Actual source code: bntr.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:  ------------------------------------------------------------

10:  x_0 = VecMedian(x_0)
12:  pg_0 = project(g_0)
13:  check convergence at pg_0
14:  needH = TaoBNKInitialize(default:BNK_INIT_INTERPOLATION)
15:  niter = 0
16:  step_accepted = false

18:  while niter <= max_it

20:     if needH
21:       If max_cg_steps > 0
22:         x_k, g_k, pg_k = TaoSolve(BNCG)
23:       end

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

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

51:     generate the reduced system Hr_k dr_k = -gr_k for variables in IA
52:     if pc_type == BNK_PC_BFGS && scale_type == BNK_SCALE_PHESS
53:       D = VecMedian(1e-6, abs(diag(Hr_k)), 1e6)
54:       scale BFGS with VecReciprocal(D)
55:     end

57:     while !stepAccepted
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:       x_{k+1} = VecMedian(x_k + d_k)
62:       s = x_{k+1} - x_k
63:       prered = dot(s, 0.5*gr_k - Hr_k*s)
64:       f_{k+1} = TaoComputeObjective(x_{k+1})
65:       actred = f_k - f_{k+1}

67:       oldTrust = trust
68:       step_accepted, trust = TaoBNKUpdateTrustRadius(default: BNK_UPDATE_REDUCTION)
69:       if step_accepted
71:         pg_{k+1} = project(g_{k+1})
72:         count the accepted Newton step
73:         needH = True
74:       else
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:         if trust == oldTrust
80:           terminate because we cannot shrink the radius any further
81:         end
82:       end

84:     end
85:     check convergence at pg_{k+1}
86:     niter += 1

88:  end
89: */

91: PetscErrorCode TaoSolve_BNTR(Tao tao)
92: {
93:   TAO_BNK           *bnk = (TAO_BNK *)tao->data;
94:   KSPConvergedReason ksp_reason;

96:   PetscReal oldTrust, prered, actred, steplen = 0.0, resnorm;
97:   PetscBool cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_FALSE;
98:   PetscInt  stepType, nDiff;

100:   PetscFunctionBegin;
101:   /* Initialize the preconditioner, KSP solver and trust radius/line search */
102:   tao->reason = TAO_CONTINUE_ITERATING;
103:   PetscCall(TaoBNKInitialize(tao, bnk->init_type, &needH));
104:   if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(PETSC_SUCCESS);

106:   /* Have not converged; continue with Newton method */
107:   while (tao->reason == TAO_CONTINUE_ITERATING) {
108:     /* Call general purpose update function */
109:     if (tao->ops->update) {
110:       PetscUseTypeMethod(tao, update, tao->niter, tao->user_update);
112:     }

114:     if (needH && bnk->inactive_idx) {
115:       /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
116:       PetscCall(TaoBNKTakeCGSteps(tao, &cgTerminate));
117:       if (cgTerminate) {
118:         tao->reason = bnk->bncg->reason;
119:         PetscFunctionReturn(PETSC_SUCCESS);
120:       }
121:       /* Compute the hessian and update the BFGS preconditioner at the new iterate */
122:       PetscCall((*bnk->computehessian)(tao));
123:       needH = PETSC_FALSE;
124:     }

126:     /* Store current solution before it changes */
127:     bnk->fold = bnk->f;
128:     PetscCall(VecCopy(tao->solution, bnk->Xold));

132:     /* Enter into trust region loops */
133:     stepAccepted = PETSC_FALSE;
134:     while (!stepAccepted && tao->reason == TAO_CONTINUE_ITERATING) {
135:       tao->ksp_its = 0;

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

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

144:       /* Check if the projection changed the step direction */
145:       if (nDiff > 0) {
146:         /* Projection changed the step, so we have to recompute the step and
147:            the predicted reduction. Leave the trust radius unchanged. */
148:         PetscCall(VecCopy(tao->solution, tao->stepdirection));
149:         PetscCall(VecAXPY(tao->stepdirection, -1.0, bnk->Xold));
150:         PetscCall(TaoBNKRecomputePred(tao, tao->stepdirection, &prered));
151:       } else {
152:         /* Step did not change, so we can just recover the pre-computed prediction */
153:         PetscCall(KSPCGGetObjFcn(tao->ksp, &prered));
154:       }
155:       prered = -prered;

157:       /* Compute the actual reduction and update the trust radius */
158:       PetscCall(TaoComputeObjective(tao, tao->solution, &bnk->f));
159:       PetscCheck(!PetscIsInfOrNanReal(bnk->f), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
160:       actred   = bnk->fold - bnk->f;
161:       oldTrust = tao->trust;
162:       PetscCall(TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted));

164:       if (stepAccepted) {
165:         /* Step is good, evaluate the gradient and flip the need-Hessian switch */
166:         steplen = 1.0;
167:         needH   = PETSC_TRUE;
168:         ++bnk->newt;
170:         PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
172:         if (bnk->active_idx) PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
174:       } else {
175:         /* Step is bad, revert old solution and re-solve with new radius*/
176:         steplen = 0.0;
177:         needH   = PETSC_FALSE;
178:         bnk->f  = bnk->fold;
179:         PetscCall(VecCopy(bnk->Xold, tao->solution));
182:         if (oldTrust == tao->trust) {
183:           /* Can't change the radius anymore so just terminate */
184:           tao->reason = TAO_DIVERGED_TR_REDUCTION;
185:         }
186:       }
187:     }
188:     /*  Check for termination */
189:     PetscCall(VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W));
190:     PetscCall(VecNorm(bnk->W, NORM_2, &resnorm));
191:     PetscCheck(!PetscIsInfOrNanReal(resnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
192:     ++tao->niter;
193:     PetscCall(TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its));
194:     PetscCall(TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen));
195:     PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
196:   }
197:   PetscFunctionReturn(PETSC_SUCCESS);
198: }

200: /*------------------------------------------------------------*/
201: static PetscErrorCode TaoSetUp_BNTR(Tao tao)
202: {
203:   KSP          ksp;
204:   PetscVoidFn *valid;

206:   PetscFunctionBegin;
207:   PetscCall(TaoSetUp_BNK(tao));
208:   PetscCall(TaoGetKSP(tao, &ksp));
210:   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);
211:   PetscFunctionReturn(PETSC_SUCCESS);
212: }

214: /*------------------------------------------------------------*/

216: static PetscErrorCode TaoSetFromOptions_BNTR(Tao tao, PetscOptionItems *PetscOptionsObject)
217: {
218:   TAO_BNK *bnk = (TAO_BNK *)tao->data;

220:   PetscFunctionBegin;
221:   PetscCall(TaoSetFromOptions_BNK(tao, PetscOptionsObject));
222:   if (bnk->update_type == BNK_UPDATE_STEP) bnk->update_type = BNK_UPDATE_REDUCTION;
223:   PetscFunctionReturn(PETSC_SUCCESS);
224: }

226: /*------------------------------------------------------------*/
227: /*MC
228:   TAOBNTR - Bounded Newton Trust Region for nonlinear minimization with bound constraints.

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

236:   Level: beginner
237: M*/
238: PETSC_EXTERN PetscErrorCode TaoCreate_BNTR(Tao tao)
239: {
240:   TAO_BNK *bnk;

242:   PetscFunctionBegin;
243:   PetscCall(TaoCreate_BNK(tao));
244:   tao->ops->solve          = TaoSolve_BNTR;
245:   tao->ops->setup          = TaoSetUp_BNTR;
246:   tao->ops->setfromoptions = TaoSetFromOptions_BNTR;

248:   bnk              = (TAO_BNK *)tao->data;
249:   bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */
250:   PetscFunctionReturn(PETSC_SUCCESS);
251: }
```