Date: 2026-06-01T23:13:45+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:  x_0 = VecMedian(x_0)
     13:  f_0, g_0 = TaoComputeObjectiveAndGradient(x_0)
     14:  pg_0 = project(g_0)
     15:  check convergence at pg_0
     16:  needH = TaoBNKInitialize(default:BNK_INIT_INTERPOLATION)
     17:  niter = 0
     18:  step_accepted = true

     20:  while niter <= max_it
     21:     niter += 1

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

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

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

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

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

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

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

    102:     check convergence at pg_{k+1}
    103:  end
    104: */

    106: PetscErrorCode TaoSolve_BNTL(Tao tao)
    107: {
    108:   TAO_BNK                     *bnk = (TAO_BNK *)tao->data;
    109:   KSPConvergedReason           ksp_reason;
    110:   TaoLineSearchConvergedReason ls_reason;

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

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

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

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

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

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

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

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

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

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

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

    230: static PetscErrorCode TaoSetUp_BNTL(Tao tao)
    231: {
    232:   KSP       ksp;
    233:   PetscBool valid;

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

    243: static PetscErrorCode TaoSetFromOptions_BNTL(Tao tao, PetscOptionItems PetscOptionsObject)
    244: {
    245:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

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

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

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

    263:   Level: beginner

    265:   Developer Note:
    266:   One should control the maximum number of cg iterations through the standard `-ksp_max_it` option not with a special
    267:   ad hoc option

    269: .seealso: `Tao`, `TAONTR`, `TAONTL`, `TAONM`, `TAOCG`, `TaoType`, `TaoCreate()`
    270: M*/
    271: PETSC_EXTERN PetscErrorCode TaoCreate_BNTL(Tao tao)
    272: {
    273:   TAO_BNK *bnk;

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

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