Actual source code: tron.c

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

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

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

     25: /*------------------------------------------------------------*/
     26: static PetscErrorCode TaoSetFromOptions_TRON(PetscOptionItems *PetscOptionsObject,Tao tao)
     27: {
     28:   TAO_TRON       *tron = (TAO_TRON *)tao->data;
     29:   PetscBool      flg;

     31:   PetscOptionsHead(PetscOptionsObject,"Newton Trust Region Method for bound constrained optimization");
     32:   PetscOptionsInt("-tao_tron_maxgpits","maximum number of gradient projections per TRON iterate","TaoSetMaxGPIts",tron->maxgpits,&tron->maxgpits,&flg);
     33:   PetscOptionsTail();
     34:   KSPSetFromOptions(tao->ksp);
     35:   return 0;
     36: }

     38: /*------------------------------------------------------------*/
     39: static PetscErrorCode TaoView_TRON(Tao tao, PetscViewer viewer)
     40: {
     41:   TAO_TRON         *tron = (TAO_TRON *)tao->data;
     42:   PetscBool        isascii;

     44:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
     45:   if (isascii) {
     46:     PetscViewerASCIIPrintf(viewer,"Total PG its: %D,",tron->total_gp_its);
     47:     PetscViewerASCIIPrintf(viewer,"PG tolerance: %g \n",(double)tron->pg_ftol);
     48:   }
     49:   return 0;
     50: }

     52: /* ---------------------------------------------------------- */
     53: static PetscErrorCode TaoSetup_TRON(Tao tao)
     54: {
     55:   TAO_TRON       *tron = (TAO_TRON *)tao->data;

     58:   /* Allocate some arrays */
     59:   VecDuplicate(tao->solution, &tron->diag);
     60:   VecDuplicate(tao->solution, &tron->X_New);
     61:   VecDuplicate(tao->solution, &tron->G_New);
     62:   VecDuplicate(tao->solution, &tron->Work);
     63:   VecDuplicate(tao->solution, &tao->gradient);
     64:   VecDuplicate(tao->solution, &tao->stepdirection);
     65:   if (!tao->XL) {
     66:     VecDuplicate(tao->solution, &tao->XL);
     67:     VecSet(tao->XL, PETSC_NINFINITY);
     68:   }
     69:   if (!tao->XU) {
     70:     VecDuplicate(tao->solution, &tao->XU);
     71:     VecSet(tao->XU, PETSC_INFINITY);
     72:   }
     73:   return 0;
     74: }

     76: static PetscErrorCode TaoSolve_TRON(Tao tao)
     77: {
     78:   TAO_TRON                     *tron = (TAO_TRON *)tao->data;
     79:   PetscInt                     its;
     80:   TaoLineSearchConvergedReason ls_reason = TAOLINESEARCH_CONTINUE_ITERATING;
     81:   PetscReal                    prered,actred,delta,f,f_new,rhok,gdx,xdiff,stepsize;

     83:   tron->pgstepsize = 1.0;
     84:   tao->trust = tao->trust0;
     85:   /*   Project the current point onto the feasible set */
     86:   TaoComputeVariableBounds(tao);
     87:   TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);

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

     92:   /* Compute the objective function and gradient */
     93:   TaoComputeObjectiveAndGradient(tao,tao->solution,&tron->f,tao->gradient);
     94:   VecNorm(tao->gradient,NORM_2,&tron->gnorm);

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

    101:   /* Initialize trust region radius */
    102:   tao->trust=tao->trust0;
    103:   if (tao->trust <= 0) {
    104:     tao->trust=PetscMax(tron->gnorm*tron->gnorm,1.0);
    105:   }

    107:   /* Initialize step sizes for the line searches */
    108:   tron->pgstepsize=1.0;
    109:   tron->stepsize=tao->trust;

    111:   tao->reason = TAO_CONTINUE_ITERATING;
    112:   TaoLogConvergenceHistory(tao,tron->f,tron->gnorm,0.0,tao->ksp_its);
    113:   TaoMonitor(tao,tao->niter,tron->f,tron->gnorm,0.0,tron->stepsize);
    114:   (*tao->ops->convergencetest)(tao,tao->cnvP);
    115:   while (tao->reason==TAO_CONTINUE_ITERATING) {
    116:     /* Call general purpose update function */
    117:     if (tao->ops->update) {
    118:       (*tao->ops->update)(tao, tao->niter, tao->user_update);
    119:     }

    121:     /* Perform projected gradient iterations */
    122:     TronGradientProjections(tao,tron);

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

    127:     tao->ksp_its=0;
    128:     f=tron->f; delta=tao->trust;
    129:     tron->n_free_last = tron->n_free;
    130:     TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);

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

    137:     /* If no free variables */
    138:     if (tron->n_free == 0) {
    139:       VecNorm(tao->gradient,NORM_2,&tron->gnorm);
    140:       TaoLogConvergenceHistory(tao,tron->f,tron->gnorm,0.0,tao->ksp_its);
    141:       TaoMonitor(tao,tao->niter,tron->f,tron->gnorm,0.0,delta);
    142:       (*tao->ops->convergencetest)(tao,tao->cnvP);
    143:       if (!tao->reason) {
    144:         tao->reason = TAO_CONVERGED_STEPTOL;
    145:       }
    146:       break;
    147:     }
    148:     /* use free_local to mask/submat gradient, hessian, stepdirection */
    149:     TaoVecGetSubVec(tao->gradient,tron->Free_Local,tao->subset_type,0.0,&tron->R);
    150:     TaoVecGetSubVec(tao->gradient,tron->Free_Local,tao->subset_type,0.0,&tron->DXFree);
    151:     VecSet(tron->DXFree,0.0);
    152:     VecScale(tron->R, -1.0);
    153:     TaoMatGetSubMat(tao->hessian, tron->Free_Local, tron->diag, tao->subset_type, &tron->H_sub);
    154:     if (tao->hessian == tao->hessian_pre) {
    155:       MatDestroy(&tron->Hpre_sub);
    156:       PetscObjectReference((PetscObject)(tron->H_sub));
    157:       tron->Hpre_sub = tron->H_sub;
    158:     } else {
    159:       TaoMatGetSubMat(tao->hessian_pre, tron->Free_Local, tron->diag, tao->subset_type,&tron->Hpre_sub);
    160:     }
    161:     KSPReset(tao->ksp);
    162:     KSPSetOperators(tao->ksp, tron->H_sub, tron->Hpre_sub);
    163:     while (1) {

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

    168:       KSPSolve(tao->ksp, tron->R, tron->DXFree);
    169:       KSPGetIterationNumber(tao->ksp,&its);
    170:       tao->ksp_its+=its;
    171:       tao->ksp_tot_its+=its;
    172:       VecSet(tao->stepdirection,0.0);

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

    177:       VecDot(tao->gradient, tao->stepdirection, &gdx);
    178:       VecCopy(tao->solution, tron->X_New);
    179:       VecCopy(tao->gradient, tron->G_New);

    181:       stepsize=1.0;f_new=f;

    183:       TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);
    184:       TaoLineSearchApply(tao->linesearch, tron->X_New, &f_new, tron->G_New, tao->stepdirection,&stepsize,&ls_reason);
    185:       TaoAddLineSearchCounts(tao);

    187:       MatMult(tao->hessian, tao->stepdirection, tron->Work);
    188:       VecAYPX(tron->Work, 0.5, tao->gradient);
    189:       VecDot(tao->stepdirection, tron->Work, &prered);
    190:       actred = f_new - f;
    191:       if ((PetscAbsScalar(actred) <= 1e-6) && (PetscAbsScalar(prered) <= 1e-6)) {
    192:         rhok = 1.0;
    193:       } else if (actred<0) {
    194:         rhok=PetscAbs(-actred/prered);
    195:       } else {
    196:         rhok=0.0;
    197:       }

    199:       /* Compare actual improvement to the quadratic model */
    200:       if (rhok > tron->eta1) { /* Accept the point */
    201:         /* d = x_new - x */
    202:         VecCopy(tron->X_New, tao->stepdirection);
    203:         VecAXPY(tao->stepdirection, -1.0, tao->solution);

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

    208:         /* Adjust trust region size */
    209:         if (rhok < tron->eta2) {
    210:           delta = PetscMin(xdiff,delta)*tron->sigma1;
    211:         } else if (rhok > tron->eta4) {
    212:           delta= PetscMin(xdiff,delta)*tron->sigma3;
    213:         } else if (rhok > tron->eta3) {
    214:           delta=PetscMin(xdiff,delta)*tron->sigma2;
    215:         }
    216:         VecBoundGradientProjection(tron->G_New,tron->X_New, tao->XL, tao->XU, tao->gradient);
    217:         ISDestroy(&tron->Free_Local);
    218:         VecWhichInactive(tao->XL,tron->X_New,tao->gradient,tao->XU,PETSC_TRUE,&tron->Free_Local);
    219:         f=f_new;
    220:         VecNorm(tao->gradient,NORM_2,&tron->gnorm);
    221:         VecCopy(tron->X_New, tao->solution);
    222:         VecCopy(tron->G_New, tao->gradient);
    223:         break;
    224:       }
    225:       else if (delta <= 1e-30) {
    226:         break;
    227:       }
    228:       else {
    229:         delta /= 4.0;
    230:       }
    231:     } /* end linear solve loop */

    233:     tron->f=f; tron->actred=actred; tao->trust=delta;
    234:     tao->niter++;
    235:     TaoLogConvergenceHistory(tao,tron->f,tron->gnorm,0.0,tao->ksp_its);
    236:     TaoMonitor(tao,tao->niter,tron->f,tron->gnorm,0.0,stepsize);
    237:     (*tao->ops->convergencetest)(tao,tao->cnvP);
    238:   }  /* END MAIN LOOP  */
    239:   return 0;
    240: }

    242: static PetscErrorCode TronGradientProjections(Tao tao,TAO_TRON *tron)
    243: {
    244:   PetscErrorCode               ierr;
    245:   PetscInt                     i;
    246:   TaoLineSearchConvergedReason ls_reason;
    247:   PetscReal                    actred=-1.0,actred_max=0.0;
    248:   PetscReal                    f_new;
    249:   /*
    250:      The gradient and function value passed into and out of this
    251:      routine should be current and correct.

    253:      The free, active, and binding variables should be already identified
    254:   */

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

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

    260:     ++tron->gp_iterates;
    261:     ++tron->total_gp_its;
    262:     f_new=tron->f;

    264:     VecCopy(tao->gradient,tao->stepdirection);
    265:     VecScale(tao->stepdirection,-1.0);
    266:     TaoLineSearchSetInitialStepLength(tao->linesearch,tron->pgstepsize);
    267:     TaoLineSearchApply(tao->linesearch, tao->solution, &f_new, tao->gradient, tao->stepdirection,
    268:                               &tron->pgstepsize, &ls_reason);
    269:     TaoAddLineSearchCounts(tao);

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

    274:     /* Update the iterate */
    275:     actred = f_new - tron->f;
    276:     actred_max = PetscMax(actred_max,-(f_new - tron->f));
    277:     tron->f = f_new;
    278:   }
    279:   return 0;
    280: }

    282: static PetscErrorCode TaoComputeDual_TRON(Tao tao, Vec DXL, Vec DXU)
    283: {

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

    292:   VecBoundGradientProjection(tao->gradient,tao->solution,tao->XL,tao->XU,tron->Work);
    293:   VecCopy(tron->Work,DXL);
    294:   VecAXPY(DXL,-1.0,tao->gradient);
    295:   VecSet(DXU,0.0);
    296:   VecPointwiseMax(DXL,DXL,DXU);

    298:   VecCopy(tao->gradient,DXU);
    299:   VecAXPY(DXU,-1.0,tron->Work);
    300:   VecSet(tron->Work,0.0);
    301:   VecPointwiseMin(DXU,tron->Work,DXU);
    302:   return 0;
    303: }

    305: /*------------------------------------------------------------*/
    306: /*MC
    307:   TAOTRON - The TRON algorithm is an active-set Newton trust region method
    308:   for bound-constrained minimization.

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

    314:   Level: beginner
    315: M*/
    316: PETSC_EXTERN PetscErrorCode TaoCreate_TRON(Tao tao)
    317: {
    318:   TAO_TRON       *tron;
    319:   const char     *morethuente_type = TAOLINESEARCHMT;

    321:   tao->ops->setup          = TaoSetup_TRON;
    322:   tao->ops->solve          = TaoSolve_TRON;
    323:   tao->ops->view           = TaoView_TRON;
    324:   tao->ops->setfromoptions = TaoSetFromOptions_TRON;
    325:   tao->ops->destroy        = TaoDestroy_TRON;
    326:   tao->ops->computedual    = TaoComputeDual_TRON;

    328:   PetscNewLog(tao,&tron);
    329:   tao->data = (void*)tron;

    331:   /* Override default settings (unless already changed) */
    332:   if (!tao->max_it_changed) tao->max_it = 50;
    333:   if (!tao->trust0_changed) tao->trust0 = 1.0;
    334:   if (!tao->steptol_changed) tao->steptol = 0.0;

    336:   /* Initialize pointers and variables */
    337:   tron->n            = 0;
    338:   tron->maxgpits     = 3;
    339:   tron->pg_ftol      = 0.001;

    341:   tron->eta1         = 1.0e-4;
    342:   tron->eta2         = 0.25;
    343:   tron->eta3         = 0.50;
    344:   tron->eta4         = 0.90;

    346:   tron->sigma1       = 0.5;
    347:   tron->sigma2       = 2.0;
    348:   tron->sigma3       = 4.0;

    350:   tron->gp_iterates  = 0; /* Cumulative number */
    351:   tron->total_gp_its = 0;
    352:   tron->n_free       = 0;

    354:   tron->DXFree=NULL;
    355:   tron->R=NULL;
    356:   tron->X_New=NULL;
    357:   tron->G_New=NULL;
    358:   tron->Work=NULL;
    359:   tron->Free_Local=NULL;
    360:   tron->H_sub=NULL;
    361:   tron->Hpre_sub=NULL;
    362:   tao->subset_type = TAO_SUBSET_SUBVEC;

    364:   TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch);
    365:   PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);
    366:   TaoLineSearchSetType(tao->linesearch,morethuente_type);
    367:   TaoLineSearchUseTaoRoutines(tao->linesearch,tao);
    368:   TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);

    370:   KSPCreate(((PetscObject)tao)->comm, &tao->ksp);
    371:   PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1);
    372:   KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix);
    373:   KSPSetType(tao->ksp,KSPSTCG);
    374:   return 0;
    375: }