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

124:   /* Have not converged; continue with Newton method */
125:   while (tao->reason == TAO_CONTINUE_ITERATING) {
126:     /* Call general purpose update function */
127:     if (tao->ops->update) {
128:       PetscUseTypeMethod(tao, update, tao->niter, tao->user_update);
129:       PetscCall(TaoComputeObjective(tao, tao->solution, &bnk->f));
130:     }

132:     if (needH && bnk->inactive_idx) {
133:       /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
134:       PetscCall(TaoBNKTakeCGSteps(tao, &cgTerminate));
135:       if (cgTerminate) {
136:         tao->reason = bnk->bncg->reason;
137:         PetscFunctionReturn(PETSC_SUCCESS);
138:       }
139:       /* Compute the hessian and update the BFGS preconditioner at the new iterate */
140:       PetscCall((*bnk->computehessian)(tao));
141:       needH = PETSC_FALSE;
142:     }

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

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

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

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

171:     /* Compute the actual reduction and update the trust radius */
172:     PetscCall(TaoComputeObjective(tao, tao->solution, &bnk->f));
173:     PetscCheck(!PetscIsInfOrNanReal(bnk->f), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
174:     actred = bnk->fold - bnk->f;
175:     PetscCall(TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted));

177:     if (stepAccepted) {
178:       /* Step is good, evaluate the gradient and the hessian */
179:       steplen = 1.0;
180:       needH   = PETSC_TRUE;
181:       ++bnk->newt;
182:       PetscCall(TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient));
183:       PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
184:       PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient));
185:       if (bnk->active_idx) PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
186:       PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm));
187:     } else {
188:       /* Trust-region rejected the step. Revert the solution. */
189:       bnk->f = bnk->fold;
190:       PetscCall(VecCopy(bnk->Xold, tao->solution));
191:       /* Trigger the line search */
192:       PetscCall(TaoBNKSafeguardStep(tao, ksp_reason, &stepType));
193:       PetscCall(TaoBNKPerformLineSearch(tao, &stepType, &steplen, &ls_reason));
194:       if (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER) {
195:         /* Line search failed, revert solution and terminate */
196:         stepAccepted = PETSC_FALSE;
197:         needH        = PETSC_FALSE;
198:         bnk->f       = bnk->fold;
199:         PetscCall(VecCopy(bnk->Xold, tao->solution));
200:         PetscCall(VecCopy(bnk->Gold, tao->gradient));
201:         PetscCall(VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient));
202:         tao->trust  = 0.0;
203:         tao->reason = TAO_DIVERGED_LS_FAILURE;
204:       } else {
205:         /* new iterate so we need to recompute the Hessian */
206:         needH = PETSC_TRUE;
207:         /* compute the projected gradient */
208:         PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
209:         PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient));
210:         if (bnk->active_idx) PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
211:         PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm));
212:         /* Line search succeeded so we should update the trust radius based on the LS step length */
213:         tao->trust = oldTrust;
214:         PetscCall(TaoBNKUpdateTrustRadius(tao, prered, actred, BNK_UPDATE_STEP, stepType, &stepAccepted));
215:         /* count the accepted step type */
216:         PetscCall(TaoBNKAddStepCounts(tao, stepType));
217:       }
218:     }

220:     /*  Check for termination */
221:     PetscCall(VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W));
222:     PetscCall(VecNorm(bnk->W, NORM_2, &resnorm));
223:     PetscCheck(!PetscIsInfOrNanReal(resnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
224:     ++tao->niter;
225:     PetscCall(TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its));
226:     PetscCall(TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen));
227:     PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
228:   }
229:   PetscFunctionReturn(PETSC_SUCCESS);
230: }

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

238:   PetscFunctionBegin;
239:   PetscCall(TaoSetUp_BNK(tao));
240:   PetscCall(TaoGetKSP(tao, &ksp));
241:   PetscCall(PetscObjectQueryFunction((PetscObject)ksp, "KSPCGSetRadius_C", &valid));
242:   PetscCheck(valid, PetscObjectComm((PetscObject)tao), PETSC_ERR_SUP, "Not for KSP type %s. Must use a trust-region CG method for KSP (e.g. KSPNASH, KSPSTCG, KSPGLTR)", ((PetscObject)ksp)->type_name);
243:   PetscFunctionReturn(PETSC_SUCCESS);
244: }

246: /*------------------------------------------------------------*/
247: static PetscErrorCode TaoSetFromOptions_BNTL(Tao tao, PetscOptionItems *PetscOptionsObject)
248: {
249:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

251:   PetscFunctionBegin;
252:   PetscCall(TaoSetFromOptions_BNK(tao, PetscOptionsObject));
253:   if (bnk->update_type == BNK_UPDATE_STEP) bnk->update_type = BNK_UPDATE_REDUCTION;
254:   PetscFunctionReturn(PETSC_SUCCESS);
255: }

257: /*------------------------------------------------------------*/
258: /*MC
259:   TAOBNTL - Bounded Newton Trust Region method with line-search fall-back for nonlinear
260:             minimization with bound constraints.

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

268:   Level: beginner
269: M*/
270: PETSC_EXTERN PetscErrorCode TaoCreate_BNTL(Tao tao)
271: {
272:   TAO_BNK *bnk;

274:   PetscFunctionBegin;
275:   PetscCall(TaoCreate_BNK(tao));
276:   tao->ops->solve          = TaoSolve_BNTL;
277:   tao->ops->setup          = TaoSetUp_BNTL;
278:   tao->ops->setfromoptions = TaoSetFromOptions_BNTL;

280:   bnk              = (TAO_BNK *)tao->data;
281:   bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */
282:   PetscFunctionReturn(PETSC_SUCCESS);
283: }