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: }