Actual source code: bnls.c

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

      4: /*
      5:  Implements Newton's Method with a line search approach for
      6:  solving 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_DIRECTION)
     13:  niter = 0
     14:  step_accepted = true

     16:  while niter < max_it
     17:     if needH
     18:       If max_cg_steps > 0
     19:         x_k, g_k, pg_k = TaoSolve(BNCG)
     20:       end

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

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

     48:     generate the reduced system Hr_k dr_k = -gr_k for variables in IA
     49:     if p > 0
     50:       Hr_k += p*
     51:     end
     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
     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:     if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
     60:       dr_k = -BFGS*gr_k for variables in I
     61:       if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
     62:         reset the BFGS preconditioner
     63:         calculate scale delta and apply it to BFGS
     64:         dr_k = -BFGS*gr_k for variables in I
     65:         if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
     66:           dr_k = -gr_k for variables in I
     67:         end
     68:       end
     69:     end

     71:     x_{k+1}, f_{k+1}, g_{k+1}, ls_failed = TaoBNKPerformLineSearch()
     72:     if ls_failed
     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:       terminate
     78:     else
     79:       pg_{k+1} = project(g_{k+1})
     80:       count the accepted step type (Newton, BFGS, scaled grad or grad)
     81:     end

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

     88: PetscErrorCode TaoSolve_BNLS(Tao tao)
     89: {
     90:   TAO_BNK                     *bnk = (TAO_BNK *)tao->data;
     91:   KSPConvergedReason           ksp_reason;
     92:   TaoLineSearchConvergedReason ls_reason;
     93:   PetscReal                    steplen = 1.0, resnorm;
     94:   PetscBool                    cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_TRUE;
     95:   PetscInt                     stepType;

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

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

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

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

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

    133:     /* Trigger the line search */
    134:     PetscCall(TaoBNKPerformLineSearch(tao, &stepType, &steplen, &ls_reason));

    136:     if (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER) {
    137:       /* Failed to find an improving point */
    138:       needH  = PETSC_FALSE;
    139:       bnk->f = bnk->fold;
    140:       PetscCall(VecCopy(bnk->Xold, tao->solution));
    141:       PetscCall(VecCopy(bnk->Gold, tao->gradient));
    142:       PetscCall(VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient));
    143:       steplen     = 0.0;
    144:       tao->reason = TAO_DIVERGED_LS_FAILURE;
    145:     } else {
    146:       /* new iterate so we need to recompute the Hessian */
    147:       needH = PETSC_TRUE;
    148:       /* compute the projected gradient */
    149:       PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
    150:       PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient));
    151:       if (bnk->active_idx) PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
    152:       PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm));
    153:       /* update the trust radius based on the step length */
    154:       PetscCall(TaoBNKUpdateTrustRadius(tao, 0.0, 0.0, BNK_UPDATE_STEP, stepType, &stepAccepted));
    155:       /* count the accepted step type */
    156:       PetscCall(TaoBNKAddStepCounts(tao, stepType));
    157:       /* active BNCG recycling for next iteration */
    158:       PetscCall(TaoSetRecycleHistory(bnk->bncg, PETSC_TRUE));
    159:     }

    161:     /*  Check for termination */
    162:     PetscCall(VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W));
    163:     PetscCall(VecNorm(bnk->W, NORM_2, &resnorm));
    164:     PetscCheck(!PetscIsInfOrNanReal(resnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated infinity or NaN");
    165:     ++tao->niter;
    166:     PetscCall(TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its));
    167:     PetscCall(TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen));
    168:     PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
    169:   }
    170:   PetscFunctionReturn(PETSC_SUCCESS);
    171: }

    173: /*MC
    174:   TAOBNLS - Bounded Newton Line Search for nonlinear minimization with bound constraints.

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

    182:   Level: beginner

    184: .seealso: `Tao`, `TAONTR`, `TAONTL`, `TAONM`, `TAOCG`, `TaoType`, `TaoCreate()`
    185: M*/
    186: PETSC_EXTERN PetscErrorCode TaoCreate_BNLS(Tao tao)
    187: {
    188:   TAO_BNK *bnk;

    190:   PetscFunctionBegin;
    191:   PetscCall(TaoCreate_BNK(tao));
    192:   tao->ops->solve = TaoSolve_BNLS;

    194:   bnk              = (TAO_BNK *)tao->data;
    195:   bnk->init_type   = BNK_INIT_DIRECTION;
    196:   bnk->update_type = BNK_UPDATE_STEP; /* trust region updates based on line search step length */
    197:   PetscFunctionReturn(PETSC_SUCCESS);
    198: }