Actual source code: lmvm.c

  1: #include <petsctaolinesearch.h>
  2: #include <../src/tao/unconstrained/impls/lmvm/lmvm.h>

  4: #define LMVM_STEP_BFGS 0
  5: #define LMVM_STEP_GRAD 1

  7: static PetscErrorCode TaoSolve_LMVM(Tao tao)
  8: {
  9:   TAO_LMVM                    *lmP = (TAO_LMVM *)tao->data;
 10:   PetscReal                    f, fold, gdx, gnorm;
 11:   PetscReal                    step      = 1.0;
 12:   PetscInt                     stepType  = LMVM_STEP_GRAD, nupdates;
 13:   TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;

 15:   PetscFunctionBegin;
 16:   if (tao->XL || tao->XU || tao->ops->computebounds) PetscCall(PetscInfo(tao, "WARNING: Variable bounds have been set but will be ignored by lmvm algorithm\n"));

 18:   /*  Check convergence criteria */
 19:   PetscCall(TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient));
 20:   PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &gnorm));

 22:   PetscCheck(!PetscIsInfOrNanReal(f) && !PetscIsInfOrNanReal(gnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");

 24:   tao->reason = TAO_CONTINUE_ITERATING;
 25:   PetscCall(TaoLogConvergenceHistory(tao, f, gnorm, 0.0, tao->ksp_its));
 26:   PetscCall(TaoMonitor(tao, tao->niter, f, gnorm, 0.0, step));
 27:   PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
 28:   if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(PETSC_SUCCESS);

 30:   /*  Set counter for gradient/reset steps */
 31:   if (!lmP->recycle) {
 32:     lmP->bfgs = 0;
 33:     lmP->grad = 0;
 34:     PetscCall(MatLMVMReset(lmP->M, PETSC_FALSE));
 35:   }

 37:   /*  Have not converged; continue with Newton method */
 38:   while (tao->reason == TAO_CONTINUE_ITERATING) {
 39:     /* Call general purpose update function */
 40:     PetscTryTypeMethod(tao, update, tao->niter, tao->user_update);

 42:     /*  Compute direction */
 43:     if (lmP->H0) {
 44:       PetscCall(MatLMVMSetJ0(lmP->M, lmP->H0));
 45:       stepType = LMVM_STEP_BFGS;
 46:     }
 47:     PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient));
 48:     PetscCall(MatSolve(lmP->M, tao->gradient, lmP->D));
 49:     PetscCall(MatLMVMGetUpdateCount(lmP->M, &nupdates));
 50:     if (nupdates > 0) stepType = LMVM_STEP_BFGS;

 52:     /*  Check for success (descent direction) */
 53:     PetscCall(VecDotRealPart(lmP->D, tao->gradient, &gdx));
 54:     if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
 55:       /* Step is not descent or direction produced not a number
 56:          We can assert bfgsUpdates > 1 in this case because
 57:          the first solve produces the scaled gradient direction,
 58:          which is guaranteed to be descent

 60:          Use steepest descent direction (scaled)
 61:       */

 63:       PetscCall(MatLMVMReset(lmP->M, PETSC_FALSE));
 64:       PetscCall(MatLMVMClearJ0(lmP->M));
 65:       PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient));
 66:       PetscCall(MatSolve(lmP->M, tao->gradient, lmP->D));

 68:       /* On a reset, the direction cannot be not a number; it is a
 69:          scaled gradient step.  No need to check for this condition. */
 70:       stepType = LMVM_STEP_GRAD;
 71:     }
 72:     PetscCall(VecScale(lmP->D, -1.0));

 74:     /*  Perform the linesearch */
 75:     fold = f;
 76:     PetscCall(VecCopy(tao->solution, lmP->Xold));
 77:     PetscCall(VecCopy(tao->gradient, lmP->Gold));

 79:     PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, lmP->D, &step, &ls_status));
 80:     PetscCall(TaoAddLineSearchCounts(tao));

 82:     if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER && (stepType != LMVM_STEP_GRAD)) {
 83:       /*  Reset factors and use scaled gradient step */
 84:       f = fold;
 85:       PetscCall(VecCopy(lmP->Xold, tao->solution));
 86:       PetscCall(VecCopy(lmP->Gold, tao->gradient));

 88:       /*  Failed to obtain acceptable iterate with BFGS step */
 89:       /*  Attempt to use the scaled gradient direction */

 91:       PetscCall(MatLMVMReset(lmP->M, PETSC_FALSE));
 92:       PetscCall(MatLMVMClearJ0(lmP->M));
 93:       PetscCall(MatLMVMUpdate(lmP->M, tao->solution, tao->gradient));
 94:       PetscCall(MatSolve(lmP->M, tao->solution, tao->gradient));

 96:       /* On a reset, the direction cannot be not a number; it is a
 97:           scaled gradient step.  No need to check for this condition. */
 98:       stepType = LMVM_STEP_GRAD;
 99:       PetscCall(VecScale(lmP->D, -1.0));

101:       /*  Perform the linesearch */
102:       PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, lmP->D, &step, &ls_status));
103:       PetscCall(TaoAddLineSearchCounts(tao));
104:     }

106:     if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER) {
107:       /*  Failed to find an improving point */
108:       f = fold;
109:       PetscCall(VecCopy(lmP->Xold, tao->solution));
110:       PetscCall(VecCopy(lmP->Gold, tao->gradient));
111:       step        = 0.0;
112:       tao->reason = TAO_DIVERGED_LS_FAILURE;
113:     } else {
114:       /* LS found valid step, so tally up step type */
115:       switch (stepType) {
116:       case LMVM_STEP_BFGS:
117:         ++lmP->bfgs;
118:         break;
119:       case LMVM_STEP_GRAD:
120:         ++lmP->grad;
121:         break;
122:       default:
123:         break;
124:       }
125:       /*  Compute new gradient norm */
126:       PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &gnorm));
127:     }

129:     /* Check convergence */
130:     tao->niter++;
131:     PetscCall(TaoLogConvergenceHistory(tao, f, gnorm, 0.0, tao->ksp_its));
132:     PetscCall(TaoMonitor(tao, tao->niter, f, gnorm, 0.0, step));
133:     PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
134:   }
135:   PetscFunctionReturn(PETSC_SUCCESS);
136: }

138: static PetscErrorCode TaoSetUp_LMVM(Tao tao)
139: {
140:   TAO_LMVM *lmP = (TAO_LMVM *)tao->data;
141:   PetscInt  n, N;
142:   PetscBool is_set, is_spd;

144:   PetscFunctionBegin;
145:   /* Existence of tao->solution checked in TaoSetUp() */
146:   if (!tao->gradient) PetscCall(VecDuplicate(tao->solution, &tao->gradient));
147:   if (!tao->stepdirection) PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));
148:   if (!lmP->D) PetscCall(VecDuplicate(tao->solution, &lmP->D));
149:   if (!lmP->Xold) PetscCall(VecDuplicate(tao->solution, &lmP->Xold));
150:   if (!lmP->Gold) PetscCall(VecDuplicate(tao->solution, &lmP->Gold));

152:   /*  Create matrix for the limited memory approximation */
153:   PetscCall(VecGetLocalSize(tao->solution, &n));
154:   PetscCall(VecGetSize(tao->solution, &N));
155:   PetscCall(MatSetSizes(lmP->M, n, n, N, N));
156:   PetscCall(MatLMVMAllocate(lmP->M, tao->solution, tao->gradient));
157:   PetscCall(MatIsSPDKnown(lmP->M, &is_set, &is_spd));
158:   PetscCheck(is_set && is_spd, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_INCOMP, "LMVM matrix is not symmetric positive-definite.");

160:   /* If the user has set a matrix to solve as the initial H0, set the options prefix here, and set up the KSP */
161:   if (lmP->H0) PetscCall(MatLMVMSetJ0(lmP->M, lmP->H0));
162:   PetscFunctionReturn(PETSC_SUCCESS);
163: }

165: /* ---------------------------------------------------------- */
166: static PetscErrorCode TaoDestroy_LMVM(Tao tao)
167: {
168:   TAO_LMVM *lmP = (TAO_LMVM *)tao->data;

170:   PetscFunctionBegin;
171:   if (tao->setupcalled) {
172:     PetscCall(VecDestroy(&lmP->Xold));
173:     PetscCall(VecDestroy(&lmP->Gold));
174:     PetscCall(VecDestroy(&lmP->D));
175:   }
176:   PetscCall(MatDestroy(&lmP->M));
177:   if (lmP->H0) PetscCall(PetscObjectDereference((PetscObject)lmP->H0));
178:   PetscCall(PetscFree(tao->data));
179:   PetscFunctionReturn(PETSC_SUCCESS);
180: }

182: /*------------------------------------------------------------*/
183: static PetscErrorCode TaoSetFromOptions_LMVM(Tao tao, PetscOptionItems *PetscOptionsObject)
184: {
185:   TAO_LMVM *lm = (TAO_LMVM *)tao->data;

187:   PetscFunctionBegin;
188:   PetscOptionsHeadBegin(PetscOptionsObject, "Limited-memory variable-metric method for unconstrained optimization");
189:   PetscCall(PetscOptionsBool("-tao_lmvm_recycle", "enable recycling of the BFGS matrix between subsequent TaoSolve() calls", "", lm->recycle, &lm->recycle, NULL));
190:   PetscCall(TaoLineSearchSetFromOptions(tao->linesearch));
191:   PetscCall(MatSetFromOptions(lm->M));
192:   PetscOptionsHeadEnd();
193:   PetscFunctionReturn(PETSC_SUCCESS);
194: }

196: /*------------------------------------------------------------*/
197: static PetscErrorCode TaoView_LMVM(Tao tao, PetscViewer viewer)
198: {
199:   TAO_LMVM *lm = (TAO_LMVM *)tao->data;
200:   PetscBool isascii;
201:   PetscInt  recycled_its;

203:   PetscFunctionBegin;
204:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
205:   if (isascii) {
206:     PetscCall(PetscViewerASCIIPushTab(viewer));
207:     PetscCall(PetscViewerASCIIPrintf(viewer, "Gradient steps: %" PetscInt_FMT "\n", lm->grad));
208:     if (lm->recycle) {
209:       PetscCall(PetscViewerASCIIPrintf(viewer, "Recycle: on\n"));
210:       recycled_its = lm->bfgs + lm->grad;
211:       PetscCall(PetscViewerASCIIPrintf(viewer, "Total recycled iterations: %" PetscInt_FMT "\n", recycled_its));
212:     }
213:     PetscCall(PetscViewerASCIIPrintf(viewer, "LMVM Matrix:\n"));
214:     PetscCall(PetscViewerASCIIPushTab(viewer));
215:     PetscCall(MatView(lm->M, viewer));
216:     PetscCall(PetscViewerASCIIPopTab(viewer));
217:     PetscCall(PetscViewerASCIIPopTab(viewer));
218:   }
219:   PetscFunctionReturn(PETSC_SUCCESS);
220: }

222: /* ---------------------------------------------------------- */

224: /*MC
225:   TAOLMVM - Limited Memory Variable Metric method is a quasi-Newton
226:   optimization solver for unconstrained minimization. It solves
227:   the Newton step
228:           Hkdk = - gk

230:   using an approximation Bk in place of Hk, where Bk is composed using
231:   the BFGS update formula. A More-Thuente line search is then used
232:   to computed the steplength in the dk direction

234:   Options Database Keys:
235: +   -tao_lmvm_recycle - enable recycling LMVM updates between TaoSolve() calls
236: -   -tao_lmvm_no_scale - (developer) disables diagonal Broyden scaling on the LMVM approximation

238:   Level: beginner
239: M*/

241: PETSC_EXTERN PetscErrorCode TaoCreate_LMVM(Tao tao)
242: {
243:   TAO_LMVM   *lmP;
244:   const char *morethuente_type = TAOLINESEARCHMT;

246:   PetscFunctionBegin;
247:   tao->ops->setup          = TaoSetUp_LMVM;
248:   tao->ops->solve          = TaoSolve_LMVM;
249:   tao->ops->view           = TaoView_LMVM;
250:   tao->ops->setfromoptions = TaoSetFromOptions_LMVM;
251:   tao->ops->destroy        = TaoDestroy_LMVM;

253:   PetscCall(PetscNew(&lmP));
254:   lmP->D       = NULL;
255:   lmP->M       = NULL;
256:   lmP->Xold    = NULL;
257:   lmP->Gold    = NULL;
258:   lmP->H0      = NULL;
259:   lmP->recycle = PETSC_FALSE;

261:   tao->data = (void *)lmP;
262:   /* Override default settings (unless already changed) */
263:   if (!tao->max_it_changed) tao->max_it = 2000;
264:   if (!tao->max_funcs_changed) tao->max_funcs = 4000;

266:   PetscCall(TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch));
267:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1));
268:   PetscCall(TaoLineSearchSetType(tao->linesearch, morethuente_type));
269:   PetscCall(TaoLineSearchUseTaoRoutines(tao->linesearch, tao));
270:   PetscCall(TaoLineSearchSetOptionsPrefix(tao->linesearch, tao->hdr.prefix));

272:   PetscCall(KSPInitializePackage());
273:   PetscCall(MatCreate(((PetscObject)tao)->comm, &lmP->M));
274:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)lmP->M, (PetscObject)tao, 1));
275:   PetscCall(MatSetType(lmP->M, MATLMVMBFGS));
276:   PetscCall(MatSetOptionsPrefix(lmP->M, "tao_lmvm_"));
277:   PetscFunctionReturn(PETSC_SUCCESS);
278: }