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

 14:  x_0 = VecMedian(x_0)
 15:  f_0, g_0 = TaoComputeObjectiveAndGradient(x_0)
 16:  pg_0 = project(g_0)
 17:  check convergence at pg_0
 18:  needH = TaoBNKInitialize(default:BNK_INIT_INTERPOLATION)
 19:  niter = 0
 20:  step_accepted = true

 22:  while niter <= max_it
 23:     niter += 1

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

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

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

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

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

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

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

104:     check convergence at pg_{k+1}
105:  end
106: */

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

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

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

123:   /* Have not converged; continue with Newton method */
124:   while (tao->reason == TAO_CONTINUE_ITERATING) {
125:     /* Call general purpose update function */
126:     if (tao->ops->update) {
127:       PetscUseTypeMethod(tao, update, tao->niter, tao->user_update);
128:       TaoComputeObjectiveAndGradient(tao, tao->solution, &bnk->f, bnk->unprojected_gradient);
129:     }

131:     if (needH && bnk->inactive_idx) {
132:       /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
133:       TaoBNKTakeCGSteps(tao, &cgTerminate);
134:       if (cgTerminate) {
135:         tao->reason = bnk->bncg->reason;
136:         return 0;
137:       }
138:       /* Compute the hessian and update the BFGS preconditioner at the new iterate */
139:       (*bnk->computehessian)(tao);
140:       needH = PETSC_FALSE;
141:     }

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

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

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

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

170:     /* Compute the actual reduction and update the trust radius */
171:     TaoComputeObjective(tao, tao->solution, &bnk->f);
173:     actred = bnk->fold - bnk->f;
174:     TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted);

176:     if (stepAccepted) {
177:       /* Step is good, evaluate the gradient and the hessian */
178:       steplen = 1.0;
179:       needH   = PETSC_TRUE;
180:       ++bnk->newt;
181:       TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient);
182:       TaoBNKEstimateActiveSet(tao, bnk->as_type);
183:       VecCopy(bnk->unprojected_gradient, tao->gradient);
184:       VecISSet(tao->gradient, bnk->active_idx, 0.0);
185:       TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);
186:     } else {
187:       /* Trust-region rejected the step. Revert the solution. */
188:       bnk->f = bnk->fold;
189:       VecCopy(bnk->Xold, tao->solution);
190:       /* Trigger the line search */
191:       TaoBNKSafeguardStep(tao, ksp_reason, &stepType);
192:       TaoBNKPerformLineSearch(tao, &stepType, &steplen, &ls_reason);
193:       if (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER) {
194:         /* Line search failed, revert solution and terminate */
195:         stepAccepted = PETSC_FALSE;
196:         needH        = PETSC_FALSE;
197:         bnk->f       = bnk->fold;
198:         VecCopy(bnk->Xold, tao->solution);
199:         VecCopy(bnk->Gold, tao->gradient);
200:         VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);
201:         tao->trust  = 0.0;
202:         tao->reason = TAO_DIVERGED_LS_FAILURE;
203:       } else {
204:         /* new iterate so we need to recompute the Hessian */
205:         needH = PETSC_TRUE;
206:         /* compute the projected gradient */
207:         TaoBNKEstimateActiveSet(tao, bnk->as_type);
208:         VecCopy(bnk->unprojected_gradient, tao->gradient);
209:         VecISSet(tao->gradient, bnk->active_idx, 0.0);
210:         TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);
211:         /* Line search succeeded so we should update the trust radius based on the LS step length */
212:         tao->trust = oldTrust;
213:         TaoBNKUpdateTrustRadius(tao, prered, actred, BNK_UPDATE_STEP, stepType, &stepAccepted);
214:         /* count the accepted step type */
215:         TaoBNKAddStepCounts(tao, stepType);
216:       }
217:     }

219:     /*  Check for termination */
220:     VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W);
221:     VecNorm(bnk->W, NORM_2, &resnorm);
223:     ++tao->niter;
224:     TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its);
225:     TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen);
226:     PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
227:   }
228:   return 0;
229: }

231: /*------------------------------------------------------------*/
232: static PetscErrorCode TaoSetUp_BNTL(Tao tao)
233: {
234:   KSP               ksp;
235:   PetscVoidFunction valid;

237:   TaoSetUp_BNK(tao);
238:   TaoGetKSP(tao, &ksp);
239:   PetscObjectQueryFunction((PetscObject)ksp, "KSPCGSetRadius_C", &valid);
241:   return 0;
242: }

244: /*------------------------------------------------------------*/
245: static PetscErrorCode TaoSetFromOptions_BNTL(Tao tao, PetscOptionItems *PetscOptionsObject)
246: {
247:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

249:   TaoSetFromOptions_BNK(tao, PetscOptionsObject);
250:   if (bnk->update_type == BNK_UPDATE_STEP) bnk->update_type = BNK_UPDATE_REDUCTION;
251:   return 0;
252: }

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

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

265:   Level: beginner
266: M*/
267: PETSC_EXTERN PetscErrorCode TaoCreate_BNTL(Tao tao)
268: {
269:   TAO_BNK *bnk;

271:   TaoCreate_BNK(tao);
272:   tao->ops->solve          = TaoSolve_BNTL;
273:   tao->ops->setup          = TaoSetUp_BNTL;
274:   tao->ops->setfromoptions = TaoSetFromOptions_BNTL;

276:   bnk              = (TAO_BNK *)tao->data;
277:   bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */
278:   return 0;
279: }