Actual source code: lcl.c
petsc-3.7.1 2016-05-15
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      1: #include <../src/tao/pde_constrained/impls/lcl/lcl.h>
      2: #include <../src/tao/matrix/lmvmmat.h>
      3: static PetscErrorCode LCLComputeLagrangianAndGradient(TaoLineSearch,Vec,PetscReal*,Vec,void*);
      4: static PetscErrorCode LCLComputeAugmentedLagrangianAndGradient(TaoLineSearch,Vec,PetscReal*,Vec,void*);
      5: static PetscErrorCode LCLScatter(TAO_LCL*,Vec,Vec,Vec);
      6: static PetscErrorCode LCLGather(TAO_LCL*,Vec,Vec,Vec);

     10: static PetscErrorCode TaoDestroy_LCL(Tao tao)
     11: {
     12:   TAO_LCL        *lclP = (TAO_LCL*)tao->data;

     16:   if (tao->setupcalled) {
     17:     MatDestroy(&lclP->R);
     18:     VecDestroy(&lclP->lamda);
     19:     VecDestroy(&lclP->lamda0);
     20:     VecDestroy(&lclP->WL);
     21:     VecDestroy(&lclP->W);
     22:     VecDestroy(&lclP->X0);
     23:     VecDestroy(&lclP->G0);
     24:     VecDestroy(&lclP->GL);
     25:     VecDestroy(&lclP->GAugL);
     26:     VecDestroy(&lclP->dbar);
     27:     VecDestroy(&lclP->U);
     28:     VecDestroy(&lclP->U0);
     29:     VecDestroy(&lclP->V);
     30:     VecDestroy(&lclP->V0);
     31:     VecDestroy(&lclP->V1);
     32:     VecDestroy(&lclP->GU);
     33:     VecDestroy(&lclP->GV);
     34:     VecDestroy(&lclP->GU0);
     35:     VecDestroy(&lclP->GV0);
     36:     VecDestroy(&lclP->GL_U);
     37:     VecDestroy(&lclP->GL_V);
     38:     VecDestroy(&lclP->GAugL_U);
     39:     VecDestroy(&lclP->GAugL_V);
     40:     VecDestroy(&lclP->GL_U0);
     41:     VecDestroy(&lclP->GL_V0);
     42:     VecDestroy(&lclP->GAugL_U0);
     43:     VecDestroy(&lclP->GAugL_V0);
     44:     VecDestroy(&lclP->DU);
     45:     VecDestroy(&lclP->DV);
     46:     VecDestroy(&lclP->WU);
     47:     VecDestroy(&lclP->WV);
     48:     VecDestroy(&lclP->g1);
     49:     VecDestroy(&lclP->g2);
     50:     VecDestroy(&lclP->con1);

     52:     VecDestroy(&lclP->r);
     53:     VecDestroy(&lclP->s);

     55:     ISDestroy(&tao->state_is);
     56:     ISDestroy(&tao->design_is);

     58:     VecScatterDestroy(&lclP->state_scatter);
     59:     VecScatterDestroy(&lclP->design_scatter);
     60:   }
     61:   PetscFree(tao->data);
     62:   return(0);
     63: }

     67: static PetscErrorCode TaoSetFromOptions_LCL(PetscOptionItems *PetscOptionsObject,Tao tao)
     68: {
     69:   TAO_LCL        *lclP = (TAO_LCL*)tao->data;

     73:   PetscOptionsHead(PetscOptionsObject,"Linearly-Constrained Augmented Lagrangian Method for PDE-constrained optimization");
     74:   PetscOptionsReal("-tao_lcl_eps1","epsilon 1 tolerance","",lclP->eps1,&lclP->eps1,NULL);
     75:   PetscOptionsReal("-tao_lcl_eps2","epsilon 2 tolerance","",lclP->eps2,&lclP->eps2,NULL);
     76:   PetscOptionsReal("-tao_lcl_rho0","init value for rho","",lclP->rho0,&lclP->rho0,NULL);
     77:   PetscOptionsReal("-tao_lcl_rhomax","max value for rho","",lclP->rhomax,&lclP->rhomax,NULL);
     78:   lclP->phase2_niter = 1;
     79:   PetscOptionsInt("-tao_lcl_phase2_niter","Number of phase 2 iterations in LCL algorithm","",lclP->phase2_niter,&lclP->phase2_niter,NULL);
     80:   lclP->verbose = PETSC_FALSE;
     81:   PetscOptionsBool("-tao_lcl_verbose","Print verbose output","",lclP->verbose,&lclP->verbose,NULL);
     82:   lclP->tau[0] = lclP->tau[1] = lclP->tau[2] = lclP->tau[3] = 1.0e-4;
     83:   PetscOptionsReal("-tao_lcl_tola","Tolerance for first forward solve","",lclP->tau[0],&lclP->tau[0],NULL);
     84:   PetscOptionsReal("-tao_lcl_tolb","Tolerance for first adjoint solve","",lclP->tau[1],&lclP->tau[1],NULL);
     85:   PetscOptionsReal("-tao_lcl_tolc","Tolerance for second forward solve","",lclP->tau[2],&lclP->tau[2],NULL);
     86:   PetscOptionsReal("-tao_lcl_told","Tolerance for second adjoint solve","",lclP->tau[3],&lclP->tau[3],NULL);
     87:   PetscOptionsTail();
     88:   TaoLineSearchSetFromOptions(tao->linesearch);
     89:   return(0);
     90: }

     94: static PetscErrorCode TaoView_LCL(Tao tao, PetscViewer viewer)
     95: {
     96:   return 0;
     97: }

    101: static PetscErrorCode TaoSetup_LCL(Tao tao)
    102: {
    103:   TAO_LCL        *lclP = (TAO_LCL*)tao->data;
    104:   PetscInt       lo, hi, nlocalstate, nlocaldesign;
    106:   IS             is_state, is_design;

    109:   if (!tao->state_is) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONGSTATE,"LCL Solver requires an initial state index set -- use TaoSetStateIS()");
    110:   VecDuplicate(tao->solution, &tao->gradient);
    111:   VecDuplicate(tao->solution, &tao->stepdirection);
    112:   VecDuplicate(tao->solution, &lclP->W);
    113:   VecDuplicate(tao->solution, &lclP->X0);
    114:   VecDuplicate(tao->solution, &lclP->G0);
    115:   VecDuplicate(tao->solution, &lclP->GL);
    116:   VecDuplicate(tao->solution, &lclP->GAugL);

    118:   VecDuplicate(tao->constraints, &lclP->lamda);
    119:   VecDuplicate(tao->constraints, &lclP->WL);
    120:   VecDuplicate(tao->constraints, &lclP->lamda0);
    121:   VecDuplicate(tao->constraints, &lclP->con1);

    123:   VecSet(lclP->lamda,0.0);

    125:   VecGetSize(tao->solution, &lclP->n);
    126:   VecGetSize(tao->constraints, &lclP->m);

    128:   VecCreate(((PetscObject)tao)->comm,&lclP->U);
    129:   VecCreate(((PetscObject)tao)->comm,&lclP->V);
    130:   ISGetLocalSize(tao->state_is,&nlocalstate);
    131:   ISGetLocalSize(tao->design_is,&nlocaldesign);
    132:   VecSetSizes(lclP->U,nlocalstate,lclP->m);
    133:   VecSetSizes(lclP->V,nlocaldesign,lclP->n-lclP->m);
    134:   VecSetType(lclP->U,((PetscObject)(tao->solution))->type_name);
    135:   VecSetType(lclP->V,((PetscObject)(tao->solution))->type_name);
    136:   VecSetFromOptions(lclP->U);
    137:   VecSetFromOptions(lclP->V);
    138:   VecDuplicate(lclP->U,&lclP->DU);
    139:   VecDuplicate(lclP->U,&lclP->U0);
    140:   VecDuplicate(lclP->U,&lclP->GU);
    141:   VecDuplicate(lclP->U,&lclP->GU0);
    142:   VecDuplicate(lclP->U,&lclP->GAugL_U);
    143:   VecDuplicate(lclP->U,&lclP->GL_U);
    144:   VecDuplicate(lclP->U,&lclP->GAugL_U0);
    145:   VecDuplicate(lclP->U,&lclP->GL_U0);
    146:   VecDuplicate(lclP->U,&lclP->WU);
    147:   VecDuplicate(lclP->U,&lclP->r);
    148:   VecDuplicate(lclP->V,&lclP->V0);
    149:   VecDuplicate(lclP->V,&lclP->V1);
    150:   VecDuplicate(lclP->V,&lclP->DV);
    151:   VecDuplicate(lclP->V,&lclP->s);
    152:   VecDuplicate(lclP->V,&lclP->GV);
    153:   VecDuplicate(lclP->V,&lclP->GV0);
    154:   VecDuplicate(lclP->V,&lclP->dbar);
    155:   VecDuplicate(lclP->V,&lclP->GAugL_V);
    156:   VecDuplicate(lclP->V,&lclP->GL_V);
    157:   VecDuplicate(lclP->V,&lclP->GAugL_V0);
    158:   VecDuplicate(lclP->V,&lclP->GL_V0);
    159:   VecDuplicate(lclP->V,&lclP->WV);
    160:   VecDuplicate(lclP->V,&lclP->g1);
    161:   VecDuplicate(lclP->V,&lclP->g2);

    163:   /* create scatters for state, design subvecs */
    164:   VecGetOwnershipRange(lclP->U,&lo,&hi);
    165:   ISCreateStride(((PetscObject)lclP->U)->comm,hi-lo,lo,1,&is_state);
    166:   VecGetOwnershipRange(lclP->V,&lo,&hi);
    167:   if (0) {
    168:     PetscInt sizeU,sizeV;
    169:     VecGetSize(lclP->U,&sizeU);
    170:     VecGetSize(lclP->V,&sizeV);
    171:     PetscPrintf(PETSC_COMM_WORLD,"size(U)=%D, size(V)=%D\n",sizeU,sizeV);
    172:   }
    173:   ISCreateStride(((PetscObject)lclP->V)->comm,hi-lo,lo,1,&is_design);
    174:   VecScatterCreate(tao->solution,tao->state_is,lclP->U,is_state,&lclP->state_scatter);
    175:   VecScatterCreate(tao->solution,tao->design_is,lclP->V,is_design,&lclP->design_scatter);
    176:   ISDestroy(&is_state);
    177:   ISDestroy(&is_design);
    178:   return(0);
    179: }

    183: static PetscErrorCode TaoSolve_LCL(Tao tao)
    184: {
    185:   TAO_LCL                      *lclP = (TAO_LCL*)tao->data;
    186:   PetscInt                     phase2_iter,nlocal,its;
    187:   TaoConvergedReason           reason = TAO_CONTINUE_ITERATING;
    188:   TaoLineSearchConvergedReason ls_reason = TAOLINESEARCH_CONTINUE_ITERATING;
    189:   PetscReal                    step=1.0,f, descent, aldescent;
    190:   PetscReal                    cnorm, mnorm;
    191:   PetscReal                    adec,r2,rGL_U,rWU;
    192:   PetscBool                    set,pset,flag,pflag,symmetric;
    193:   PetscErrorCode               ierr;

    196:   lclP->rho = lclP->rho0;
    197:   VecGetLocalSize(lclP->U,&nlocal);
    198:   VecGetLocalSize(lclP->V,&nlocal);
    199:   MatCreateLMVM(((PetscObject)tao)->comm,nlocal,lclP->n-lclP->m,&lclP->R);
    200:   MatLMVMAllocateVectors(lclP->R,lclP->V);
    201:   lclP->recompute_jacobian_flag = PETSC_TRUE;

    203:   /* Scatter to U,V */
    204:   LCLScatter(lclP,tao->solution,lclP->U,lclP->V);

    206:   /* Evaluate Function, Gradient, Constraints, and Jacobian */
    207:   TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);
    208:   TaoComputeJacobianState(tao,tao->solution,tao->jacobian_state,tao->jacobian_state_pre,tao->jacobian_state_inv);
    209:   TaoComputeJacobianDesign(tao,tao->solution,tao->jacobian_design);
    210:   TaoComputeConstraints(tao,tao->solution, tao->constraints);

    212:   /* Scatter gradient to GU,GV */
    213:   LCLScatter(lclP,tao->gradient,lclP->GU,lclP->GV);

    215:   /* Evaluate Lagrangian function and gradient */
    216:   /* p0 */
    217:   VecSet(lclP->lamda,0.0); /*  Initial guess in CG */
    218:   MatIsSymmetricKnown(tao->jacobian_state,&set,&flag);
    219:   if (tao->jacobian_state_pre) {
    220:     MatIsSymmetricKnown(tao->jacobian_state_pre,&pset,&pflag);
    221:   } else {
    222:     pset = pflag = PETSC_TRUE;
    223:   }
    224:   if (set && pset && flag && pflag) symmetric = PETSC_TRUE;
    225:   else symmetric = PETSC_FALSE;

    227:   lclP->solve_type = LCL_ADJOINT2;
    228:   if (tao->jacobian_state_inv) {
    229:     if (symmetric) {
    230:       MatMult(tao->jacobian_state_inv, lclP->GU, lclP->lamda); } else {
    231:       MatMultTranspose(tao->jacobian_state_inv, lclP->GU, lclP->lamda);
    232:     }
    233:   } else {
    234:     KSPSetOperators(tao->ksp, tao->jacobian_state, tao->jacobian_state_pre);
    235:     if (symmetric) {
    236:       KSPSolve(tao->ksp, lclP->GU,  lclP->lamda);
    237:     } else {
    238:       KSPSolveTranspose(tao->ksp, lclP->GU,  lclP->lamda);
    239:     }
    240:     KSPGetIterationNumber(tao->ksp,&its);
    241:     tao->ksp_its+=its;
    242:     tao->ksp_tot_its+=its;
    243:   }
    244:   VecCopy(lclP->lamda,lclP->lamda0);
    245:   LCLComputeAugmentedLagrangianAndGradient(tao->linesearch,tao->solution,&lclP->aug,lclP->GAugL,tao);

    247:   LCLScatter(lclP,lclP->GL,lclP->GL_U,lclP->GL_V);
    248:   LCLScatter(lclP,lclP->GAugL,lclP->GAugL_U,lclP->GAugL_V);

    250:   /* Evaluate constraint norm */
    251:   VecNorm(tao->constraints, NORM_2, &cnorm);
    252:   VecNorm(lclP->GAugL, NORM_2, &mnorm);

    254:   /* Monitor convergence */
    255:   TaoMonitor(tao, tao->niter,f,mnorm,cnorm,step,&reason);

    257:   while (reason == TAO_CONTINUE_ITERATING) {
    258:     tao->ksp_its=0;
    259:     /* Compute a descent direction for the linearly constrained subproblem
    260:        minimize f(u+du, v+dv)
    261:        s.t. A(u0,v0)du + B(u0,v0)dv = -g(u0,v0) */

    263:     /* Store the points around the linearization */
    264:     VecCopy(lclP->U, lclP->U0);
    265:     VecCopy(lclP->V, lclP->V0);
    266:     VecCopy(lclP->GU,lclP->GU0);
    267:     VecCopy(lclP->GV,lclP->GV0);
    268:     VecCopy(lclP->GAugL_U,lclP->GAugL_U0);
    269:     VecCopy(lclP->GAugL_V,lclP->GAugL_V0);
    270:     VecCopy(lclP->GL_U,lclP->GL_U0);
    271:     VecCopy(lclP->GL_V,lclP->GL_V0);

    273:     lclP->aug0 = lclP->aug;
    274:     lclP->lgn0 = lclP->lgn;

    276:     /* Given the design variables, we need to project the current iterate
    277:        onto the linearized constraint.  We choose to fix the design variables
    278:        and solve the linear system for the state variables.  The resulting
    279:        point is the Newton direction */

    281:     /* Solve r = A\con */
    282:     lclP->solve_type = LCL_FORWARD1;
    283:     VecSet(lclP->r,0.0); /*  Initial guess in CG */

    285:     if (tao->jacobian_state_inv) {
    286:       MatMult(tao->jacobian_state_inv, tao->constraints, lclP->r);
    287:     } else {
    288:       KSPSetOperators(tao->ksp, tao->jacobian_state, tao->jacobian_state_pre);
    289:       KSPSolve(tao->ksp, tao->constraints,  lclP->r);
    290:       KSPGetIterationNumber(tao->ksp,&its);
    291:       tao->ksp_its+=its;
    292:       tao->ksp_tot_its+=tao->ksp_its;
    293:     }

    295:     /* Set design step direction dv to zero */
    296:     VecSet(lclP->s, 0.0);

    298:     /*
    299:        Check sufficient descent for constraint merit function .5*||con||^2
    300:        con' Ak r >= eps1 ||r||^(2+eps2)
    301:     */

    303:     /* Compute WU= Ak' * con */
    304:     if (symmetric)  {
    305:       MatMult(tao->jacobian_state,tao->constraints,lclP->WU);
    306:     } else {
    307:       MatMultTranspose(tao->jacobian_state,tao->constraints,lclP->WU);
    308:     }
    309:     /* Compute r * Ak' * con */
    310:     VecDot(lclP->r,lclP->WU,&rWU);

    312:     /* compute ||r||^(2+eps2) */
    313:     VecNorm(lclP->r,NORM_2,&r2);
    314:     r2 = PetscPowScalar(r2,2.0+lclP->eps2);
    315:     adec = lclP->eps1 * r2;

    317:     if (rWU < adec) {
    318:       PetscInfo(tao,"Newton direction not descent for constraint, feasibility phase required\n");
    319:       if (lclP->verbose) {
    320:         PetscPrintf(PETSC_COMM_WORLD,"Newton direction not descent for constraint: %g -- using steepest descent\n",(double)descent);
    321:       }

    323:       PetscInfo(tao,"Using steepest descent direction instead.\n");
    324:       VecSet(lclP->r,0.0);
    325:       VecAXPY(lclP->r,-1.0,lclP->WU);
    326:       VecDot(lclP->r,lclP->r,&rWU);
    327:       VecNorm(lclP->r,NORM_2,&r2);
    328:       r2 = PetscPowScalar(r2,2.0+lclP->eps2);
    329:       VecDot(lclP->r,lclP->GAugL_U,&descent);
    330:       adec = lclP->eps1 * r2;
    331:     }

    334:     /*
    335:        Check descent for aug. lagrangian
    336:        r' (GUk - Ak'*yk - rho*Ak'*con) <= -eps1 ||r||^(2+eps2)
    337:           GL_U = GUk - Ak'*yk
    338:           WU   = Ak'*con
    339:                                          adec=eps1||r||^(2+eps2)

    341:        ==>
    342:        Check r'GL_U - rho*r'WU <= adec
    343:     */

    345:     VecDot(lclP->r,lclP->GL_U,&rGL_U);
    346:     aldescent =  rGL_U - lclP->rho*rWU;
    347:     if (aldescent > -adec) {
    348:       if (lclP->verbose) {
    349:         PetscPrintf(PETSC_COMM_WORLD," Newton direction not descent for augmented Lagrangian: %g",(double)aldescent);
    350:       }
    351:       PetscInfo1(tao,"Newton direction not descent for augmented Lagrangian: %g\n",(double)aldescent);
    352:       lclP->rho =  (rGL_U - adec)/rWU;
    353:       if (lclP->rho > lclP->rhomax) {
    354:         lclP->rho = lclP->rhomax;
    355:         SETERRQ1(PETSC_COMM_WORLD,0,"rho=%g > rhomax, case not implemented.  Increase rhomax (-tao_lcl_rhomax)",(double)lclP->rho);
    356:       }
    357:       if (lclP->verbose) {
    358:         PetscPrintf(PETSC_COMM_WORLD,"  Increasing penalty parameter to %g\n",(double)lclP->rho);
    359:       }
    360:       PetscInfo1(tao,"  Increasing penalty parameter to %g\n",(double)lclP->rho);
    361:     }

    363:     LCLComputeAugmentedLagrangianAndGradient(tao->linesearch,tao->solution,&lclP->aug,lclP->GAugL,tao);
    364:     LCLScatter(lclP,lclP->GL,lclP->GL_U,lclP->GL_V);
    365:     LCLScatter(lclP,lclP->GAugL,lclP->GAugL_U,lclP->GAugL_V);

    367:     /* We now minimize the augmented Lagrangian along the Newton direction */
    368:     VecScale(lclP->r,-1.0);
    369:     LCLGather(lclP, lclP->r,lclP->s,tao->stepdirection);
    370:     VecScale(lclP->r,-1.0);
    371:     LCLGather(lclP, lclP->GAugL_U0, lclP->GAugL_V0, lclP->GAugL);
    372:     LCLGather(lclP, lclP->U0,lclP->V0,lclP->X0);

    374:     lclP->recompute_jacobian_flag = PETSC_TRUE;

    376:     TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);
    377:     TaoLineSearchSetType(tao->linesearch, TAOLINESEARCHMT);
    378:     TaoLineSearchSetFromOptions(tao->linesearch);
    379:     TaoLineSearchApply(tao->linesearch, tao->solution, &lclP->aug, lclP->GAugL, tao->stepdirection, &step, &ls_reason);
    380:     if (lclP->verbose) {
    381:       PetscPrintf(PETSC_COMM_WORLD,"Steplength = %g\n",(double)step);
    382:     }

    384:     LCLScatter(lclP,tao->solution,lclP->U,lclP->V);
    385:     TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);
    386:     LCLScatter(lclP,tao->gradient,lclP->GU,lclP->GV);

    388:     LCLScatter(lclP,lclP->GAugL,lclP->GAugL_U,lclP->GAugL_V);

    390:     /* Check convergence */
    391:     VecNorm(lclP->GAugL, NORM_2, &mnorm);
    392:     VecNorm(tao->constraints, NORM_2, &cnorm);
    393:     TaoMonitor(tao,tao->niter,f,mnorm,cnorm,step,&reason);
    394:     if (reason != TAO_CONTINUE_ITERATING){
    395:       break;
    396:     }

    398:     /* TODO: use a heuristic to choose how many iterations should be performed within phase 2 */
    399:     for (phase2_iter=0; phase2_iter<lclP->phase2_niter; phase2_iter++){
    400:       /* We now minimize the objective function starting from the fraction of
    401:          the Newton point accepted by applying one step of a reduced-space
    402:          method.  The optimization problem is:

    404:          minimize f(u+du, v+dv)
    405:          s. t.    A(u0,v0)du + B(u0,v0)du = -alpha g(u0,v0)

    407:          In particular, we have that
    408:          du = -inv(A)*(Bdv + alpha g) */

    410:       TaoComputeJacobianState(tao,lclP->X0,tao->jacobian_state,tao->jacobian_state_pre,tao->jacobian_state_inv);
    411:       TaoComputeJacobianDesign(tao,lclP->X0,tao->jacobian_design);

    413:       /* Store V and constraints */
    414:       VecCopy(lclP->V, lclP->V1);
    415:       VecCopy(tao->constraints,lclP->con1);

    417:       /* Compute multipliers */
    418:       /* p1 */
    419:       VecSet(lclP->lamda,0.0); /*  Initial guess in CG */
    420:       lclP->solve_type = LCL_ADJOINT1;
    421:       MatIsSymmetricKnown(tao->jacobian_state,&set,&flag);
    422:       if (tao->jacobian_state_pre) {
    423:         MatIsSymmetricKnown(tao->jacobian_state_pre,&pset,&pflag);
    424:       } else {
    425:         pset = pflag = PETSC_TRUE;
    426:       }
    427:       if (set && pset && flag && pflag) symmetric = PETSC_TRUE;
    428:       else symmetric = PETSC_FALSE;

    430:       if (tao->jacobian_state_inv) {
    431:         if (symmetric) {
    432:           MatMult(tao->jacobian_state_inv, lclP->GAugL_U, lclP->lamda);
    433:         } else {
    434:           MatMultTranspose(tao->jacobian_state_inv, lclP->GAugL_U, lclP->lamda);
    435:         }
    436:       } else {
    437:         if (symmetric) {
    438:           KSPSolve(tao->ksp, lclP->GAugL_U,  lclP->lamda);
    439:         } else {
    440:           KSPSolveTranspose(tao->ksp, lclP->GAugL_U,  lclP->lamda);
    441:         }
    442:         KSPGetIterationNumber(tao->ksp,&its);
    443:         tao->ksp_its+=its;
    444:         tao->ksp_tot_its+=its;
    445:       }
    446:       MatMultTranspose(tao->jacobian_design,lclP->lamda,lclP->g1);
    447:       VecAXPY(lclP->g1,-1.0,lclP->GAugL_V);

    449:       /* Compute the limited-memory quasi-newton direction */
    450:       if (tao->niter > 0) {
    451:         MatLMVMSolve(lclP->R,lclP->g1,lclP->s);
    452:         VecDot(lclP->s,lclP->g1,&descent);
    453:         if (descent <= 0) {
    454:           if (lclP->verbose) {
    455:             PetscPrintf(PETSC_COMM_WORLD,"Reduced-space direction not descent: %g\n",(double)descent);
    456:           }
    457:           VecCopy(lclP->g1,lclP->s);
    458:         }
    459:       } else {
    460:         VecCopy(lclP->g1,lclP->s);
    461:       }
    462:       VecScale(lclP->g1,-1.0);

    464:       /* Recover the full space direction */
    465:       MatMult(tao->jacobian_design,lclP->s,lclP->WU);
    466:       /* VecSet(lclP->r,0.0); */ /*  Initial guess in CG */
    467:       lclP->solve_type = LCL_FORWARD2;
    468:       if (tao->jacobian_state_inv) {
    469:         MatMult(tao->jacobian_state_inv,lclP->WU,lclP->r);
    470:       } else {
    471:         KSPSolve(tao->ksp, lclP->WU, lclP->r);
    472:         KSPGetIterationNumber(tao->ksp,&its);
    473:         tao->ksp_its += its;
    474:         tao->ksp_tot_its+=its;
    475:       }

    477:       /* We now minimize the augmented Lagrangian along the direction -r,s */
    478:       VecScale(lclP->r, -1.0);
    479:       LCLGather(lclP,lclP->r,lclP->s,tao->stepdirection);
    480:       VecScale(lclP->r, -1.0);
    481:       lclP->recompute_jacobian_flag = PETSC_TRUE;

    483:       TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);
    484:       TaoLineSearchSetType(tao->linesearch,TAOLINESEARCHMT);
    485:       TaoLineSearchSetFromOptions(tao->linesearch);
    486:       TaoLineSearchApply(tao->linesearch, tao->solution, &lclP->aug, lclP->GAugL, tao->stepdirection,&step,&ls_reason);
    487:       if (lclP->verbose){
    488:         PetscPrintf(PETSC_COMM_WORLD,"Reduced-space steplength =  %g\n",(double)step);
    489:       }

    491:       LCLScatter(lclP,tao->solution,lclP->U,lclP->V);
    492:       LCLScatter(lclP,lclP->GL,lclP->GL_U,lclP->GL_V);
    493:       LCLScatter(lclP,lclP->GAugL,lclP->GAugL_U,lclP->GAugL_V);
    494:       TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);
    495:       LCLScatter(lclP,tao->gradient,lclP->GU,lclP->GV);

    497:       /* Compute the reduced gradient at the new point */

    499:       TaoComputeJacobianState(tao,lclP->X0,tao->jacobian_state,tao->jacobian_state_pre,tao->jacobian_state_inv);
    500:       TaoComputeJacobianDesign(tao,lclP->X0,tao->jacobian_design);

    502:       /* p2 */
    503:       /* Compute multipliers, using lamda-rho*con as an initial guess in PCG */
    504:       if (phase2_iter==0){
    505:         VecWAXPY(lclP->lamda,-lclP->rho,lclP->con1,lclP->lamda0);
    506:       } else {
    507:         VecAXPY(lclP->lamda,-lclP->rho,tao->constraints);
    508:       }

    510:       MatIsSymmetricKnown(tao->jacobian_state,&set,&flag);
    511:       if (tao->jacobian_state_pre) {
    512:         MatIsSymmetricKnown(tao->jacobian_state_pre,&pset,&pflag);
    513:       } else {
    514:         pset = pflag = PETSC_TRUE;
    515:       }
    516:       if (set && pset && flag && pflag) symmetric = PETSC_TRUE;
    517:       else symmetric = PETSC_FALSE;

    519:       lclP->solve_type = LCL_ADJOINT2;
    520:       if (tao->jacobian_state_inv) {
    521:         if (symmetric) {
    522:           MatMult(tao->jacobian_state_inv, lclP->GU, lclP->lamda);
    523:         } else {
    524:           MatMultTranspose(tao->jacobian_state_inv, lclP->GU, lclP->lamda);
    525:         }
    526:       } else {
    527:         if (symmetric) {
    528:           KSPSolve(tao->ksp, lclP->GU,  lclP->lamda);
    529:         } else {
    530:           KSPSolveTranspose(tao->ksp, lclP->GU,  lclP->lamda);
    531:         }
    532:         KSPGetIterationNumber(tao->ksp,&its);
    533:         tao->ksp_its += its;
    534:         tao->ksp_tot_its += its;
    535:       }

    537:       MatMultTranspose(tao->jacobian_design,lclP->lamda,lclP->g2);
    538:       VecAXPY(lclP->g2,-1.0,lclP->GV);

    540:       VecScale(lclP->g2,-1.0);

    542:       /* Update the quasi-newton approximation */
    543:       if (phase2_iter >= 0){
    544:         MatLMVMSetPrev(lclP->R,lclP->V1,lclP->g1);
    545:       }
    546:       MatLMVMUpdate(lclP->R,lclP->V,lclP->g2);
    547:       /* Use "-tao_ls_type gpcg -tao_ls_ftol 0 -tao_lmm_broyden_phi 0.0 -tao_lmm_scale_type scalar" to obtain agreement with Matlab code */

    549:     }

    551:     VecCopy(lclP->lamda,lclP->lamda0);

    553:     /* Evaluate Function, Gradient, Constraints, and Jacobian */
    554:     TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);
    555:     LCLScatter(lclP,tao->solution,lclP->U,lclP->V);
    556:     LCLScatter(lclP,tao->gradient,lclP->GU,lclP->GV);

    558:     TaoComputeJacobianState(tao,tao->solution,tao->jacobian_state,tao->jacobian_state_pre,tao->jacobian_state_inv);
    559:     TaoComputeJacobianDesign(tao,tao->solution,tao->jacobian_design);
    560:     TaoComputeConstraints(tao,tao->solution, tao->constraints);

    562:     LCLComputeAugmentedLagrangianAndGradient(tao->linesearch,tao->solution,&lclP->aug,lclP->GAugL,tao);

    564:     VecNorm(lclP->GAugL, NORM_2, &mnorm);

    566:     /* Evaluate constraint norm */
    567:     VecNorm(tao->constraints, NORM_2, &cnorm);

    569:     /* Monitor convergence */
    570:     tao->niter++;
    571:     TaoMonitor(tao, tao->niter,f,mnorm,cnorm,step,&reason);
    572:   }
    573:   MatDestroy(&lclP->R);
    574:   return(0);
    575: }

    577: /*MC
    578:  TAOLCL - linearly constrained lagrangian method for pde-constrained optimization

    580: + -tao_lcl_eps1 - epsilon 1 tolerance
    581: . -tao_lcl_eps2","epsilon 2 tolerance","",lclP->eps2,&lclP->eps2,NULL);
    582: . -tao_lcl_rho0","init value for rho","",lclP->rho0,&lclP->rho0,NULL);
    583: . -tao_lcl_rhomax","max value for rho","",lclP->rhomax,&lclP->rhomax,NULL);
    584: . -tao_lcl_phase2_niter - Number of phase 2 iterations in LCL algorithm
    585: . -tao_lcl_verbose - Print verbose output if True
    586: . -tao_lcl_tola - Tolerance for first forward solve
    587: . -tao_lcl_tolb - Tolerance for first adjoint solve
    588: . -tao_lcl_tolc - Tolerance for second forward solve
    589: - -tao_lcl_told - Tolerance for second adjoint solve

    591:   Level: beginner
    592: M*/
    595: PETSC_EXTERN PetscErrorCode TaoCreate_LCL(Tao tao)
    596: {
    597:   TAO_LCL        *lclP;
    599:   const char     *morethuente_type = TAOLINESEARCHMT;

    602:   tao->ops->setup = TaoSetup_LCL;
    603:   tao->ops->solve = TaoSolve_LCL;
    604:   tao->ops->view = TaoView_LCL;
    605:   tao->ops->setfromoptions = TaoSetFromOptions_LCL;
    606:   tao->ops->destroy = TaoDestroy_LCL;
    607:   PetscNewLog(tao,&lclP);
    608:   tao->data = (void*)lclP;

    610:   /* Override default settings (unless already changed) */
    611:   if (!tao->max_it_changed) tao->max_it = 200;
    612:   if (!tao->catol_changed) tao->catol = 1.0e-4;
    613:   if (!tao->gatol_changed) tao->gttol = 1.0e-4;
    614:   if (!tao->grtol_changed) tao->gttol = 1.0e-4;
    615:   if (!tao->gttol_changed) tao->gttol = 1.0e-4;
    616:   lclP->rho0 = 1.0e-4;
    617:   lclP->rhomax=1e5;
    618:   lclP->eps1 = 1.0e-8;
    619:   lclP->eps2 = 0.0;
    620:   lclP->solve_type=2;
    621:   lclP->tau[0] = lclP->tau[1] = lclP->tau[2] = lclP->tau[3] = 1.0e-4;
    622:   TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch);
    623:   TaoLineSearchSetType(tao->linesearch, morethuente_type);
    624:   TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);

    626:   TaoLineSearchSetObjectiveAndGradientRoutine(tao->linesearch,LCLComputeAugmentedLagrangianAndGradient, tao);
    627:   KSPCreate(((PetscObject)tao)->comm,&tao->ksp);
    628:   KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix);
    629:   KSPSetFromOptions(tao->ksp);
    630:   return(0);
    631: }

    635: static PetscErrorCode LCLComputeLagrangianAndGradient(TaoLineSearch ls, Vec X, PetscReal *f, Vec G, void *ptr)
    636: {
    637:   Tao            tao = (Tao)ptr;
    638:   TAO_LCL        *lclP = (TAO_LCL*)tao->data;
    639:   PetscBool      set,pset,flag,pflag,symmetric;
    640:   PetscReal      cdotl;

    644:   TaoComputeObjectiveAndGradient(tao,X,f,G);
    645:   LCLScatter(lclP,G,lclP->GU,lclP->GV);
    646:   if (lclP->recompute_jacobian_flag) {
    647:     TaoComputeJacobianState(tao,X,tao->jacobian_state,tao->jacobian_state_pre,tao->jacobian_state_inv);
    648:     TaoComputeJacobianDesign(tao,X,tao->jacobian_design);
    649:   }
    650:   TaoComputeConstraints(tao,X, tao->constraints);
    651:   MatIsSymmetricKnown(tao->jacobian_state,&set,&flag);
    652:   if (tao->jacobian_state_pre) {
    653:     MatIsSymmetricKnown(tao->jacobian_state_pre,&pset,&pflag);
    654:   } else {
    655:     pset = pflag = PETSC_TRUE;
    656:   }
    657:   if (set && pset && flag && pflag) symmetric = PETSC_TRUE;
    658:   else symmetric = PETSC_FALSE;

    660:   VecDot(lclP->lamda0, tao->constraints, &cdotl);
    661:   lclP->lgn = *f - cdotl;

    663:   /* Gradient of Lagrangian GL = G - J' * lamda */
    664:   /*      WU = A' * WL
    665:           WV = B' * WL */
    666:   if (symmetric) {
    667:     MatMult(tao->jacobian_state,lclP->lamda0,lclP->GL_U);
    668:   } else {
    669:     MatMultTranspose(tao->jacobian_state,lclP->lamda0,lclP->GL_U);
    670:   }
    671:   MatMultTranspose(tao->jacobian_design,lclP->lamda0,lclP->GL_V);
    672:   VecScale(lclP->GL_U,-1.0);
    673:   VecScale(lclP->GL_V,-1.0);
    674:   VecAXPY(lclP->GL_U,1.0,lclP->GU);
    675:   VecAXPY(lclP->GL_V,1.0,lclP->GV);
    676:   LCLGather(lclP,lclP->GL_U,lclP->GL_V,lclP->GL);

    678:   f[0] = lclP->lgn;
    679:   VecCopy(lclP->GL,G);
    680:   return(0);
    681: }

    685: static PetscErrorCode LCLComputeAugmentedLagrangianAndGradient(TaoLineSearch ls, Vec X, PetscReal *f, Vec G, void *ptr)
    686: {
    687:   Tao            tao = (Tao)ptr;
    688:   TAO_LCL        *lclP = (TAO_LCL*)tao->data;
    689:   PetscReal      con2;
    690:   PetscBool      flag,pflag,set,pset,symmetric;

    694:   LCLComputeLagrangianAndGradient(tao->linesearch,X,f,G,tao);
    695:   LCLScatter(lclP,G,lclP->GL_U,lclP->GL_V);
    696:   VecDot(tao->constraints,tao->constraints,&con2);
    697:   lclP->aug = lclP->lgn + 0.5*lclP->rho*con2;

    699:   /* Gradient of Aug. Lagrangian GAugL = GL + rho * J' c */
    700:   /*      WU = A' * c
    701:           WV = B' * c */
    702:   MatIsSymmetricKnown(tao->jacobian_state,&set,&flag);
    703:   if (tao->jacobian_state_pre) {
    704:     MatIsSymmetricKnown(tao->jacobian_state_pre,&pset,&pflag);
    705:   } else {
    706:     pset = pflag = PETSC_TRUE;
    707:   }
    708:   if (set && pset && flag && pflag) symmetric = PETSC_TRUE;
    709:   else symmetric = PETSC_FALSE;

    711:   if (symmetric) {
    712:     MatMult(tao->jacobian_state,tao->constraints,lclP->GAugL_U);
    713:   } else {
    714:     MatMultTranspose(tao->jacobian_state,tao->constraints,lclP->GAugL_U);
    715:   }

    717:   MatMultTranspose(tao->jacobian_design,tao->constraints,lclP->GAugL_V);
    718:   VecAYPX(lclP->GAugL_U,lclP->rho,lclP->GL_U);
    719:   VecAYPX(lclP->GAugL_V,lclP->rho,lclP->GL_V);
    720:   LCLGather(lclP,lclP->GAugL_U,lclP->GAugL_V,lclP->GAugL);

    722:   f[0] = lclP->aug;
    723:   VecCopy(lclP->GAugL,G);
    724:   return(0);
    725: }

    729: PetscErrorCode LCLGather(TAO_LCL *lclP, Vec u, Vec v, Vec x)
    730: {
    733:   VecScatterBegin(lclP->state_scatter, u, x, INSERT_VALUES, SCATTER_REVERSE);
    734:   VecScatterEnd(lclP->state_scatter, u, x, INSERT_VALUES, SCATTER_REVERSE);
    735:   VecScatterBegin(lclP->design_scatter, v, x, INSERT_VALUES, SCATTER_REVERSE);
    736:   VecScatterEnd(lclP->design_scatter, v, x, INSERT_VALUES, SCATTER_REVERSE);
    737:   return(0);

    739: }
    742: PetscErrorCode LCLScatter(TAO_LCL *lclP, Vec x, Vec u, Vec v)
    743: {
    746:   VecScatterBegin(lclP->state_scatter, x, u, INSERT_VALUES, SCATTER_FORWARD);
    747:   VecScatterEnd(lclP->state_scatter, x, u, INSERT_VALUES, SCATTER_FORWARD);
    748:   VecScatterBegin(lclP->design_scatter, x, v, INSERT_VALUES, SCATTER_FORWARD);
    749:   VecScatterEnd(lclP->design_scatter, x, v, INSERT_VALUES, SCATTER_FORWARD);
    750:   return(0);

    752: }