Date: 2022-03-31T04:48:58+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:   PetscInt                     stepType = LMVM_STEP_GRAD, nupdates;
     13:   TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;

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

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

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

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

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

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

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

     64:          Use steepest descent direction (scaled)
     65:       */

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

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

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

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

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

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

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

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

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

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

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

    142: static PetscErrorCode TaoSetUp_LMVM(Tao tao)
    143: {
    144:   TAO_LMVM       *lmP = (TAO_LMVM *)tao->data;
    145:   PetscInt       n,N;
    146:   PetscBool      is_spd;

    148:   /* Existence of tao->solution checked in TaoSetUp() */
    149:   if (!tao->gradient) VecDuplicate(tao->solution,&tao->gradient);
    150:   if (!tao->stepdirection) VecDuplicate(tao->solution,&tao->stepdirection);
    151:   if (!lmP->D) VecDuplicate(tao->solution,&lmP->D);
    152:   if (!lmP->Xold) VecDuplicate(tao->solution,&lmP->Xold);
    153:   if (!lmP->Gold) VecDuplicate(tao->solution,&lmP->Gold);

    155:   /*  Create matrix for the limited memory approximation */
    156:   VecGetLocalSize(tao->solution,&n);
    157:   VecGetSize(tao->solution,&N);
    158:   MatSetSizes(lmP->M, n, n, N, N);
    159:   MatLMVMAllocate(lmP->M,tao->solution,tao->gradient);
    160:   MatGetOption(lmP->M, MAT_SPD, &is_spd);

    163:   /* If the user has set a matrix to solve as the initial H0, set the options prefix here, and set up the KSP */
    164:   if (lmP->H0) {
    165:     MatLMVMSetJ0(lmP->M, lmP->H0);
    166:   }

    168:   return 0;
    169: }

    171: /* ---------------------------------------------------------- */
    172: static PetscErrorCode TaoDestroy_LMVM(Tao tao)
    173: {
    174:   TAO_LMVM       *lmP = (TAO_LMVM *)tao->data;

    176:   if (tao->setupcalled) {
    177:     VecDestroy(&lmP->Xold);
    178:     VecDestroy(&lmP->Gold);
    179:     VecDestroy(&lmP->D);
    180:   }
    181:   MatDestroy(&lmP->M);
    182:   if (lmP->H0) {
    183:     PetscObjectDereference((PetscObject)lmP->H0);
    184:   }
    185:   PetscFree(tao->data);

    187:   return 0;
    188: }

    190: /*------------------------------------------------------------*/
    191: static PetscErrorCode TaoSetFromOptions_LMVM(PetscOptionItems *PetscOptionsObject,Tao tao)
    192: {
    193:   TAO_LMVM       *lm = (TAO_LMVM *)tao->data;

    195:   PetscOptionsHead(PetscOptionsObject,"Limited-memory variable-metric method for unconstrained optimization");
    196:   PetscOptionsBool("-tao_lmvm_recycle","enable recycling of the BFGS matrix between subsequent TaoSolve() calls","",lm->recycle,&lm->recycle,NULL);
    197:   TaoLineSearchSetFromOptions(tao->linesearch);
    198:   MatSetFromOptions(lm->M);
    199:   PetscOptionsTail();
    200:   return 0;
    201: }

    203: /*------------------------------------------------------------*/
    204: static PetscErrorCode TaoView_LMVM(Tao tao, PetscViewer viewer)
    205: {
    206:   TAO_LMVM       *lm = (TAO_LMVM *)tao->data;
    207:   PetscBool      isascii;
    208:   PetscInt       recycled_its;

    210:   PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii);
    211:   if (isascii) {
    212:     PetscViewerASCIIPrintf(viewer, "  Gradient steps: %D\n", lm->grad);
    213:     if (lm->recycle) {
    214:       PetscViewerASCIIPrintf(viewer, "  Recycle: on\n");
    215:       recycled_its = lm->bfgs + lm->grad;
    216:       PetscViewerASCIIPrintf(viewer, "  Total recycled iterations: %D\n", recycled_its);
    217:     }
    218:   }
    219:   return 0;
    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:   tao->ops->setup = TaoSetUp_LMVM;
    247:   tao->ops->solve = TaoSolve_LMVM;
    248:   tao->ops->view = TaoView_LMVM;
    249:   tao->ops->setfromoptions = TaoSetFromOptions_LMVM;
    250:   tao->ops->destroy = TaoDestroy_LMVM;

    252:   PetscNewLog(tao,&lmP);
    253:   lmP->D = NULL;
    254:   lmP->M = NULL;
    255:   lmP->Xold = NULL;
    256:   lmP->Gold = NULL;
    257:   lmP->H0   = NULL;
    258:   lmP->recycle = PETSC_FALSE;

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

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

    271:   KSPInitializePackage();
    272:   MatCreate(((PetscObject)tao)->comm, &lmP->M);
    273:   PetscObjectIncrementTabLevel((PetscObject)lmP->M, (PetscObject)tao, 1);
    274:   MatSetType(lmP->M, MATLMVMBFGS);
    275:   MatSetOptionsPrefix(lmP->M, "tao_lmvm_");
    276:   return 0;
    277: }