Actual source code: tron.c

      1: #include <../src/tao/bound/impls/tron/tron.h>
      2: #include <../src/tao/matrix/submatfree.h>

      5: /* TRON Routines */
      6: static PetscErrorCode TronGradientProjections(Tao,TAO_TRON*);
      7: /*------------------------------------------------------------*/
      8: static PetscErrorCode TaoDestroy_TRON(Tao tao)
      9: {
     10:   TAO_TRON       *tron = (TAO_TRON *)tao->data;

     14:   VecDestroy(&tron->X_New);
     15:   VecDestroy(&tron->G_New);
     16:   VecDestroy(&tron->Work);
     17:   VecDestroy(&tron->DXFree);
     18:   VecDestroy(&tron->R);
     19:   VecDestroy(&tron->diag);
     20:   VecScatterDestroy(&tron->scatter);
     21:   ISDestroy(&tron->Free_Local);
     22:   MatDestroy(&tron->H_sub);
     23:   MatDestroy(&tron->Hpre_sub);
     24:   PetscFree(tao->data);
     25:   return(0);
     26: }

     28: /*------------------------------------------------------------*/
     29: static PetscErrorCode TaoSetFromOptions_TRON(PetscOptionItems *PetscOptionsObject,Tao tao)
     30: {
     31:   TAO_TRON       *tron = (TAO_TRON *)tao->data;
     33:   PetscBool      flg;

     36:   PetscOptionsHead(PetscOptionsObject,"Newton Trust Region Method for bound constrained optimization");
     37:   PetscOptionsInt("-tao_tron_maxgpits","maximum number of gradient projections per TRON iterate","TaoSetMaxGPIts",tron->maxgpits,&tron->maxgpits,&flg);
     38:   PetscOptionsTail();
     39:   TaoLineSearchSetFromOptions(tao->linesearch);
     40:   KSPSetFromOptions(tao->ksp);
     41:   return(0);
     42: }

     44: /*------------------------------------------------------------*/
     45: static PetscErrorCode TaoView_TRON(Tao tao, PetscViewer viewer)
     46: {
     47:   TAO_TRON         *tron = (TAO_TRON *)tao->data;
     48:   PetscBool        isascii;
     49:   PetscErrorCode   ierr;

     52:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
     53:   if (isascii) {
     54:     PetscViewerASCIIPrintf(viewer,"Total PG its: %D,",tron->total_gp_its);
     55:     PetscViewerASCIIPrintf(viewer,"PG tolerance: %g \n",(double)tron->pg_ftol);
     56:   }
     57:   return(0);
     58: }

     60: /* ---------------------------------------------------------- */
     61: static PetscErrorCode TaoSetup_TRON(Tao tao)
     62: {
     64:   TAO_TRON       *tron = (TAO_TRON *)tao->data;

     68:   /* Allocate some arrays */
     69:   VecDuplicate(tao->solution, &tron->diag);
     70:   VecDuplicate(tao->solution, &tron->X_New);
     71:   VecDuplicate(tao->solution, &tron->G_New);
     72:   VecDuplicate(tao->solution, &tron->Work);
     73:   VecDuplicate(tao->solution, &tao->gradient);
     74:   VecDuplicate(tao->solution, &tao->stepdirection);
     75:   if (!tao->XL) {
     76:     VecDuplicate(tao->solution, &tao->XL);
     77:     VecSet(tao->XL, PETSC_NINFINITY);
     78:   }
     79:   if (!tao->XU) {
     80:     VecDuplicate(tao->solution, &tao->XU);
     81:     VecSet(tao->XU, PETSC_INFINITY);
     82:   }
     83:   return(0);
     84: }

     86: static PetscErrorCode TaoSolve_TRON(Tao tao)
     87: {
     88:   TAO_TRON                     *tron = (TAO_TRON *)tao->data;
     89:   PetscErrorCode               ierr;
     90:   PetscInt                     its;
     91:   TaoLineSearchConvergedReason ls_reason = TAOLINESEARCH_CONTINUE_ITERATING;
     92:   PetscReal                    prered,actred,delta,f,f_new,rhok,gdx,xdiff,stepsize;

     95:   tron->pgstepsize = 1.0;
     96:   tao->trust = tao->trust0;
     97:   /*   Project the current point onto the feasible set */
     98:   TaoComputeVariableBounds(tao);
     99:   TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);

    101:   /* Project the initial point onto the feasible region */
    102:   VecMedian(tao->XL,tao->solution,tao->XU,tao->solution);

    104:   /* Compute the objective function and gradient */
    105:   TaoComputeObjectiveAndGradient(tao,tao->solution,&tron->f,tao->gradient);
    106:   VecNorm(tao->gradient,NORM_2,&tron->gnorm);
    107:   if (PetscIsInfOrNanReal(tron->f) || PetscIsInfOrNanReal(tron->gnorm)) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_USER, "User provided compute function generated Inf or NaN");

    109:   /* Project the gradient and calculate the norm */
    110:   VecBoundGradientProjection(tao->gradient,tao->solution,tao->XL,tao->XU,tao->gradient);
    111:   VecNorm(tao->gradient,NORM_2,&tron->gnorm);

    113:   /* Initialize trust region radius */
    114:   tao->trust=tao->trust0;
    115:   if (tao->trust <= 0) {
    116:     tao->trust=PetscMax(tron->gnorm*tron->gnorm,1.0);
    117:   }

    119:   /* Initialize step sizes for the line searches */
    120:   tron->pgstepsize=1.0;
    121:   tron->stepsize=tao->trust;

    123:   tao->reason = TAO_CONTINUE_ITERATING;
    124:   TaoLogConvergenceHistory(tao,tron->f,tron->gnorm,0.0,tao->ksp_its);
    125:   TaoMonitor(tao,tao->niter,tron->f,tron->gnorm,0.0,tron->stepsize);
    126:   (*tao->ops->convergencetest)(tao,tao->cnvP);
    127:   while (tao->reason==TAO_CONTINUE_ITERATING){
    128:     /* Call general purpose update function */
    129:     if (tao->ops->update) {
    130:       (*tao->ops->update)(tao, tao->niter, tao->user_update);
    131:     }

    133:     /* Perform projected gradient iterations */
    134:     TronGradientProjections(tao,tron);

    136:     VecBoundGradientProjection(tao->gradient,tao->solution,tao->XL,tao->XU,tao->gradient);
    137:     VecNorm(tao->gradient,NORM_2,&tron->gnorm);

    139:     tao->ksp_its=0;
    140:     f=tron->f; delta=tao->trust;
    141:     tron->n_free_last = tron->n_free;
    142:     TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);

    144:     /* Generate index set (IS) of which bound constraints are active */
    145:     ISDestroy(&tron->Free_Local);
    146:     VecWhichInactive(tao->XL,tao->solution,tao->gradient,tao->XU,PETSC_TRUE,&tron->Free_Local);
    147:     ISGetSize(tron->Free_Local, &tron->n_free);

    149:     /* If no free variables */
    150:     if (tron->n_free == 0) {
    151:       VecNorm(tao->gradient,NORM_2,&tron->gnorm);
    152:       TaoLogConvergenceHistory(tao,tron->f,tron->gnorm,0.0,tao->ksp_its);
    153:       TaoMonitor(tao,tao->niter,tron->f,tron->gnorm,0.0,delta);
    154:       (*tao->ops->convergencetest)(tao,tao->cnvP);
    155:       if (!tao->reason) {
    156:         tao->reason = TAO_CONVERGED_STEPTOL;
    157:       }
    158:       break;
    159:     }
    160:     /* use free_local to mask/submat gradient, hessian, stepdirection */
    161:     TaoVecGetSubVec(tao->gradient,tron->Free_Local,tao->subset_type,0.0,&tron->R);
    162:     TaoVecGetSubVec(tao->gradient,tron->Free_Local,tao->subset_type,0.0,&tron->DXFree);
    163:     VecSet(tron->DXFree,0.0);
    164:     VecScale(tron->R, -1.0);
    165:     TaoMatGetSubMat(tao->hessian, tron->Free_Local, tron->diag, tao->subset_type, &tron->H_sub);
    166:     if (tao->hessian == tao->hessian_pre) {
    167:       MatDestroy(&tron->Hpre_sub);
    168:       PetscObjectReference((PetscObject)(tron->H_sub));
    169:       tron->Hpre_sub = tron->H_sub;
    170:     } else {
    171:       TaoMatGetSubMat(tao->hessian_pre, tron->Free_Local, tron->diag, tao->subset_type,&tron->Hpre_sub);
    172:     }
    173:     KSPReset(tao->ksp);
    174:     KSPSetOperators(tao->ksp, tron->H_sub, tron->Hpre_sub);
    175:     while (1) {

    177:       /* Approximately solve the reduced linear system */
    178:       KSPCGSetRadius(tao->ksp,delta);

    180:       KSPSolve(tao->ksp, tron->R, tron->DXFree);
    181:       KSPGetIterationNumber(tao->ksp,&its);
    182:       tao->ksp_its+=its;
    183:       tao->ksp_tot_its+=its;
    184:       VecSet(tao->stepdirection,0.0);

    186:       /* Add dxfree matrix to compute step direction vector */
    187:       VecISAXPY(tao->stepdirection,tron->Free_Local,1.0,tron->DXFree);

    189:       VecDot(tao->gradient, tao->stepdirection, &gdx);
    190:       VecCopy(tao->solution, tron->X_New);
    191:       VecCopy(tao->gradient, tron->G_New);

    193:       stepsize=1.0;f_new=f;

    195:       TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);
    196:       TaoLineSearchApply(tao->linesearch, tron->X_New, &f_new, tron->G_New, tao->stepdirection,&stepsize,&ls_reason);
    197:       TaoAddLineSearchCounts(tao);

    199:       MatMult(tao->hessian, tao->stepdirection, tron->Work);
    200:       VecAYPX(tron->Work, 0.5, tao->gradient);
    201:       VecDot(tao->stepdirection, tron->Work, &prered);
    202:       actred = f_new - f;
    203:       if ((PetscAbsScalar(actred) <= 1e-6) && (PetscAbsScalar(prered) <= 1e-6)) {
    204:         rhok = 1.0;
    205:       } else if (actred<0) {
    206:         rhok=PetscAbs(-actred/prered);
    207:       } else {
    208:         rhok=0.0;
    209:       }

    211:       /* Compare actual improvement to the quadratic model */
    212:       if (rhok > tron->eta1) { /* Accept the point */
    213:         /* d = x_new - x */
    214:         VecCopy(tron->X_New, tao->stepdirection);
    215:         VecAXPY(tao->stepdirection, -1.0, tao->solution);

    217:         VecNorm(tao->stepdirection, NORM_2, &xdiff);
    218:         xdiff *= stepsize;

    220:         /* Adjust trust region size */
    221:         if (rhok < tron->eta2){
    222:           delta = PetscMin(xdiff,delta)*tron->sigma1;
    223:         } else if (rhok > tron->eta4){
    224:           delta= PetscMin(xdiff,delta)*tron->sigma3;
    225:         } else if (rhok > tron->eta3){
    226:           delta=PetscMin(xdiff,delta)*tron->sigma2;
    227:         }
    228:         VecBoundGradientProjection(tron->G_New,tron->X_New, tao->XL, tao->XU, tao->gradient);
    229:         ISDestroy(&tron->Free_Local);
    230:         VecWhichInactive(tao->XL,tron->X_New,tao->gradient,tao->XU,PETSC_TRUE,&tron->Free_Local);
    231:         f=f_new;
    232:         VecNorm(tao->gradient,NORM_2,&tron->gnorm);
    233:         VecCopy(tron->X_New, tao->solution);
    234:         VecCopy(tron->G_New, tao->gradient);
    235:         break;
    236:       }
    237:       else if (delta <= 1e-30) {
    238:         break;
    239:       }
    240:       else {
    241:         delta /= 4.0;
    242:       }
    243:     } /* end linear solve loop */

    245:     tron->f=f; tron->actred=actred; tao->trust=delta;
    246:     tao->niter++;
    247:     TaoLogConvergenceHistory(tao,tron->f,tron->gnorm,0.0,tao->ksp_its);
    248:     TaoMonitor(tao,tao->niter,tron->f,tron->gnorm,0.0,stepsize);
    249:     (*tao->ops->convergencetest)(tao,tao->cnvP);
    250:   }  /* END MAIN LOOP  */
    251:   return(0);
    252: }

    254: static PetscErrorCode TronGradientProjections(Tao tao,TAO_TRON *tron)
    255: {
    256:   PetscErrorCode               ierr;
    257:   PetscInt                     i;
    258:   TaoLineSearchConvergedReason ls_reason;
    259:   PetscReal                    actred=-1.0,actred_max=0.0;
    260:   PetscReal                    f_new;
    261:   /*
    262:      The gradient and function value passed into and out of this
    263:      routine should be current and correct.

    265:      The free, active, and binding variables should be already identified
    266:   */

    269:   for (i=0;i<tron->maxgpits;++i){

    271:     if (-actred <= (tron->pg_ftol)*actred_max) break;

    273:     ++tron->gp_iterates;
    274:     ++tron->total_gp_its;
    275:     f_new=tron->f;

    277:     VecCopy(tao->gradient,tao->stepdirection);
    278:     VecScale(tao->stepdirection,-1.0);
    279:     TaoLineSearchSetInitialStepLength(tao->linesearch,tron->pgstepsize);
    280:     TaoLineSearchApply(tao->linesearch, tao->solution, &f_new, tao->gradient, tao->stepdirection,
    281:                               &tron->pgstepsize, &ls_reason);
    282:     TaoAddLineSearchCounts(tao);

    284:     VecBoundGradientProjection(tao->gradient,tao->solution,tao->XL,tao->XU,tao->gradient);
    285:     VecNorm(tao->gradient,NORM_2,&tron->gnorm);

    287:     /* Update the iterate */
    288:     actred = f_new - tron->f;
    289:     actred_max = PetscMax(actred_max,-(f_new - tron->f));
    290:     tron->f = f_new;
    291:   }
    292:   return(0);
    293: }

    295: static PetscErrorCode TaoComputeDual_TRON(Tao tao, Vec DXL, Vec DXU)
    296: {

    298:   TAO_TRON       *tron = (TAO_TRON *)tao->data;

    305:   if (!tron->Work || !tao->gradient) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Dual variables don't exist yet or no longer exist.\n");

    307:   VecBoundGradientProjection(tao->gradient,tao->solution,tao->XL,tao->XU,tron->Work);
    308:   VecCopy(tron->Work,DXL);
    309:   VecAXPY(DXL,-1.0,tao->gradient);
    310:   VecSet(DXU,0.0);
    311:   VecPointwiseMax(DXL,DXL,DXU);

    313:   VecCopy(tao->gradient,DXU);
    314:   VecAXPY(DXU,-1.0,tron->Work);
    315:   VecSet(tron->Work,0.0);
    316:   VecPointwiseMin(DXU,tron->Work,DXU);
    317:   return(0);
    318: }

    320: /*------------------------------------------------------------*/
    321: /*MC
    322:   TAOTRON - The TRON algorithm is an active-set Newton trust region method
    323:   for bound-constrained minimization.

    325:   Options Database Keys:
    326: + -tao_tron_maxgpits - maximum number of gradient projections per TRON iterate
    327: - -tao_subset_type - "subvec","mask","matrix-free", strategies for handling active-sets

    329:   Level: beginner
    330: M*/
    331: PETSC_EXTERN PetscErrorCode TaoCreate_TRON(Tao tao)
    332: {
    333:   TAO_TRON       *tron;
    335:   const char     *morethuente_type = TAOLINESEARCHMT;

    338:   tao->ops->setup          = TaoSetup_TRON;
    339:   tao->ops->solve          = TaoSolve_TRON;
    340:   tao->ops->view           = TaoView_TRON;
    341:   tao->ops->setfromoptions = TaoSetFromOptions_TRON;
    342:   tao->ops->destroy        = TaoDestroy_TRON;
    343:   tao->ops->computedual    = TaoComputeDual_TRON;

    345:   PetscNewLog(tao,&tron);
    346:   tao->data = (void*)tron;

    348:   /* Override default settings (unless already changed) */
    349:   if (!tao->max_it_changed) tao->max_it = 50;
    350:   if (!tao->trust0_changed) tao->trust0 = 1.0;
    351:   if (!tao->steptol_changed) tao->steptol = 0.0;

    353:   /* Initialize pointers and variables */
    354:   tron->n            = 0;
    355:   tron->maxgpits     = 3;
    356:   tron->pg_ftol      = 0.001;

    358:   tron->eta1         = 1.0e-4;
    359:   tron->eta2         = 0.25;
    360:   tron->eta3         = 0.50;
    361:   tron->eta4         = 0.90;

    363:   tron->sigma1       = 0.5;
    364:   tron->sigma2       = 2.0;
    365:   tron->sigma3       = 4.0;

    367:   tron->gp_iterates  = 0; /* Cumulative number */
    368:   tron->total_gp_its = 0;
    369:   tron->n_free       = 0;

    371:   tron->DXFree=NULL;
    372:   tron->R=NULL;
    373:   tron->X_New=NULL;
    374:   tron->G_New=NULL;
    375:   tron->Work=NULL;
    376:   tron->Free_Local=NULL;
    377:   tron->H_sub=NULL;
    378:   tron->Hpre_sub=NULL;
    379:   tao->subset_type = TAO_SUBSET_SUBVEC;

    381:   TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch);
    382:   PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);
    383:   TaoLineSearchSetType(tao->linesearch,morethuente_type);
    384:   TaoLineSearchUseTaoRoutines(tao->linesearch,tao);
    385:   TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);

    387:   KSPCreate(((PetscObject)tao)->comm, &tao->ksp);
    388:   PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1);
    389:   KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix);
    390:   KSPSetType(tao->ksp,KSPSTCG);
    391:   return(0);
    392: }