao->ksp, tao->hessian, tao->hessian_pre);CHKERRQ(ierr); 246 /* Solve the Newton system of equations */ 247 ierr = KSPCGSetRadius(tao->ksp,tl->max_radius);CHKERRQ(ierr); 248 ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr); 249 ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr); 250 tao->ksp_its+=its; 251 tao->ksp_tot_its+=its; 252 ierr = KSPCGGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr); 253 254 if (0.0 == tao->trust) { 255 /* Radius was uninitialized; use the norm of the direction */ 256 if (norm_d > 0.0) { 257 tao->trust = norm_d; 258 259 /* Modify the radius if it is too large or small */ 260 tao->trust = PetscMax(tao->trust, tl->min_radius); 261 tao->trust = PetscMin(tao->trust, tl->max_radius); 262 } else { 263 /* The direction was bad; set radius to default value and re-solve 264 the trust-region subproblem to get a direction */ 265 tao->trust = tao->trust0; 266 267 /* Modify the radius if it is too large or small */ 268 tao->trust = PetscMax(tao->trust, tl->min_radius); 269 tao->trust = PetscMin(tao->trust, tl->max_radius); 270 271 ierr = KSPCGSetRadius(tao->ksp,tl->max_radius);CHKERRQ(ierr); 272 ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr); 273 ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr); 274 tao->ksp_its+=its; 275 tao->ksp_tot_its+=its; 276 ierr = KSPCGGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr); 277 278 if (norm_d == 0.0) SETERRQ(PETSC_COMM_SELF,1, "Initial direction zero"); 279 } 280 } 281 282 ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr); 283 ierr = KSPGetConvergedReason(tao->ksp, &ksp_reason);CHKERRQ(ierr); 284 if ((KSP_DIVERGED_INDEFINITE_PC == ksp_reason) && (tl->bfgs_pre)) { 285 /* Preconditioner is numerically indefinite; reset the 286 approximate if using BFGS preconditioning. */ 287 ierr = MatLMVMReset(tl->M, PETSC_FALSE);CHKERRQ(ierr); 288 ierr = MatLMVMUpdate(tl->M, tao->solution, tao->gradient);CHKERRQ(ierr); 289 bfgsUpdates = 1; 290 } 291 292 /* Check trust-region reduction conditions */ 293 tr_reject = 0; 294 if (NTL_UPDATE_REDUCTION == tl->update_type) { 295 /* Get predicted reduction */ 296 ierr = KSPCGGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr); 297 if (prered >= 0.0) { 298 /* The predicted reduction has the wrong sign. This cannot 299 happen in infinite precision arithmetic. Step should 300 be rejected! */ 301 tao->trust = tl->alpha1 * PetscMin(tao->trust, norm_d); 302 tr_reject = 1; 303 } else { 304 /* Compute trial step and function value */ 305 ierr = VecCopy(tao->solution, tl->W);CHKERRQ(ierr); 306 ierr = VecAXPY(tl->W, 1.0, tao->stepdirection);CHKERRQ(ierr); 307 ierr = TaoComputeObjective(tao, tl->W, &ftrial);CHKERRQ(ierr); 308 309 if (PetscIsInfOrNanReal(ftrial)) { 310 tao->trust = tl->alpha1 * PetscMin(tao->trust, norm_d); 311 tr_reject = 1; 312 } else { 313 /* Compute and actual reduction */ 314 actred = f - ftrial; 315 prered = -prered; 316 if ((PetscAbsScalar(actred) <= tl->epsilon) && 317 (PetscAbsScalar(prered) <= tl->epsilon)) { 318 kappa = 1.0; 319 } else { 320 kappa = actred / prered; 321 } 322 323 /* Accept of reject the step and update radius */ 324 if (kappa < tl->eta1) { 325 /* Reject the step */ 326 tao->trust = tl->alpha1 * PetscMin(tao->trust, norm_d); 327 tr_reject = 1; 328 } else { 329 /* Accept the step */ 330 if (kappa < tl->eta2) { 331 /* Marginal bad step */ 332 tao->trust = tl->alpha2 * PetscMin(tao->trust, norm_d); 333 } else if (kappa < tl->eta3) { 334 /* Reasonable step */ 335 tao->trust = tl->alpha3 * tao->trust; 336 } else if (kappa < tl->eta4) { 337 /* Good step */ 338 tao->trust = PetscMax(tl->alpha4 * norm_d, tao->trust); 339 } else { 340 /* Very good step */ 341 tao->trust = PetscMax(tl->alpha5 * norm_d, tao->trust); 342 } 343 } 344 } 345 } 346 } else { 347 /* Get predicted reduction */ 348 ierr = KSPCGGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr); 349 if (prered >= 0.0) { 350 /* The predicted reduction has the wrong sign. This cannot 351 happen in infinite precision arithmetic. Step should 352 be rejected! */ 353 tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d); 354 tr_reject = 1; 355 } else { 356 ierr = VecCopy(tao->solution, tl->W);CHKERRQ(ierr); 357 ierr = VecAXPY(tl->W, 1.0, tao->stepdirection);CHKERRQ(ierr); 358 ierr = TaoComputeObjective(tao, tl->W, &ftrial);CHKERRQ(ierr); 359 if (PetscIsInfOrNanReal(ftrial)) { 360 tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d); 361 tr_reject = 1; 362 } else { 363 ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr); 364 365 actred = f - ftrial; 366 prered = -prered; 367 if ((PetscAbsScalar(actred) <= tl->epsilon) && 368 (PetscAbsScalar(prered) <= tl->epsilon)) { 369 kappa = 1.0; 370 } else { 371 kappa = actred / prered; 372 } 373 374 tau_1 = tl->theta * gdx / (tl->theta * gdx - (1.0 - tl->theta) * prered + actred); 375 tau_2 = tl->theta * gdx / (tl->theta * gdx + (1.0 + tl->theta) * prered - actred); 376 tau_min = PetscMin(tau_1, tau_2); 377 tau_max = PetscMax(tau_1, tau_2); 378 379 if (kappa >= 1.0 - tl->mu1) { 380 /* Great agreement; accept step and update radius */ 381 if (tau_max < 1.0) { 382 tao->trust = PetscMax(tao->trust, tl->gamma3 * norm_d); 383 } else if (tau_max > tl->gamma4) { 384 tao->trust = PetscMax(tao->trust, tl->gamma4 * norm_d); 385 } else { 386 tao->trust = PetscMax(tao->trust, tau_max * norm_d); 387 } 388 } else if (kappa >= 1.0 - tl->mu2) { 389 /* Good agreement */ 390 391 if (tau_max < tl->gamma2) { 392 tao->trust = tl->gamma2 * PetscMin(tao->trust, norm_d); 393 } else if (tau_max > tl->gamma3) { 394 tao->trust = PetscMax(tao->trust, tl->gamma3 * norm_d); 395 } else if (tau_max < 1.0) { 396 tao->trust = tau_max * PetscMin(tao->trust, norm_d); 397 } else { 398 tao->trust = PetscMax(tao->trust, tau_max * norm_d); 399 } 400 } else { 401 /* Not good agreement */ 402 if (tau_min > 1.0) { 403 tao->trust = tl->gamma2 * PetscMin(tao->trust, norm_d); 404 } else if (tau_max < tl->gamma1) { 405 tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d); 406 } else if ((tau_min < tl->gamma1) && (tau_max >= 1.0)) { 407 tao->trust = tl->gamma1 * PetscMin(tao->trust, norm_d); 408 } else if ((tau_1 >= tl->gamma1) && (tau_1 < 1.0) && ((tau_2 < tl->gamma1) || (tau_2 >= 1.0))) { 409 tao->trust = tau_1 * PetscMin(tao->trust, norm_d); 410 } else if ((tau_2 >= tl->gamma1) && (tau_2 < 1.0) && ((tau_1 < tl->gamma1) || (tau_2 >= 1.0))) { 411 tao->trust = tau_2 * PetscMin(tao->trust, norm_d); 412 } else { 413 tao->trust = tau_max * PetscMin(tao->trust, norm_d); 414 } 415 tr_reject = 1; 416 } 417 } 418 } 419 } 420 421 if (tr_reject) { 422 /* The trust-region constraints rejected the step. Apply a linesearch. 423 Check for descent direction. */ 424 ierr = VecDot(tao->stepdirection, tao->gradient, &gdx);CHKERRQ(ierr); 425 if ((gdx >= 0.0) || PetscIsInfOrNanReal(gdx)) { 426 /* Newton step is not descent or direction produced Inf or NaN */ 427 428 if (!tl->bfgs_pre) { 429 /* We don't have the bfgs matrix around and updated 430 Must use gradient direction in this case */ 431 ierr = VecCopy(tao->gradient, tao->stepdirection);CHKERRQ(ierr); 432 ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr); 433 ++tl->grad; 434 stepType = NTL_GRADIENT; 435 } else { 436 /* Attempt to use the BFGS direction */ 437 ierr = MatSolve(tl->M, tao->gradient, tao->stepdirection);CHKERRQ(ierr); 438 ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr); 439 440 /* Check for success (descent direction) */ 441 ierr = VecDot(tao->stepdirection, tao->gradient, &gdx);CHKERRQ(ierr); 442 if ((gdx >= 0) || PetscIsInfOrNanReal(gdx)) { 443 /* BFGS direction is not descent or direction produced not a number 444 We can assert bfgsUpdates > 1 in this case because 445 the first solve produces the scaled gradient direction, 446 which is guaranteed to be descent */ 447 448 /* Use steepest descent direction (scaled) */ 449 ierr = MatLMVMReset(tl->M, PETSC_FALSE);CHKERRQ(ierr); 450 ierr = MatLMVMUpdate(tl->M, tao->solution, tao->gradient);CHKERRQ(ierr); 451 ierr = MatSolve(tl->M, tao->gradient, tao->stepdirection);CHKERRQ(ierr); 452 ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr); 453 454 bfgsUpdates = 1; 455 ++tl->grad; 456 stepType = NTL_GRADIENT; 457 } else { 458 ierr = MatLMVMGetUpdateCount(tl->M, &bfgsUpdates);CHKERRQ(ierr); 459 if (1 == bfgsUpdates) { 460 /* The first BFGS direction is always the scaled gradient */ 461 ++tl->grad; 462 stepType = NTL_GRADIENT; 463 } else { 464 ++tl->bfgs; 465 stepType = NTL_BFGS; 466 } 467 } 468 } 469 } else { 470 /* Computed Newton step is descent */ 471 ++tl->newt; 472 stepType = NTL_NEWTON; 473 } 474 475 /* Perform the linesearch */ 476 fold = f; 477 ierr = VecCopy(tao->solution, tl->Xold);CHKERRQ(ierr); 478 ierr = VecCopy(tao->gradient, tl->Gold);CHKERRQ(ierr); 479 480 step = 1.0; 481 ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, tao->stepdirection, &step, &ls_reason);CHKERRQ(ierr); 482 ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr); 483 484 while (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER && stepType != NTL_GRADIENT) { /* Linesearch failed */ 485 /* Linesearch failed */ 486 f = fold; 487 ierr = VecCopy(tl->Xold, tao->solution);CHKERRQ(ierr); 488 ierr = VecCopy(tl->Gold, tao->gradient);CHKERRQ(ierr); 489 490 switch(stepType) { 491 case NTL_NEWTON: 492 /* Failed to obtain acceptable iterate with Newton step */ 493 494 if (tl->bfgs_pre) { 495 /* We don't have the bfgs matrix around and being updated 496 Must use gradient direction in this case */ 497 ierr = VecCopy(tao->gradient, tao->stepdirection);CHKERRQ(ierr); 498 ++tl->grad; 499 stepType = NTL_GRADIENT; 500 } else { 501 /* Attempt to use the BFGS direction */ 502 ierr = MatSolve(tl->M, tao->gradient, tao->stepdirection);CHKERRQ(ierr); 503 504 505 /* Check for success (descent direction) */ 506 ierr = VecDot(tao->stepdirection, tao->gradient, &gdx);CHKERRQ(ierr); 507 if ((gdx <= 0) || PetscIsInfOrNanReal(gdx)) { 508 /* BFGS direction is not descent or direction produced 509 not a number. We can assert bfgsUpdates > 1 in this case 510 Use steepest descent direction (scaled) */ 511 ierr = MatLMVMReset(tl->M, PETSC_FALSE);CHKERRQ(ierr); 512 ierr = MatLMVMUpdate(tl->M, tao->solution, tao->gradient);CHKERRQ(ierr); 513 ierr = MatSolve(tl->M, tao->gradient, tao->stepdirection);CHKERRQ(ierr); 514 515 bfgsUpdates = 1; 516 ++tl->grad; 517 stepType = NTL_GRADIENT; 518 } else { 519 ierr = MatLMVMGetUpdateCount(tl->M, &bfgsUpdates);CHKERRQ(ierr); 520 if (1 == bfgsUpdates) { 521 /* The first BFGS direction is always the scaled gradient */ 522 ++tl->grad; 523 stepType = NTL_GRADIENT; 524 } else { 525 ++tl->bfgs; 526 stepType = NTL_BFGS; 527 } 528 } 529 } 530 break; 531 532 case NTL_BFGS: 533 /* Can only enter if pc_type == NTL_PC_BFGS 534 Failed to obtain acceptable iterate with BFGS step 535 Attempt to use the scaled gradient direction */ 536 ierr = MatLMVMReset(tl->M, PETSC_FALSE);CHKERRQ(ierr); 537 ierr = MatLMVMUpdate(tl->M, tao->solution, tao->gradient);CHKERRQ(ierr); 538 ierr = MatSolve(tl->M, tao->gradient, tao->stepdirection);CHKERRQ(ierr); 539 540 bfgsUpdates = 1; 541 ++tl->grad; 542 stepType = NTL_GRADIENT; 543 break; 544 } 545 ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr); 546 547 /* This may be incorrect; linesearch has values for stepmax and stepmin 548 that should be reset. */ 549 step = 1.0; 550 ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, tao->stepdirection, &step, &ls_reason);CHKERRQ(ierr); 551 ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr); 552 } 553 554 if (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER) { 555 /* Failed to find an improving point */ 556 f = fold; 557 ierr = VecCopy(tl->Xold, tao->solution);CHKERRQ(ierr); 558 ierr = VecCopy(tl->Gold, tao->gradient);CHKERRQ(ierr); 559 tao->trust = 0.0; 560 step = 0.0; 561 tao->reason = TAO_DIVERGED_LS_FAILURE; 562 break; 563 } else if (stepType == NTL_NEWTON) { 564 if (step < tl->nu1) { 565 /* Very bad step taken; reduce radius */ 566 tao->trust = tl->omega1 * PetscMin(norm_d, tao->trust); 567 } else if (step < tl->nu2) { 568 /* Reasonably bad step taken; reduce radius */ 569 tao->trust = tl->omega2 * PetscMin(norm_d, tao->trust); 570 } else if (step < tl->nu3) { 571 /* Reasonable step was taken; leave radius alone */ 572 if (tl->omega3 < 1.0) { 573 tao->trust = tl->omega3 * PetscMin(norm_d, tao->trust); 574 } else if (tl->omega3 > 1.0) { 575 tao->trust = PetscMax(tl->omega3 * norm_d, tao->trust); 576 } 577 } else if (step < tl->nu4) { 578 /* Full step taken; increase the radius */ 579 tao->trust = PetscMax(tl->omega4 * norm_d, tao->trust); 580 } else { 581 /* More than full step taken; increase the radius */ 582 tao->trust = PetscMax(tl->omega5 * norm_d, tao->trust); 583 } 584 } else { 585 /* Newton step was not good; reduce the radius */ 586 tao->trust = tl->omega1 * PetscMin(norm_d, tao->trust); 587 } 588 } else { 589 /* Trust-region step is accepted */ 590 ierr = VecCopy(tl->W, tao->solution);CHKERRQ(ierr); 591 f = ftrial; 592 ierr = TaoComputeGradient(tao, tao->solution, tao->gradient);CHKERRQ(ierr); 593 ++tl->ntrust; 594 } 595 596 /* The radius may have been increased; modify if it is too large */ 597 tao->trust = PetscMin(tao->trust, tl->max_radius); 598 599 /* Check for converged */ 600 ierr = VecNorm(tao->gradient, NORM_2, &gnorm);CHKERRQ(ierr); 601 if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1,"User provided compute function generated Not-a-Number"); 602 needH = 1; 603 604 ierr = TaoLogConvergenceHistory(tao,f,gnorm,0.0,tao->ksp_its);CHKERRQ(ierr); 605 ierr = TaoMonitor(tao,tao->niter,f,gnorm,0.0,step);CHKERRQ(ierr); 606 ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr); 607 } 608 PetscFunctionReturn(0); 609 } 610 611 /* ---------------------------------------------------------- */ 612 static PetscErrorCode TaoSetUp_NTL(Tao tao) 613 { 614 TAO_NTL *tl = (TAO_NTL *)tao->data; 615 PetscErrorCode ierr; 616 617 PetscFunctionBegin; 618 if (!tao->gradient) {ierr = VecDuplicate(tao->solution, &tao->gradient);CHKERRQ(ierr); } 619 if (!tao->stepdirection) {ierr = VecDuplicate(tao->solution, &tao->stepdirection);CHKERRQ(ierr);} 620 if (!tl->W) { ierr = VecDuplicate(tao->solution, &tl->W);CHKERRQ(ierr);} 621 if (!tl->Xold) { ierr = VecDuplicate(tao->solution, &tl->Xold);CHKERRQ(ierr);} 622 if (!tl->Gold) { ierr = VecDuplicate(tao->solution, &tl->Gold);CHKERRQ(ierr);} 623 tl->bfgs_pre = 0; 624 tl->M = 0; 625 PetscFunctionReturn(0); 626 } 627 628 /*------------------------------------------------------------*/ 629 static PetscErrorCode TaoDestroy_NTL(Tao tao) 630 { 631 TAO_NTL *tl = (TAO_NTL *)tao->data; 632 PetscErrorCode ierr; 633 634 PetscFunctionBegin; 635 if (tao->setupcalled) { 636 ierr = VecDestroy(&tl->W);CHKERRQ(ierr); 637 ierr = VecDestroy(&tl->Xold);CHKERRQ(ierr); 638 ierr = VecDestroy(&tl->Gold);CHKERRQ(ierr); 639 } 640 ierr = PetscFree(tao->data);CHKERRQ(ierr); 641 PetscFunctionReturn(0); 642 } 643 644 /*------------------------------------------------------------*/ 645 static PetscErrorCode TaoSetFromOptions_NTL(PetscOptionItems *PetscOptionsObject,Tao tao) 646 { 647 TAO_NTL *tl = (TAO_NTL *)tao->data; 648 PetscErrorCode ierr; 649 650 PetscFunctionBegin; 651 ierr = PetscOptionsHead(PetscOptionsObject,"Newton trust region with line search method for unconstrained optimization");CHKERRQ(ierr); 652 ierr = PetscOptionsEList("-tao_ntl_init_type", "radius initialization type", "", NTL_INIT, NTL_INIT_TYPES, NTL_INIT[tl->init_type], &tl->init_type,NULL);CHKERRQ(ierr); 653 ierr = PetscOptionsEList("-tao_ntl_update_type", "radius update type", "", NTL_UPDATE, NTL_UPDATE_TYPES, NTL_UPDATE[tl->update_type], &tl->update_type,NULL);CHKERRQ(ierr); 654 ierr = PetscOptionsReal("-tao_ntl_eta1", "poor steplength; reduce radius", "", tl->eta1, &tl->eta1,NULL);CHKERRQ(ierr); 655 ierr = PetscOptionsReal("-tao_ntl_eta2", "reasonable steplength; leave radius alone", "", tl->eta2, &tl->eta2,NULL);CHKERRQ(ierr); 656 ierr = PetscOptionsReal("-tao_ntl_eta3", "good steplength; increase radius", "", tl->eta3, &tl->eta3,NULL);CHKERRQ(ierr); 657 ierr = PetscOptionsReal("-tao_ntl_eta4", "excellent steplength; greatly increase radius", "", tl->eta4, &tl->eta4,NULL);CHKERRQ(ierr); 658 ierr = PetscOptionsReal("-tao_ntl_alpha1", "", "", tl->alpha1, &tl->alpha1,NULL);CHKERRQ(ierr); 659 ierr = PetscOptionsReal("-tao_ntl_alpha2", "", "", tl->alpha2, &tl->alpha2,NULL);CHKERRQ(ierr); 660 ierr = PetscOptionsReal("-tao_ntl_alpha3", "", "", tl->alpha3, &tl->alpha3,NULL);CHKERRQ(ierr); 661 ierr = PetscOptionsReal("-tao_ntl_alpha4", "", "", tl->alpha4, &tl->alpha4,NULL);CHKERRQ(ierr); 662 ierr = PetscOptionsReal("-tao_ntl_alpha5", "", "", tl->alpha5, &tl->alpha5,NULL);CHKERRQ(ierr); 663 ierr = PetscOptionsReal("-tao_ntl_nu1", "poor steplength; reduce radius", "", tl->nu1, &tl->nu1,NULL);CHKERRQ(ierr); 664 ierr = PetscOptionsReal("-tao_ntl_nu2", "reasonable steplength; leave radius alone", "", tl->nu2, &tl->nu2,NULL);CHKERRQ(ierr); 665 ierr = PetscOptionsReal("-tao_ntl_nu3", "good steplength; increase radius", "", tl->nu3, &tl->nu3,NULL);CHKERRQ(ierr); 666 ierr = PetscOptionsReal("-tao_ntl_nu4", "excellent steplength; greatly increase radius", "", tl->nu4, &tl->nu4,NULL);CHKERRQ(ierr); 667 ierr = PetscOptionsReal("-tao_ntl_omega1", "", "", tl->omega1, &tl->omega1,NULL);CHKERRQ(ierr); 668 ierr = PetscOptionsReal("-tao_ntl_omega2", "", "", tl->omega2, &tl->omega2,NULL);CHKERRQ(ierr); 669 ierr = PetscOptionsReal("-tao_ntl_omega3", "", "", tl->omega3, &tl->omega3,NULL);CHKERRQ(ierr); 670 ierr = PetscOptionsReal("-tao_ntl_omega4", "", "", tl->omega4, &tl->omega4,NULL);CHKERRQ(ierr); 671 ierr = PetscOptionsReal("-tao_ntl_omega5", "", "", tl->omega5, &tl->omega5,NULL);CHKERRQ(ierr); 672 ierr = PetscOptionsReal("-tao_ntl_mu1_i", "", "", tl->mu1_i, &tl->mu1_i,NULL);CHKERRQ(ierr); 673 ierr = PetscOptionsReal("-tao_ntl_mu2_i", "", "", tl->mu2_i, &tl->mu2_i,NULL);CHKERRQ(ierr); 674 ierr = PetscOptionsReal("-tao_ntl_gamma1_i", "", "", tl->gamma1_i, &tl->gamma1_i,NULL);CHKERRQ(ierr); 675 ierr = PetscOptionsReal("-tao_ntl_gamma2_i", "", "", tl->gamma2_i, &tl->gamma2_i,NULL);CHKERRQ(ierr); 676 ierr = PetscOptionsReal("-tao_ntl_gamma3_i", "", "", tl->gamma3_i, &tl->gamma3_i,NULL);CHKERRQ(ierr); 677 ierr = PetscOptionsReal("-tao_ntl_gamma4_i", "", "", tl->gamma4_i, &tl->gamma4_i,NULL);CHKERRQ(ierr); 678 ierr = PetscOptionsReal("-tao_ntl_theta_i", "", "", tl->theta_i, &tl->theta_i,NULL);CHKERRQ(ierr); 679 ierr = PetscOptionsReal("-tao_ntl_mu1", "", "", tl->mu1, &tl->mu1,NULL);CHKERRQ(ierr); 680 ierr = PetscOptionsReal("-tao_ntl_mu2", "", "", tl->mu2, &tl->mu2,NULL);CHKERRQ(ierr); 681 ierr = PetscOptionsReal("-tao_ntl_gamma1", "", "", tl->gamma1, &tl->gamma1,NULL);CHKERRQ(ierr); 682 ierr = PetscOptionsReal("-tao_ntl_gamma2", "", "", tl->gamma2, &tl->gamma2,NULL);CHKERRQ(ierr); 683 ierr = PetscOptionsReal("-tao_ntl_gamma3", "", "", tl->gamma3, &tl->gamma3,NULL);CHKERRQ(ierr); 684 ierr = PetscOptionsReal("-tao_ntl_gamma4", "", "", tl->gamma4, &tl->gamma4,NULL);CHKERRQ(ierr); 685 ierr = PetscOptionsReal("-tao_ntl_theta", "", "", tl->theta, &tl->theta,NULL);CHKERRQ(ierr); 686 ierr = PetscOptionsReal("-tao_ntl_min_radius", "lower bound on initial radius", "", tl->min_radius, &tl->min_radius,NULL);CHKERRQ(ierr); 687 ierr = PetscOptionsReal("-tao_ntl_max_radius", "upper bound on radius", "", tl->max_radius, &tl->max_radius,NULL);CHKERRQ(ierr); 688 ierr = PetscOptionsReal("-tao_ntl_epsilon", "tolerance used when computing actual and predicted reduction", "", tl->epsilon, &tl->epsilon,NULL);CHKERRQ(ierr); 689 ierr = PetscOptionsTail();CHKERRQ(ierr); 690 ierr = TaoLineSearchSetFromOptions(tao->linesearch);CHKERRQ(ierr); 691 ierr = KSPSetFromOptions(tao->ksp);CHKERRQ(ierr); 692 PetscFunctionReturn(0); 693 } 694 695 /*------------------------------------------------------------*/ 696 static PetscErrorCode TaoView_NTL(Tao tao, PetscViewer viewer) 697 { 698 TAO_NTL *tl = (TAO_NTL *)tao->data; 699 PetscBool isascii; 700 PetscErrorCode ierr; 701 702 PetscFunctionBegin; 703 ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr); 704 if (isascii) { 705 ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr); 706 ierr = PetscViewerASCIIPrintf(viewer, "Trust-region steps: %D\n", tl->ntrust);CHKERRQ(ierr); 707 ierr = PetscViewerASCIIPrintf(viewer, "Newton search steps: %D\n", tl->newt);CHKERRQ(ierr); 708 ierr = PetscViewerASCIIPrintf(viewer, "BFGS search steps: %D\n", tl->bfgs);CHKERRQ(ierr); 709 ierr = PetscViewerASCIIPrintf(viewer, "Gradient search steps: %D\n", tl->grad);CHKERRQ(ierr); 710 ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr); 711 } 712 PetscFunctionReturn(0); 713 } 714 715 /* ---------------------------------------------------------- */ 716 /*MC 717 TAONTR - Newton's method with trust region and linesearch 718 for unconstrained minimization. 719 At each iteration, the Newton trust region method solves the system for d 720 and performs a line search in the d direction: 721 722 min_d .5 dT Hk d + gkT d, s.t. ||d|| < Delta_k 723 724 Options Database Keys: 725 + -tao_ntl_pc_type - "none","ahess","bfgs","petsc" 726 . -tao_ntl_bfgs_scale_type - type of scaling with bfgs pc, "ahess" or "bfgs" 727 . -tao_ntl_init_type - "constant","direction","interpolation" 728 . -tao_ntl_update_type - "reduction","interpolation" 729 . -tao_ntl_min_radius - lower bound on trust region radius 730 . -tao_ntl_max_radius - upper bound on trust region radius 731 . -tao_ntl_epsilon - tolerance for accepting actual / predicted reduction 732 . -tao_ntl_mu1_i - mu1 interpolation init factor 733 . -tao_ntl_mu2_i - mu2 interpolation init factor 734 . -tao_ntl_gamma1_i - gamma1 interpolation init factor 735 . -tao_ntl_gamma2_i - gamma2 interpolation init factor 736 . -tao_ntl_gamma3_i - gamma3 interpolation init factor 737 . -tao_ntl_gamma4_i - gamma4 interpolation init factor 738 . -tao_ntl_theta_i - thetha1 interpolation init factor 739 . -tao_ntl_eta1 - eta1 reduction update factor 740 . -tao_ntl_eta2 - eta2 reduction update factor 741 . -tao_ntl_eta3 - eta3 reduction update factor 742 . -tao_ntl_eta4 - eta4 reduction update factor 743 . -tao_ntl_alpha1 - alpha1 reduction update factor 744 . -tao_ntl_alpha2 - alpha2 reduction update factor 745 . -tao_ntl_alpha3 - alpha3 reduction update factor 746 . -tao_ntl_alpha4 - alpha4 reduction update factor 747 . -tao_ntl_alpha4 - alpha4 reduction update factor 748 . -tao_ntl_mu1 - mu1 interpolation update 749 . -tao_ntl_mu2 - mu2 interpolation update 750 . -tao_ntl_gamma1 - gamma1 interpolcation update 751 . -tao_ntl_gamma2 - gamma2 interpolcation update 752 . -tao_ntl_gamma3 - gamma3 interpolcation update 753 . -tao_ntl_gamma4 - gamma4 interpolation update 754 - -tao_ntl_theta - theta1 interpolation update 755 756 Level: beginner 757 M*/ 758 759 PETSC_EXTERN PetscErrorCode TaoCreate_NTL(Tao tao) 760 { 761 TAO_NTL *tl; 762 PetscErrorCode ierr; 763 const char *morethuente_type = TAOLINESEARCHMT; 764 765 PetscFunctionBegin; 766 ierr = PetscNewLog(tao,&tl);CHKERRQ(ierr); 767 tao->ops->setup = TaoSetUp_NTL; 768 tao->ops->solve = TaoSolve_NTL; 769 tao->ops->view = TaoView_NTL; 770 tao->ops->setfromoptions = TaoSetFromOptions_NTL; 771 tao->ops->destroy = TaoDestroy_NTL; 772 773 /* Override default settings (unless already changed) */ 774 if (!tao->max_it_changed) tao->max_it = 50; 775 if (!tao->trust0_changed) tao->trust0 = 100.0; 776 777 tao->data = (void*)tl; 778 779 /* Default values for trust-region radius update based on steplength */ 780 tl->nu1 = 0.25; 781 tl->nu2 = 0.50; 782 tl->nu3 = 1.00; 783 tl->nu4 = 1.25; 784 785 tl->omega1 = 0.25; 786 tl->omega2 = 0.50; 787 tl->omega3 = 1.00; 788 tl->omega4 = 2.00; 789 tl->omega5 = 4.00; 790 791 /* Default values for trust-region radius update based on reduction */ 792 tl->eta1 = 1.0e-4; 793 tl->eta2 = 0.25; 794 tl->eta3 = 0.50; 795 tl->eta4 = 0.90; 796 797 tl->alpha1 = 0.25; 798 tl->alpha2 = 0.50; 799 tl->alpha3 = 1.00; 800 tl->alpha4 = 2.00; 801 tl->alpha5 = 4.00; 802 803 /* Default values for trust-region radius update based on interpolation */ 804 tl->mu1 = 0.10; 805 tl->mu2 = 0.50; 806 807 tl->gamma1 = 0.25; 808 tl->gamma2 = 0.50; 809 tl->gamma3 = 2.00; 810 tl->gamma4 = 4.00; 811 812 tl->theta = 0.05; 813 814 /* Default values for trust region initialization based on interpolation */ 815 tl->mu1_i = 0.35; 816 tl->mu2_i = 0.50; 817 818 tl->gamma1_i = 0.0625; 819 tl->gamma2_i = 0.5; 820 tl->gamma3_i = 2.0; 821 tl->gamma4_i = 5.0; 822 823 tl->theta_i = 0.25; 824 825 /* Remaining parameters */ 826 tl->min_radius = 1.0e-10; 827 tl->max_radius = 1.0e10; 828 tl->epsilon = 1.0e-6; 829 830 tl->init_type = NTL_INIT_INTERPOLATION; 831 tl->update_type = NTL_UPDATE_REDUCTION; 832 833 ierr = TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch);CHKERRQ(ierr); 834 ierr = PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);CHKERRQ(ierr); 835 ierr = TaoLineSearchSetType(tao->linesearch, morethuente_type);CHKERRQ(ierr); 836 ierr = TaoLineSearchUseTaoRoutines(tao->linesearch, tao);CHKERRQ(ierr); 837 ierr = TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);CHKERRQ(ierr); 838 ierr = KSPCreate(((PetscObject)tao)->comm,&tao->ksp);CHKERRQ(ierr); 839 ierr = PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1);CHKERRQ(ierr); 840 ierr = KSPSetOptionsPrefix(tao->ksp,tao->hdr.prefix);CHKERRQ(ierr); 841 ierr = KSPSetType(tao->ksp,KSPCGSTCG);CHKERRQ(ierr); 842 PetscFunctionReturn(0); 843 } 844