Actual source code: bntr.c

      1: #include <../src/tao/bound/impls/bnk/bnk.h>
      2: #include <petscksp.h>

      4: /*
      5:  Implements Newton's Method with a trust region approach for solving
      6:  bound constrained minimization problems.

      8:  ------------------------------------------------------------

     10:  x_0 = VecMedian(x_0)
     11:  f_0, g_0= TaoComputeObjectiveAndGradient(x_0)
     12:  pg_0 = project(g_0)
     13:  check convergence at pg_0
     14:  needH = TaoBNKInitialize(default:BNK_INIT_INTERPOLATION)
     15:  niter = 0
     16:  step_accepted = false

     18:  while niter <= max_it

     20:     if needH
     21:       If max_cg_steps > 0
     22:         x_k, g_k, pg_k = TaoSolve(BNCG)
     23:       end

     25:       H_k = TaoComputeHessian(x_k)
     26:       if pc_type == BNK_PC_BFGS
     27:         add correction to BFGS approx
     28:         if scale_type == BNK_SCALE_AHESS
     29:           D = VecMedian(1e-6, abs(diag(H_k)), 1e6)
     30:           scale BFGS with VecReciprocal(D)
     31:         end
     32:       end
     33:       needH = False
     34:     end

     36:     if pc_type = BNK_PC_BFGS
     37:       B_k = BFGS
     38:     else
     39:       B_k = VecMedian(1e-6, abs(diag(H_k)), 1e6)
     40:       B_k = VecReciprocal(B_k)
     41:     end
     42:     w = x_k - VecMedian(x_k - 0.001*B_k*g_k)
     43:     eps = min(eps, norm2(w))
     44:     determine the active and inactive index sets such that
     45:       L = {i : (x_k)_i <= l_i + eps && (g_k)_i > 0}
     46:       U = {i : (x_k)_i >= u_i - eps && (g_k)_i < 0}
     47:       F = {i : l_i = (x_k)_i = u_i}
     48:       A = {L + U + F}
     49:       IA = {i : i not in A}

     51:     generate the reduced system Hr_k dr_k = -gr_k for variables in IA
     52:     if pc_type == BNK_PC_BFGS && scale_type == BNK_SCALE_PHESS
     53:       D = VecMedian(1e-6, abs(diag(Hr_k)), 1e6)
     54:       scale BFGS with VecReciprocal(D)
     55:     end

     57:     while !stepAccepted
     58:       solve Hr_k dr_k = -gr_k
     59:       set d_k to (l - x) for variables in L, (u - x) for variables in U, and 0 for variables in F

     61:       x_{k+1} = VecMedian(x_k + d_k)
     62:       s = x_{k+1} - x_k
     63:       prered = dot(s, 0.5*gr_k - Hr_k*s)
     64:       f_{k+1} = TaoComputeObjective(x_{k+1})
     65:       actred = f_k - f_{k+1}

     67:       oldTrust = trust
     68:       step_accepted, trust = TaoBNKUpdateTrustRadius(default: BNK_UPDATE_REDUCTION)
     69:       if step_accepted
     70:         g_{k+1} = TaoComputeGradient(x_{k+1})
     71:         pg_{k+1} = project(g_{k+1})
     72:         count the accepted Newton step
     73:         needH = True
     74:       else
     75:         f_{k+1} = f_k
     76:         x_{k+1} = x_k
     77:         g_{k+1} = g_k
     78:         pg_{k+1} = pg_k
     79:         if trust == oldTrust
     80:           terminate because we cannot shrink the radius any further
     81:         end
     82:       end

     84:     end
     85:     check convergence at pg_{k+1}
     86:     niter += 1

     88:  end
     89: */

     91: PetscErrorCode TaoSolve_BNTR(Tao tao)
     92: {
     93:   TAO_BNK           *bnk = (TAO_BNK *)tao->data;
     94:   KSPConvergedReason ksp_reason;

     96:   PetscReal oldTrust, prered, actred, steplen = 0.0, resnorm;
     97:   PetscBool cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_FALSE;
     98:   PetscInt  stepType, nDiff;

    100:   PetscFunctionBegin;
    101:   /* Initialize the preconditioner, KSP solver and trust radius/line search */
    102:   tao->reason = TAO_CONTINUE_ITERATING;
    103:   PetscCall(TaoBNKInitialize(tao, bnk->init_type, &needH));
    104:   if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(PETSC_SUCCESS);

    106:   /* Have not converged; continue with Newton method */
    107:   while (tao->reason == TAO_CONTINUE_ITERATING) {
    108:     /* Call general purpose update function */
    109:     if (tao->ops->update) {
    110:       PetscUseTypeMethod(tao, update, tao->niter, tao->user_update);
    111:       PetscCall(TaoComputeObjective(tao, tao->solution, &bnk->f));
    112:     }

    114:     if (needH && bnk->inactive_idx) {
    115:       /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
    116:       PetscCall(TaoBNKTakeCGSteps(tao, &cgTerminate));
    117:       if (cgTerminate) {
    118:         tao->reason = bnk->bncg->reason;
    119:         PetscFunctionReturn(PETSC_SUCCESS);
    120:       }
    121:       /* Compute the hessian and update the BFGS preconditioner at the new iterate */
    122:       PetscCall((*bnk->computehessian)(tao));
    123:       needH = PETSC_FALSE;
    124:     }

    126:     /* Store current solution before it changes */
    127:     bnk->fold = bnk->f;
    128:     PetscCall(VecCopy(tao->solution, bnk->Xold));
    129:     PetscCall(VecCopy(tao->gradient, bnk->Gold));
    130:     PetscCall(VecCopy(bnk->unprojected_gradient, bnk->unprojected_gradient_old));

    132:     /* Enter into trust region loops */
    133:     stepAccepted = PETSC_FALSE;
    134:     while (!stepAccepted && tao->reason == TAO_CONTINUE_ITERATING) {
    135:       tao->ksp_its = 0;

    137:       /* Use the common BNK kernel to compute the Newton step (for inactive variables only) */
    138:       PetscCall((*bnk->computestep)(tao, shift, &ksp_reason, &stepType));

    140:       /* Temporarily accept the step and project it into the bounds */
    141:       PetscCall(VecAXPY(tao->solution, 1.0, tao->stepdirection));
    142:       PetscCall(TaoBoundSolution(tao->solution, tao->XL, tao->XU, 0.0, &nDiff, tao->solution));

    144:       /* Check if the projection changed the step direction */
    145:       if (nDiff > 0) {
    146:         /* Projection changed the step, so we have to recompute the step and
    147:            the predicted reduction. Leave the trust radius unchanged. */
    148:         PetscCall(VecCopy(tao->solution, tao->stepdirection));
    149:         PetscCall(VecAXPY(tao->stepdirection, -1.0, bnk->Xold));
    150:         PetscCall(TaoBNKRecomputePred(tao, tao->stepdirection, &prered));
    151:       } else {
    152:         /* Step did not change, so we can just recover the pre-computed prediction */
    153:         PetscCall(KSPCGGetObjFcn(tao->ksp, &prered));
    154:       }
    155:       prered = -prered;

    157:       /* Compute the actual reduction and update the trust radius */
    158:       PetscCall(TaoComputeObjective(tao, tao->solution, &bnk->f));
    159:       PetscCheck(!PetscIsInfOrNanReal(bnk->f), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
    160:       actred   = bnk->fold - bnk->f;
    161:       oldTrust = tao->trust;
    162:       PetscCall(TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted));

    164:       if (stepAccepted) {
    165:         /* Step is good, evaluate the gradient and flip the need-Hessian switch */
    166:         steplen = 1.0;
    167:         needH   = PETSC_TRUE;
    168:         ++bnk->newt;
    169:         PetscCall(TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient));
    170:         PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
    171:         PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient));
    172:         if (bnk->active_idx) PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
    173:         PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm));
    174:       } else {
    175:         /* Step is bad, revert old solution and re-solve with new radius*/
    176:         steplen = 0.0;
    177:         needH   = PETSC_FALSE;
    178:         bnk->f  = bnk->fold;
    179:         PetscCall(VecCopy(bnk->Xold, tao->solution));
    180:         PetscCall(VecCopy(bnk->Gold, tao->gradient));
    181:         PetscCall(VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient));
    182:         if (oldTrust == tao->trust) {
    183:           /* Can't change the radius anymore so just terminate */
    184:           tao->reason = TAO_DIVERGED_TR_REDUCTION;
    185:         }
    186:       }
    187:     }
    188:     /*  Check for termination */
    189:     PetscCall(VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W));
    190:     PetscCall(VecNorm(bnk->W, NORM_2, &resnorm));
    191:     PetscCheck(!PetscIsInfOrNanReal(resnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
    192:     ++tao->niter;
    193:     PetscCall(TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its));
    194:     PetscCall(TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen));
    195:     PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
    196:   }
    197:   PetscFunctionReturn(PETSC_SUCCESS);
    198: }

    200: /*------------------------------------------------------------*/
    201: static PetscErrorCode TaoSetUp_BNTR(Tao tao)
    202: {
    203:   KSP          ksp;
    204:   PetscVoidFn *valid;

    206:   PetscFunctionBegin;
    207:   PetscCall(TaoSetUp_BNK(tao));
    208:   PetscCall(TaoGetKSP(tao, &ksp));
    209:   PetscCall(PetscObjectQueryFunction((PetscObject)ksp, "KSPCGSetRadius_C", &valid));
    210:   PetscCheck(valid, PetscObjectComm((PetscObject)tao), PETSC_ERR_SUP, "Not for KSP type %s. Must use a trust-region CG method for KSP (e.g. KSPNASH, KSPSTCG, KSPGLTR)", ((PetscObject)ksp)->type_name);
    211:   PetscFunctionReturn(PETSC_SUCCESS);
    212: }

    214: /*------------------------------------------------------------*/

    216: static PetscErrorCode TaoSetFromOptions_BNTR(Tao tao, PetscOptionItems *PetscOptionsObject)
    217: {
    218:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

    220:   PetscFunctionBegin;
    221:   PetscCall(TaoSetFromOptions_BNK(tao, PetscOptionsObject));
    222:   if (bnk->update_type == BNK_UPDATE_STEP) bnk->update_type = BNK_UPDATE_REDUCTION;
    223:   PetscFunctionReturn(PETSC_SUCCESS);
    224: }

    226: /*------------------------------------------------------------*/
    227: /*MC
    228:   TAOBNTR - Bounded Newton Trust Region for nonlinear minimization with bound constraints.

    230:   Options Database Keys:
    231: + -tao_bnk_max_cg_its - maximum number of bounded conjugate-gradient iterations taken in each Newton loop
    232: . -tao_bnk_init_type - trust radius initialization method ("constant", "direction", "interpolation")
    233: . -tao_bnk_update_type - trust radius update method ("step", "direction", "interpolation")
    234: - -tao_bnk_as_type - active-set estimation method ("none", "bertsekas")

    236:   Level: beginner
    237: M*/
    238: PETSC_EXTERN PetscErrorCode TaoCreate_BNTR(Tao tao)
    239: {
    240:   TAO_BNK *bnk;

    242:   PetscFunctionBegin;
    243:   PetscCall(TaoCreate_BNK(tao));
    244:   tao->ops->solve          = TaoSolve_BNTR;
    245:   tao->ops->setup          = TaoSetUp_BNTR;
    246:   tao->ops->setfromoptions = TaoSetFromOptions_BNTR;

    248:   bnk              = (TAO_BNK *)tao->data;
    249:   bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */
    250:   PetscFunctionReturn(PETSC_SUCCESS);
    251: }