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

     16:  while niter <= max_it

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

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

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

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

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

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

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

     82:     end
     83:     check convergence at pg_{k+1}
     84:     niter += 1

     86:  end
     87: */

     89: PetscErrorCode TaoSolve_BNTR(Tao tao)
     90: {
     91:   TAO_BNK           *bnk = (TAO_BNK *)tao->data;
     92:   KSPConvergedReason ksp_reason;

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

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

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

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

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

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

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

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

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

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

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

    198: static PetscErrorCode TaoSetUp_BNTR(Tao tao)
    199: {
    200:   KSP       ksp;
    201:   PetscBool valid;

    203:   PetscFunctionBegin;
    204:   PetscCall(TaoSetUp_BNK(tao));
    205:   PetscCall(TaoGetKSP(tao, &ksp));
    206:   PetscCall(PetscObjectHasFunction((PetscObject)ksp, "KSPCGSetRadius_C", &valid));
    207:   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);
    208:   PetscFunctionReturn(PETSC_SUCCESS);
    209: }

    211: static PetscErrorCode TaoSetFromOptions_BNTR(Tao tao, PetscOptionItems PetscOptionsObject)
    212: {
    213:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

    215:   PetscFunctionBegin;
    216:   PetscCall(TaoSetFromOptions_BNK(tao, PetscOptionsObject));
    217:   if (bnk->update_type == BNK_UPDATE_STEP) bnk->update_type = BNK_UPDATE_REDUCTION;
    218:   PetscFunctionReturn(PETSC_SUCCESS);
    219: }

    221: /*MC
    222:   TAOBNTR - Bounded Newton Trust Region for nonlinear minimization with bound constraints.

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

    230:   Level: beginner

    232: .seealso: `Tao`, `TAONTR`, `TAONTL`, `TAONM`, `TAOCG`, `TaoType`, `TaoCreate()`
    233: M*/
    234: PETSC_EXTERN PetscErrorCode TaoCreate_BNTR(Tao tao)
    235: {
    236:   TAO_BNK *bnk;

    238:   PetscFunctionBegin;
    239:   PetscCall(TaoCreate_BNK(tao));
    240:   tao->ops->solve          = TaoSolve_BNTR;
    241:   tao->ops->setup          = TaoSetUp_BNTR;
    242:   tao->ops->setfromoptions = TaoSetFromOptions_BNTR;

    244:   bnk              = (TAO_BNK *)tao->data;
    245:   bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */
    246:   PetscFunctionReturn(PETSC_SUCCESS);
    247: }