Actual source code: bntl.c

petsc-master 2019-08-22
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  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.
  7:  
  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.
 11:  
 12:  ------------------------------------------------------------
 13:  
 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
 24:     
 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
 88:       
 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:   PetscErrorCode               ierr;
111:   TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
112:   KSPConvergedReason           ksp_reason;
113:   TaoLineSearchConvergedReason ls_reason;

115:   PetscReal                    oldTrust, prered, actred, steplen, resnorm;
116:   PetscBool                    cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_FALSE;
117:   PetscInt                     stepType, nDiff;
118: 
120:   /* Initialize the preconditioner, KSP solver and trust radius/line search */
121:   tao->reason = TAO_CONTINUE_ITERATING;
122:   TaoBNKInitialize(tao, bnk->init_type, &needH);
123:   if (tao->reason != TAO_CONTINUE_ITERATING) return(0);

125:   /* Have not converged; continue with Newton method */
126:   while (tao->reason == TAO_CONTINUE_ITERATING) {
127:     /* Call general purpose update function */
128:     if (tao->ops->update) {
129:       (*tao->ops->update)(tao, tao->niter, tao->user_update);
130:     }
131:     ++tao->niter;
132: 
133:     if (needH && bnk->inactive_idx) {
134:       /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
135:       TaoBNKTakeCGSteps(tao, &cgTerminate);
136:       if (cgTerminate) {
137:         tao->reason = bnk->bncg->reason;
138:         return(0);
139:       }
140:       /* Compute the hessian and update the BFGS preconditioner at the new iterate */
141:       (*bnk->computehessian)(tao);
142:       needH = PETSC_FALSE;
143:     }
144: 
145:     /* Use the common BNK kernel to compute the Newton step (for inactive variables only) */
146:     (*bnk->computestep)(tao, shift, &ksp_reason, &stepType);

148:     /* Store current solution before it changes */
149:     oldTrust = tao->trust;
150:     bnk->fold = bnk->f;
151:     VecCopy(tao->solution, bnk->Xold);
152:     VecCopy(tao->gradient, bnk->Gold);
153:     VecCopy(bnk->unprojected_gradient, bnk->unprojected_gradient_old);
154: 
155:     /* Temporarily accept the step and project it into the bounds */
156:     VecAXPY(tao->solution, 1.0, tao->stepdirection);
157:     TaoBoundSolution(tao->solution, tao->XL,tao->XU, 0.0, &nDiff, tao->solution);
158: 
159:     /* Check if the projection changed the step direction */
160:     if (nDiff > 0) {
161:       /* Projection changed the step, so we have to recompute the step and 
162:          the predicted reduction. Leave the trust radius unchanged. */
163:       VecCopy(tao->solution, tao->stepdirection);
164:       VecAXPY(tao->stepdirection, -1.0, bnk->Xold);
165:       TaoBNKRecomputePred(tao, tao->stepdirection, &prered);
166:     } else {
167:       /* Step did not change, so we can just recover the pre-computed prediction */
168:       KSPCGGetObjFcn(tao->ksp, &prered);
169:     }
170:     prered = -prered;
171: 
172:     /* Compute the actual reduction and update the trust radius */
173:     TaoComputeObjective(tao, tao->solution, &bnk->f);
174:     if (PetscIsInfOrNanReal(bnk->f)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
175:     actred = bnk->fold - bnk->f;
176:     TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted);
177: 
178:     if (stepAccepted) {
179:       /* Step is good, evaluate the gradient and the hessian */
180:       steplen = 1.0;
181:       needH = PETSC_TRUE;
182:       ++bnk->newt;
183:       TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient);
184:       TaoBNKEstimateActiveSet(tao, bnk->as_type);
185:       VecCopy(bnk->unprojected_gradient, tao->gradient);
186:       VecISSet(tao->gradient, bnk->active_idx, 0.0);
187:       TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);
188:     } else {
189:       /* Trust-region rejected the step. Revert the solution. */
190:       bnk->f = bnk->fold;
191:       VecCopy(bnk->Xold, tao->solution);
192:       /* Trigger the line search */
193:       TaoBNKSafeguardStep(tao, ksp_reason, &stepType);
194:       TaoBNKPerformLineSearch(tao, &stepType, &steplen, &ls_reason);
195:       if (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER) {
196:         /* Line search failed, revert solution and terminate */
197:         stepAccepted = PETSC_FALSE;
198:         needH = PETSC_FALSE;
199:         bnk->f = bnk->fold;
200:         VecCopy(bnk->Xold, tao->solution);
201:         VecCopy(bnk->Gold, tao->gradient);
202:         VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);
203:         tao->trust = 0.0;
204:         tao->reason = TAO_DIVERGED_LS_FAILURE;
205:       } else {
206:         /* new iterate so we need to recompute the Hessian */
207:         needH = PETSC_TRUE;
208:         /* compute the projected gradient */
209:         TaoBNKEstimateActiveSet(tao, bnk->as_type);
210:         VecCopy(bnk->unprojected_gradient, tao->gradient);
211:         VecISSet(tao->gradient, bnk->active_idx, 0.0);
212:         TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);
213:         /* Line search succeeded so we should update the trust radius based on the LS step length */
214:         tao->trust = oldTrust;
215:         TaoBNKUpdateTrustRadius(tao, prered, actred, BNK_UPDATE_STEP, stepType, &stepAccepted);
216:         /* count the accepted step type */
217:         TaoBNKAddStepCounts(tao, stepType);
218:       }
219:     }

221:     /*  Check for termination */
222:     VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W);
223:     VecNorm(bnk->W, NORM_2, &resnorm);
224:     if (PetscIsInfOrNanReal(resnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
225:     TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its);
226:     TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen);
227:     (*tao->ops->convergencetest)(tao, tao->cnvP);
228:   }
229:   return(0);
230: }

232: /*------------------------------------------------------------*/
233: static PetscErrorCode TaoSetFromOptions_BNTL(PetscOptionItems *PetscOptionsObject,Tao tao)
234: {
235:   TAO_BNK        *bnk = (TAO_BNK *)tao->data;

239:   TaoSetFromOptions_BNK(PetscOptionsObject, tao);
240:   if (bnk->update_type == BNK_UPDATE_STEP) bnk->update_type = BNK_UPDATE_REDUCTION;
241:   if (!bnk->is_nash && !bnk->is_stcg && !bnk->is_gltr) SETERRQ(PETSC_COMM_SELF,1,"Must use a trust-region CG method for KSP (KSPNASH, KSPSTCG, KSPGLTR)");
242:   return(0);
243: }

245: /*------------------------------------------------------------*/
246: /*MC
247:   TAOBNTL - Bounded Newton Trust Region method with line-search fall-back for nonlinear 
248:             minimization with bound constraints.

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

256:   Level: beginner
257: M*/
258: PETSC_EXTERN PetscErrorCode TaoCreate_BNTL(Tao tao)
259: {
260:   TAO_BNK        *bnk;
262: 
264:   TaoCreate_BNK(tao);
265:   tao->ops->solve=TaoSolve_BNTL;
266:   tao->ops->setfromoptions=TaoSetFromOptions_BNTL;
267: 
268:   bnk = (TAO_BNK *)tao->data;
269:   bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */
270:   return(0);
271: }