Date: 2022-03-31T04:49:02+00:00

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:  ------------------------------------------------------------

     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_DIRECTION)
     15:  niter = 0
     16:  step_accepted = true

     18:  while niter < max_it
     19:     niter += 1

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

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

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

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

     63:     if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
     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:         reset the BFGS preconditioner
     67:         calculate scale delta and apply it to BFGS
     68:         dr_k = -BFGS*gr_k for variables in I
     69:         if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
     70:           dr_k = -gr_k for variables in I
     71:         end
     72:       end
     73:     end

     75:     x_{k+1}, f_{k+1}, g_{k+1}, ls_failed = TaoBNKPerformLineSearch()
     76:     if ls_failed
     77:       f_{k+1} = f_k
     78:       x_{k+1} = x_k
     79:       g_{k+1} = g_k
     80:       pg_{k+1} = pg_k
     81:       terminate
     82:     else
     83:       pg_{k+1} = project(g_{k+1})
     84:       count the accepted step type (Newton, BFGS, scaled grad or grad)
     85:     end

     87:     check convergence at pg_{k+1}
     88:  end
     89: */

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

    100:   /* Initialize the preconditioner, KSP solver and trust radius/line search */
    101:   tao->reason = TAO_CONTINUE_ITERATING;
    102:   TaoBNKInitialize(tao, bnk->init_type, &needH);
    103:   if (tao->reason != TAO_CONTINUE_ITERATING) return 0;

    105:   /* Have not converged; continue with Newton method */
    106:   while (tao->reason == TAO_CONTINUE_ITERATING) {
    107:     /* Call general purpose update function */
    108:     if (tao->ops->update) {
    109:       (*tao->ops->update)(tao, tao->niter, tao->user_update);
    110:     }
    111:     ++tao->niter;

    113:     if (needH && bnk->inactive_idx) {
    114:       /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
    115:       TaoBNKTakeCGSteps(tao, &cgTerminate);
    116:       if (cgTerminate) {
    117:         tao->reason = bnk->bncg->reason;
    118:         return 0;
    119:       }
    120:       /* Compute the hessian and update the BFGS preconditioner at the new iterate */
    121:       (*bnk->computehessian)(tao);
    122:       needH = PETSC_FALSE;
    123:     }

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

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

    135:     /* Trigger the line search */
    136:     TaoBNKPerformLineSearch(tao, &stepType, &steplen, &ls_reason);

    138:     if (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER) {
    139:       /* Failed to find an improving point */
    140:       needH = PETSC_FALSE;
    141:       bnk->f = bnk->fold;
    142:       VecCopy(bnk->Xold, tao->solution);
    143:       VecCopy(bnk->Gold, tao->gradient);
    144:       VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);
    145:       steplen = 0.0;
    146:       tao->reason = TAO_DIVERGED_LS_FAILURE;
    147:     } else {
    148:       /* new iterate so we need to recompute the Hessian */
    149:       needH = PETSC_TRUE;
    150:       /* compute the projected gradient */
    151:       TaoBNKEstimateActiveSet(tao, bnk->as_type);
    152:       VecCopy(bnk->unprojected_gradient, tao->gradient);
    153:       VecISSet(tao->gradient, bnk->active_idx, 0.0);
    154:       TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);
    155:       /* update the trust radius based on the step length */
    156:       TaoBNKUpdateTrustRadius(tao, 0.0, 0.0, BNK_UPDATE_STEP, stepType, &stepAccepted);
    157:       /* count the accepted step type */
    158:       TaoBNKAddStepCounts(tao, stepType);
    159:       /* active BNCG recycling for next iteration */
    160:       TaoSetRecycleHistory(bnk->bncg, PETSC_TRUE);
    161:     }

    163:     /*  Check for termination */
    164:     VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W);
    165:     VecNorm(bnk->W, NORM_2, &resnorm);
    167:     TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its);
    168:     TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen);
    169:     (*tao->ops->convergencetest)(tao, tao->cnvP);
    170:   }
    171:   return 0;
    172: }

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

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

    184:   Level: beginner
    185: M*/
    186: PETSC_EXTERN PetscErrorCode TaoCreate_BNLS(Tao tao)
    187: {
    188:   TAO_BNK        *bnk;

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

    193:   bnk = (TAO_BNK *)tao->data;
    194:   bnk->init_type = BNK_INIT_DIRECTION;
    195:   bnk->update_type = BNK_UPDATE_STEP; /* trust region updates based on line search step length */
    196:   return 0;
    197: }