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: x_0 = VecMedian(x_0)
9: f_0, g_0= TaoComputeObjectiveAndGradient(x_0)
10: pg_0 = project(g_0)
11: check convergence at pg_0
12: needH = TaoBNKInitialize(default:BNK_INIT_INTERPOLATION)
13: niter = 0
14: step_accepted = false
16: while niter <= max_it
18: if needH
19: If max_cg_steps > 0
20: x_k, g_k, pg_k = TaoSolve(BNCG)
21: end
23: H_k = TaoComputeHessian(x_k)
24: if pc_type == BNK_PC_BFGS
25: add correction to BFGS approx
26: if scale_type == BNK_SCALE_AHESS
27: D = VecMedian(1e-6, abs(diag(H_k)), 1e6)
28: scale BFGS with VecReciprocal(D)
29: end
30: end
31: needH = False
32: end
34: if pc_type = BNK_PC_BFGS
35: B_k = BFGS
36: else
37: B_k = VecMedian(1e-6, abs(diag(H_k)), 1e6)
38: B_k = VecReciprocal(B_k)
39: end
40: w = x_k - VecMedian(x_k - 0.001*B_k*g_k)
41: eps = min(eps, norm2(w))
42: determine the active and inactive index sets such that
43: L = {i : (x_k)_i <= l_i + eps && (g_k)_i > 0}
44: U = {i : (x_k)_i >= u_i - eps && (g_k)_i < 0}
45: F = {i : l_i = (x_k)_i = u_i}
46: A = {L + U + F}
47: IA = {i : i not in A}
49: generate the reduced system Hr_k dr_k = -gr_k for variables in IA
50: if pc_type == BNK_PC_BFGS && scale_type == BNK_SCALE_PHESS
51: D = VecMedian(1e-6, abs(diag(Hr_k)), 1e6)
52: scale BFGS with VecReciprocal(D)
53: end
55: while !stepAccepted
56: solve Hr_k dr_k = -gr_k
57: set d_k to (l - x) for variables in L, (u - x) for variables in U, and 0 for variables in F
59: x_{k+1} = VecMedian(x_k + d_k)
60: s = x_{k+1} - x_k
61: prered = dot(s, 0.5*gr_k - Hr_k*s)
62: f_{k+1} = TaoComputeObjective(x_{k+1})
63: actred = f_k - f_{k+1}
65: oldTrust = trust
66: step_accepted, trust = TaoBNKUpdateTrustRadius(default: BNK_UPDATE_REDUCTION)
67: if step_accepted
68: g_{k+1} = TaoComputeGradient(x_{k+1})
69: pg_{k+1} = project(g_{k+1})
70: count the accepted Newton step
71: needH = True
72: else
73: f_{k+1} = f_k
74: x_{k+1} = x_k
75: g_{k+1} = g_k
76: pg_{k+1} = pg_k
77: if trust == oldTrust
78: terminate because we cannot shrink the radius any further
79: end
80: end
82: end
83: check convergence at pg_{k+1}
84: niter += 1
86: end
87: */
89: PetscErrorCode TaoSolve_BNTR(Tao tao)
90: {
91: TAO_BNK *bnk = (TAO_BNK *)tao->data;
92: KSPConvergedReason ksp_reason;
94: PetscReal oldTrust, prered, actred, steplen = 0.0, resnorm;
95: PetscBool cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_FALSE;
96: PetscInt stepType, nDiff;
98: PetscFunctionBegin;
99: /* Initialize the preconditioner, KSP solver and trust radius/line search */
100: tao->reason = TAO_CONTINUE_ITERATING;
101: PetscCall(TaoBNKInitialize(tao, bnk->init_type, &needH));
102: if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(PETSC_SUCCESS);
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: PetscUseTypeMethod(tao, update, tao->niter, tao->user_update);
109: PetscCall(TaoComputeObjective(tao, tao->solution, &bnk->f));
110: }
112: if (needH && bnk->inactive_idx) {
113: /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
114: PetscCall(TaoBNKTakeCGSteps(tao, &cgTerminate));
115: if (cgTerminate) {
116: tao->reason = bnk->bncg->reason;
117: PetscFunctionReturn(PETSC_SUCCESS);
118: }
119: /* Compute the hessian and update the BFGS preconditioner at the new iterate */
120: PetscCall((*bnk->computehessian)(tao));
121: needH = PETSC_FALSE;
122: }
124: /* Store current solution before it changes */
125: bnk->fold = bnk->f;
126: PetscCall(VecCopy(tao->solution, bnk->Xold));
127: PetscCall(VecCopy(tao->gradient, bnk->Gold));
128: PetscCall(VecCopy(bnk->unprojected_gradient, bnk->unprojected_gradient_old));
130: /* Enter into trust region loops */
131: stepAccepted = PETSC_FALSE;
132: while (!stepAccepted && tao->reason == TAO_CONTINUE_ITERATING) {
133: tao->ksp_its = 0;
135: /* Use the common BNK kernel to compute the Newton step (for inactive variables only) */
136: PetscCall((*bnk->computestep)(tao, shift, &ksp_reason, &stepType));
138: /* Temporarily accept the step and project it into the bounds */
139: PetscCall(VecAXPY(tao->solution, 1.0, tao->stepdirection));
140: PetscCall(TaoBoundSolution(tao->solution, tao->XL, tao->XU, 0.0, &nDiff, tao->solution));
142: /* Check if the projection changed the step direction */
143: if (nDiff > 0) {
144: /* Projection changed the step, so we have to recompute the step and
145: the predicted reduction. Leave the trust radius unchanged. */
146: PetscCall(VecCopy(tao->solution, tao->stepdirection));
147: PetscCall(VecAXPY(tao->stepdirection, -1.0, bnk->Xold));
148: PetscCall(TaoBNKRecomputePred(tao, tao->stepdirection, &prered));
149: } else {
150: /* Step did not change, so we can just recover the pre-computed prediction */
151: PetscCall(KSPCGGetObjFcn(tao->ksp, &prered));
152: }
153: prered = -prered;
155: /* Compute the actual reduction and update the trust radius */
156: PetscCall(TaoComputeObjective(tao, tao->solution, &bnk->f));
157: PetscCheck(!PetscIsInfOrNanReal(bnk->f), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated infinity or NaN");
158: actred = bnk->fold - bnk->f;
159: oldTrust = tao->trust;
160: PetscCall(TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted));
162: if (stepAccepted) {
163: /* Step is good, evaluate the gradient and flip the need-Hessian switch */
164: steplen = 1.0;
165: needH = PETSC_TRUE;
166: ++bnk->newt;
167: PetscCall(TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient));
168: PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
169: PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient));
170: if (bnk->active_idx) PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
171: PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm));
172: } else {
173: /* Step is bad, revert old solution and re-solve with new radius*/
174: steplen = 0.0;
175: needH = PETSC_FALSE;
176: bnk->f = bnk->fold;
177: PetscCall(VecCopy(bnk->Xold, tao->solution));
178: PetscCall(VecCopy(bnk->Gold, tao->gradient));
179: PetscCall(VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient));
180: if (oldTrust == tao->trust) {
181: /* Can't change the radius anymore so just terminate */
182: tao->reason = TAO_DIVERGED_TR_REDUCTION;
183: }
184: }
185: }
186: /* Check for termination */
187: PetscCall(VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W));
188: PetscCall(VecNorm(bnk->W, NORM_2, &resnorm));
189: PetscCheck(!PetscIsInfOrNanReal(resnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated infinity or NaN");
190: ++tao->niter;
191: PetscCall(TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its));
192: PetscCall(TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen));
193: PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
194: }
195: PetscFunctionReturn(PETSC_SUCCESS);
196: }
198: static PetscErrorCode TaoSetUp_BNTR(Tao tao)
199: {
200: KSP ksp;
201: PetscBool valid;
203: PetscFunctionBegin;
204: PetscCall(TaoSetUp_BNK(tao));
205: PetscCall(TaoGetKSP(tao, &ksp));
206: PetscCall(PetscObjectHasFunction((PetscObject)ksp, "KSPCGSetRadius_C", &valid));
207: 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);
208: PetscFunctionReturn(PETSC_SUCCESS);
209: }
211: static PetscErrorCode TaoSetFromOptions_BNTR(Tao tao, PetscOptionItems PetscOptionsObject)
212: {
213: TAO_BNK *bnk = (TAO_BNK *)tao->data;
215: PetscFunctionBegin;
216: PetscCall(TaoSetFromOptions_BNK(tao, PetscOptionsObject));
217: if (bnk->update_type == BNK_UPDATE_STEP) bnk->update_type = BNK_UPDATE_REDUCTION;
218: PetscFunctionReturn(PETSC_SUCCESS);
219: }
221: /*MC
222: TAOBNTR - Bounded Newton Trust Region for nonlinear minimization with bound constraints.
224: Options Database Keys:
225: + -tao_bnk_max_cg_its - maximum number of bounded conjugate-gradient iterations taken in each Newton loop
226: . -tao_bnk_init_type - trust radius initialization method ("constant", "direction", "interpolation")
227: . -tao_bnk_update_type - trust radius update method ("step", "direction", "interpolation")
228: - -tao_bnk_as_type - active-set estimation method ("none", "bertsekas")
230: Level: beginner
231: M*/
232: PETSC_EXTERN PetscErrorCode TaoCreate_BNTR(Tao tao)
233: {
234: TAO_BNK *bnk;
236: PetscFunctionBegin;
237: PetscCall(TaoCreate_BNK(tao));
238: tao->ops->solve = TaoSolve_BNTR;
239: tao->ops->setup = TaoSetUp_BNTR;
240: tao->ops->setfromoptions = TaoSetFromOptions_BNTR;
242: bnk = (TAO_BNK *)tao->data;
243: bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */
244: PetscFunctionReturn(PETSC_SUCCESS);
245: }