Date: 2022-03-04T17:39:49+00:00

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:   PetscErrorCode               ierr;
     13:   PetscInt                     stepType = LMVM_STEP_GRAD, nupdates;
     14:   TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;

     18:   if (tao->XL || tao->XU || tao->ops->computebounds) {
     19:     PetscInfo(tao,"WARNING: Variable bounds have been set but will be ignored by lmvm algorithm\n");
     20:   }

     22:   /*  Check convergence criteria */
     23:   TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient);
     24:   TaoGradientNorm(tao, tao->gradient,NORM_2,&gnorm);

     26:   if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_USER, "User provided compute function generated Inf or NaN");

     28:   tao->reason = TAO_CONTINUE_ITERATING;
     29:   TaoLogConvergenceHistory(tao,f,gnorm,0.0,tao->ksp_its);
     30:   TaoMonitor(tao,tao->niter,f,gnorm,0.0,step);
     31:   (*tao->ops->convergencetest)(tao,tao->cnvP);
     32:   if (tao->reason != TAO_CONTINUE_ITERATING) return(0);

     34:   /*  Set counter for gradient/reset steps */
     35:   if (!lmP->recycle) {
     36:     lmP->bfgs = 0;
     37:     lmP->grad = 0;
     38:     MatLMVMReset(lmP->M, PETSC_FALSE);
     39:   }

     41:   /*  Have not converged; continue with Newton method */
     42:   while (tao->reason == TAO_CONTINUE_ITERATING) {
     43:     /* Call general purpose update function */
     44:     if (tao->ops->update) {
     45:       (*tao->ops->update)(tao, tao->niter, tao->user_update);
     46:     }

     48:     /*  Compute direction */
     49:     if (lmP->H0) {
     50:       MatLMVMSetJ0(lmP->M, lmP->H0);
     51:       stepType = LMVM_STEP_BFGS;
     52:     }
     53:     MatLMVMUpdate(lmP->M,tao->solution,tao->gradient);
     54:     MatSolve(lmP->M, tao->gradient, lmP->D);
     55:     MatLMVMGetUpdateCount(lmP->M, &nupdates);
     56:     if (nupdates > 0) stepType = LMVM_STEP_BFGS;

     58:     /*  Check for success (descent direction) */
     59:     VecDot(lmP->D, tao->gradient, &gdx);
     60:     if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
     61:       /* Step is not descent or direction produced not a number
     62:          We can assert bfgsUpdates > 1 in this case because
     63:          the first solve produces the scaled gradient direction,
     64:          which is guaranteed to be descent

     66:          Use steepest descent direction (scaled)
     67:       */

     69:       MatLMVMReset(lmP->M, PETSC_FALSE);
     70:       MatLMVMClearJ0(lmP->M);
     71:       MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);
     72:       MatSolve(lmP->M,tao->gradient, lmP->D);

     74:       /* On a reset, the direction cannot be not a number; it is a
     75:          scaled gradient step.  No need to check for this condition. */
     76:       stepType = LMVM_STEP_GRAD;
     77:     }
     78:     VecScale(lmP->D, -1.0);

     80:     /*  Perform the linesearch */
     81:     fold = f;
     82:     VecCopy(tao->solution, lmP->Xold);
     83:     VecCopy(tao->gradient, lmP->Gold);

     85:     TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, lmP->D, &step,&ls_status);
     86:     TaoAddLineSearchCounts(tao);

     88:     if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER && (stepType != LMVM_STEP_GRAD)) {
     89:       /*  Reset factors and use scaled gradient step */
     90:       f = fold;
     91:       VecCopy(lmP->Xold, tao->solution);
     92:       VecCopy(lmP->Gold, tao->gradient);

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

     97:       MatLMVMReset(lmP->M, PETSC_FALSE);
     98:       MatLMVMClearJ0(lmP->M);
     99:       MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);
    100:       MatSolve(lmP->M, tao->solution, tao->gradient);

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

    107:       /*  Perform the linesearch */
    108:       TaoLineSearchApply(tao->linesearch, tao->solution, &f, tao->gradient, lmP->D, &step, &ls_status);
    109:       TaoAddLineSearchCounts(tao);
    110:     }

    112:     if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER) {
    113:       /*  Failed to find an improving point */
    114:       f = fold;
    115:       VecCopy(lmP->Xold, tao->solution);
    116:       VecCopy(lmP->Gold, tao->gradient);
    117:       step = 0.0;
    118:       tao->reason = TAO_DIVERGED_LS_FAILURE;
    119:     } else {
    120:       /* LS found valid step, so tally up step type */
    121:       switch (stepType) {
    122:       case LMVM_STEP_BFGS:
    123:         ++lmP->bfgs;
    124:         break;
    125:       case LMVM_STEP_GRAD:
    126:         ++lmP->grad;
    127:         break;
    128:       default:
    129:         break;
    130:       }
    131:       /*  Compute new gradient norm */
    132:       TaoGradientNorm(tao, tao->gradient,NORM_2,&gnorm);
    133:     }

    135:     /* Check convergence */
    136:     tao->niter++;
    137:     TaoLogConvergenceHistory(tao,f,gnorm,0.0,tao->ksp_its);
    138:     TaoMonitor(tao,tao->niter,f,gnorm,0.0,step);
    139:     (*tao->ops->convergencetest)(tao,tao->cnvP);
    140:   }
    141:   return(0);
    142: }

    144: static PetscErrorCode TaoSetUp_LMVM(Tao tao)
    145: {
    146:   TAO_LMVM       *lmP = (TAO_LMVM *)tao->data;
    147:   PetscInt       n,N;
    149:   PetscBool      is_spd;

    152:   /* Existence of tao->solution checked in TaoSetUp() */
    153:   if (!tao->gradient) {VecDuplicate(tao->solution,&tao->gradient);  }
    154:   if (!tao->stepdirection) {VecDuplicate(tao->solution,&tao->stepdirection);  }
    155:   if (!lmP->D) {VecDuplicate(tao->solution,&lmP->D);  }
    156:   if (!lmP->Xold) {VecDuplicate(tao->solution,&lmP->Xold);  }
    157:   if (!lmP->Gold) {VecDuplicate(tao->solution,&lmP->Gold);  }

    159:   /*  Create matrix for the limited memory approximation */
    160:   VecGetLocalSize(tao->solution,&n);
    161:   VecGetSize(tao->solution,&N);
    162:   MatSetSizes(lmP->M, n, n, N, N);
    163:   MatLMVMAllocate(lmP->M,tao->solution,tao->gradient);
    164:   MatGetOption(lmP->M, MAT_SPD, &is_spd);
    165:   if (!is_spd) SETERRQ(PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_INCOMP, "LMVM matrix is not symmetric positive-definite.");

    167:   /* If the user has set a matrix to solve as the initial H0, set the options prefix here, and set up the KSP */
    168:   if (lmP->H0) {
    169:     MatLMVMSetJ0(lmP->M, lmP->H0);
    170:   }

    172:   return(0);
    173: }

    175: /* ---------------------------------------------------------- */
    176: static PetscErrorCode TaoDestroy_LMVM(Tao tao)
    177: {
    178:   TAO_LMVM       *lmP = (TAO_LMVM *)tao->data;

    182:   if (tao->setupcalled) {
    183:     VecDestroy(&lmP->Xold);
    184:     VecDestroy(&lmP->Gold);
    185:     VecDestroy(&lmP->D);
    186:   }
    187:   MatDestroy(&lmP->M);
    188:   if (lmP->H0) {
    189:     PetscObjectDereference((PetscObject)lmP->H0);
    190:   }
    191:   PetscFree(tao->data);

    193:   return(0);
    194: }

    196: /*------------------------------------------------------------*/
    197: static PetscErrorCode TaoSetFromOptions_LMVM(PetscOptionItems *PetscOptionsObject,Tao tao)
    198: {
    199:   TAO_LMVM       *lm = (TAO_LMVM *)tao->data;

    203:   PetscOptionsHead(PetscOptionsObject,"Limited-memory variable-metric method for unconstrained optimization");
    204:   PetscOptionsBool("-tao_lmvm_recycle","enable recycling of the BFGS matrix between subsequent TaoSolve() calls","",lm->recycle,&lm->recycle,NULL);
    205:   TaoLineSearchSetFromOptions(tao->linesearch);
    206:   MatSetFromOptions(lm->M);
    207:   PetscOptionsTail();
    208:   return(0);
    209: }

    211: /*------------------------------------------------------------*/
    212: static PetscErrorCode TaoView_LMVM(Tao tao, PetscViewer viewer)
    213: {
    214:   TAO_LMVM       *lm = (TAO_LMVM *)tao->data;
    215:   PetscBool      isascii;
    216:   PetscInt       recycled_its;

    220:   PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii);
    221:   if (isascii) {
    222:     PetscViewerASCIIPrintf(viewer, "  Gradient steps: %D\n", lm->grad);
    223:     if (lm->recycle) {
    224:       PetscViewerASCIIPrintf(viewer, "  Recycle: on\n");
    225:       recycled_its = lm->bfgs + lm->grad;
    226:       PetscViewerASCIIPrintf(viewer, "  Total recycled iterations: %D\n", recycled_its);
    227:     }
    228:   }
    229:   return(0);
    230: }

    232: /* ---------------------------------------------------------- */

    234: /*MC
    235:   TAOLMVM - Limited Memory Variable Metric method is a quasi-Newton
    236:   optimization solver for unconstrained minimization. It solves
    237:   the Newton step
    238:           Hkdk = - gk

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

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

    248:   Level: beginner
    249: M*/

    251: PETSC_EXTERN PetscErrorCode TaoCreate_LMVM(Tao tao)
    252: {
    253:   TAO_LMVM       *lmP;
    254:   const char     *morethuente_type = TAOLINESEARCHMT;

    258:   tao->ops->setup = TaoSetUp_LMVM;
    259:   tao->ops->solve = TaoSolve_LMVM;
    260:   tao->ops->view = TaoView_LMVM;
    261:   tao->ops->setfromoptions = TaoSetFromOptions_LMVM;
    262:   tao->ops->destroy = TaoDestroy_LMVM;

    264:   PetscNewLog(tao,&lmP);
    265:   lmP->D = NULL;
    266:   lmP->M = NULL;
    267:   lmP->Xold = NULL;
    268:   lmP->Gold = NULL;
    269:   lmP->H0   = NULL;
    270:   lmP->recycle = PETSC_FALSE;

    272:   tao->data = (void*)lmP;
    273:   /* Override default settings (unless already changed) */
    274:   if (!tao->max_it_changed) tao->max_it = 2000;
    275:   if (!tao->max_funcs_changed) tao->max_funcs = 4000;

    277:   TaoLineSearchCreate(((PetscObject)tao)->comm,&tao->linesearch);
    278:   PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);
    279:   TaoLineSearchSetType(tao->linesearch,morethuente_type);
    280:   TaoLineSearchUseTaoRoutines(tao->linesearch,tao);
    281:   TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);

    283:   KSPInitializePackage();
    284:   MatCreate(((PetscObject)tao)->comm, &lmP->M);
    285:   PetscObjectIncrementTabLevel((PetscObject)lmP->M, (PetscObject)tao, 1);
    286:   MatSetType(lmP->M, MATLMVMBFGS);
    287:   MatSetOptionsPrefix(lmP->M, "tao_lmvm_");
    288:   return(0);
    289: }