Date: 2022-08-02T03:15:13+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:     if needH
     20:       If max_cg_steps > 0
     21:         x_k, g_k, pg_k = TaoSolve(BNCG)
     22:       end

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

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

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

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

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

     85:     niter += 1
     86:     check convergence at pg_{k+1}
     87:  end
     88: */

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

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

    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:       (*tao->ops->update)(tao, tao->niter, tao->user_update);
    109:     }

    111:     if (needH && bnk->inactive_idx) {
    112:       /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
    113:       TaoBNKTakeCGSteps(tao, &cgTerminate);
    114:       if (cgTerminate) {
    115:         tao->reason = bnk->bncg->reason;
    116:         return 0;
    117:       }
    118:       /* Compute the hessian and update the BFGS preconditioner at the new iterate */
    119:       (*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:     (*bnk->computestep)(tao, shift, &ksp_reason, &stepType);
    125:     TaoBNKSafeguardStep(tao, ksp_reason, &stepType);

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

    133:     /* Trigger the line search */
    134:     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:       VecCopy(bnk->Xold, tao->solution);
    141:       VecCopy(bnk->Gold, tao->gradient);
    142:       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:       TaoBNKEstimateActiveSet(tao, bnk->as_type);
    150:       VecCopy(bnk->unprojected_gradient, tao->gradient);
    151:       VecISSet(tao->gradient, bnk->active_idx, 0.0);
    152:       TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);
    153:       /* update the trust radius based on the step length */
    154:       TaoBNKUpdateTrustRadius(tao, 0.0, 0.0, BNK_UPDATE_STEP, stepType, &stepAccepted);
    155:       /* count the accepted step type */
    156:       TaoBNKAddStepCounts(tao, stepType);
    157:       /* active BNCG recycling for next iteration */
    158:       TaoSetRecycleHistory(bnk->bncg, PETSC_TRUE);
    159:     }

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

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

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

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

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

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