Date: 2026-03-01T05:25:15+00:00

Actual source code: bntl.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:  In this variant, the trust region failures trigger a line search with
      9:  the existing Newton step instead of re-solving the step with a
     10:  different radius.

     12:  ------------------------------------------------------------

     14:  x_0 = VecMedian(x_0)
     15:  f_0, g_0 = TaoComputeObjectiveAndGradient(x_0)
     16:  pg_0 = project(g_0)
     17:  check convergence at pg_0
     18:  needH = TaoBNKInitialize(default:BNK_INIT_INTERPOLATION)
     19:  niter = 0
     20:  step_accepted = true

     22:  while niter <= max_it
     23:     niter += 1

     25:     if needH
     26:       If max_cg_steps > 0
     27:         x_k, g_k, pg_k = TaoSolve(BNCG)
     28:       end

     30:       H_k = TaoComputeHessian(x_k)
     31:       if pc_type == BNK_PC_BFGS
     32:         add correction to BFGS approx
     33:         if scale_type == BNK_SCALE_AHESS
     34:           D = VecMedian(1e-6, abs(diag(H_k)), 1e6)
     35:           scale BFGS with VecReciprocal(D)
     36:         end
     37:       end
     38:       needH = False
     39:     end

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

     56:     generate the reduced system Hr_k dr_k = -gr_k for variables in IA
     57:     if pc_type == BNK_PC_BFGS && scale_type == BNK_SCALE_PHESS
     58:       D = VecMedian(1e-6, abs(diag(Hr_k)), 1e6)
     59:       scale BFGS with VecReciprocal(D)
     60:     end
     61:     solve Hr_k dr_k = -gr_k
     62:     set d_k to (l - x) for variables in L, (u - x) for variables in U, and 0 for variables in F

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

     70:     oldTrust = trust
     71:     step_accepted, trust = TaoBNKUpdateTrustRadius(default: BNK_UPDATE_REDUCTION)
     72:     if step_accepted
     73:       g_{k+1} = TaoComputeGradient(x_{k+1})
     74:       pg_{k+1} = project(g_{k+1})
     75:       count the accepted Newton step
     76:     else
     77:       if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
     78:         dr_k = -BFGS*gr_k for variables in I
     79:         if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
     80:           reset the BFGS preconditioner
     81:           calculate scale delta and apply it to BFGS
     82:           dr_k = -BFGS*gr_k for variables in I
     83:           if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
     84:             dr_k = -gr_k for variables in I
     85:           end
     86:         end
     87:       end

     89:       x_{k+1}, f_{k+1}, g_{k+1}, ls_failed = TaoBNKPerformLineSearch()
     90:       if ls_failed
     91:         f_{k+1} = f_k
     92:         x_{k+1} = x_k
     93:         g_{k+1} = g_k
     94:         pg_{k+1} = pg_k
     95:         terminate
     96:       else
     97:         pg_{k+1} = project(g_{k+1})
     98:         trust = oldTrust
     99:         trust = TaoBNKUpdateTrustRadius(BNK_UPDATE_STEP)
    100:         count the accepted step type (Newton, BFGS, scaled grad or grad)
    101:       end
    102:     end

    104:     check convergence at pg_{k+1}
    105:  end
    106: */

    108: PetscErrorCode TaoSolve_BNTL(Tao tao)
    109: {
    110:   TAO_BNK                     *bnk = (TAO_BNK *)tao->data;
    111:   KSPConvergedReason           ksp_reason;
    112:   TaoLineSearchConvergedReason ls_reason;

    114:   PetscReal oldTrust, prered, actred, steplen, resnorm;
    115:   PetscBool cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_FALSE;
    116:   PetscInt  stepType, nDiff;

    118:   PetscFunctionBegin;
    119:   /* Initialize the preconditioner, KSP solver and trust radius/line search */
    120:   tao->reason = TAO_CONTINUE_ITERATING;
    121:   PetscCall(TaoBNKInitialize(tao, bnk->init_type, &needH));
    122:   if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(PETSC_SUCCESS);

    124:   /* Have not converged; continue with Newton method */
    125:   while (tao->reason == TAO_CONTINUE_ITERATING) {
    126:     /* Call general purpose update function */
    127:     if (tao->ops->update) {
    128:       PetscUseTypeMethod(tao, update, tao->niter, tao->user_update);
    129:       PetscCall(TaoComputeObjective(tao, tao->solution, &bnk->f));
    130:     }

    132:     if (needH && bnk->inactive_idx) {
    133:       /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
    134:       PetscCall(TaoBNKTakeCGSteps(tao, &cgTerminate));
    135:       if (cgTerminate) {
    136:         tao->reason = bnk->bncg->reason;
    137:         PetscFunctionReturn(PETSC_SUCCESS);
    138:       }
    139:       /* Compute the hessian and update the BFGS preconditioner at the new iterate */
    140:       PetscCall((*bnk->computehessian)(tao));
    141:       needH = PETSC_FALSE;
    142:     }

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

    147:     /* Store current solution before it changes */
    148:     oldTrust  = tao->trust;
    149:     bnk->fold = bnk->f;
    150:     PetscCall(VecCopy(tao->solution, bnk->Xold));
    151:     PetscCall(VecCopy(tao->gradient, bnk->Gold));
    152:     PetscCall(VecCopy(bnk->unprojected_gradient, bnk->unprojected_gradient_old));

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

    158:     /* Check if the projection changed the step direction */
    159:     if (nDiff > 0) {
    160:       /* Projection changed the step, so we have to recompute the step and
    161:          the predicted reduction. Leave the trust radius unchanged. */
    162:       PetscCall(VecCopy(tao->solution, tao->stepdirection));
    163:       PetscCall(VecAXPY(tao->stepdirection, -1.0, bnk->Xold));
    164:       PetscCall(TaoBNKRecomputePred(tao, tao->stepdirection, &prered));
    165:     } else {
    166:       /* Step did not change, so we can just recover the pre-computed prediction */
    167:       PetscCall(KSPCGGetObjFcn(tao->ksp, &prered));
    168:     }
    169:     prered = -prered;

    171:     /* Compute the actual reduction and update the trust radius */
    172:     PetscCall(TaoComputeObjective(tao, tao->solution, &bnk->f));
    173:     PetscCheck(!PetscIsInfOrNanReal(bnk->f), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
    174:     actred = bnk->fold - bnk->f;
    175:     PetscCall(TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted));

    177:     if (stepAccepted) {
    178:       /* Step is good, evaluate the gradient and the hessian */
    179:       steplen = 1.0;
    180:       needH   = PETSC_TRUE;
    181:       ++bnk->newt;
    182:       PetscCall(TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient));
    183:       PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
    184:       PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient));
    185:       if (bnk->active_idx) PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
    186:       PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm));
    187:     } else {
    188:       /* Trust-region rejected the step. Revert the solution. */
    189:       bnk->f = bnk->fold;
    190:       PetscCall(VecCopy(bnk->Xold, tao->solution));
    191:       /* Trigger the line search */
    192:       PetscCall(TaoBNKSafeguardStep(tao, ksp_reason, &stepType));
    193:       PetscCall(TaoBNKPerformLineSearch(tao, &stepType, &steplen, &ls_reason));
    194:       if (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER) {
    195:         /* Line search failed, revert solution and terminate */
    196:         stepAccepted = PETSC_FALSE;
    197:         needH        = PETSC_FALSE;
    198:         bnk->f       = bnk->fold;
    199:         PetscCall(VecCopy(bnk->Xold, tao->solution));
    200:         PetscCall(VecCopy(bnk->Gold, tao->gradient));
    201:         PetscCall(VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient));
    202:         tao->trust  = 0.0;
    203:         tao->reason = TAO_DIVERGED_LS_FAILURE;
    204:       } else {
    205:         /* new iterate so we need to recompute the Hessian */
    206:         needH = PETSC_TRUE;
    207:         /* compute the projected gradient */
    208:         PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
    209:         PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient));
    210:         if (bnk->active_idx) PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
    211:         PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm));
    212:         /* Line search succeeded so we should update the trust radius based on the LS step length */
    213:         tao->trust = oldTrust;
    214:         PetscCall(TaoBNKUpdateTrustRadius(tao, prered, actred, BNK_UPDATE_STEP, stepType, &stepAccepted));
    215:         /* count the accepted step type */
    216:         PetscCall(TaoBNKAddStepCounts(tao, stepType));
    217:       }
    218:     }

    220:     /*  Check for termination */
    221:     PetscCall(VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W));
    222:     PetscCall(VecNorm(bnk->W, NORM_2, &resnorm));
    223:     PetscCheck(!PetscIsInfOrNanReal(resnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
    224:     ++tao->niter;
    225:     PetscCall(TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its));
    226:     PetscCall(TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen));
    227:     PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
    228:   }
    229:   PetscFunctionReturn(PETSC_SUCCESS);
    230: }

    232: static PetscErrorCode TaoSetUp_BNTL(Tao tao)
    233: {
    234:   KSP       ksp;
    235:   PetscBool valid;

    237:   PetscFunctionBegin;
    238:   PetscCall(TaoSetUp_BNK(tao));
    239:   PetscCall(TaoGetKSP(tao, &ksp));
    240:   PetscCall(PetscObjectHasFunction((PetscObject)ksp, "KSPCGSetRadius_C", &valid));
    241:   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);
    242:   PetscFunctionReturn(PETSC_SUCCESS);
    243: }

    245: static PetscErrorCode TaoSetFromOptions_BNTL(Tao tao, PetscOptionItems PetscOptionsObject)
    246: {
    247:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

    249:   PetscFunctionBegin;
    250:   PetscCall(TaoSetFromOptions_BNK(tao, PetscOptionsObject));
    251:   if (bnk->update_type == BNK_UPDATE_STEP) bnk->update_type = BNK_UPDATE_REDUCTION;
    252:   PetscFunctionReturn(PETSC_SUCCESS);
    253: }

    255: /*MC
    256:   TAOBNTL - Bounded Newton Trust Region method with line-search fall-back for nonlinear
    257:             minimization with bound constraints.

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

    265:   Level: beginner

    267:   Developer Note:
    268:   One should control the maximum number of cg iterations through the standard pc_max_it option not with a special
    269:   ad hoc option

    271: M*/
    272: PETSC_EXTERN PetscErrorCode TaoCreate_BNTL(Tao tao)
    273: {
    274:   TAO_BNK *bnk;

    276:   PetscFunctionBegin;
    277:   PetscCall(TaoCreate_BNK(tao));
    278:   tao->ops->solve          = TaoSolve_BNTL;
    279:   tao->ops->setup          = TaoSetUp_BNTL;
    280:   tao->ops->setfromoptions = TaoSetFromOptions_BNTL;

    282:   bnk              = (TAO_BNK *)tao->data;
    283:   bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */
    284:   PetscFunctionReturn(PETSC_SUCCESS);
    285: }