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)
11: f_0, g_0= TaoComputeObjectiveAndGradient(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
70: g_{k+1} = TaoComputeGradient(x_{k+1})
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: /* Initialize the preconditioner, KSP solver and trust radius/line search */
101: tao->reason = TAO_CONTINUE_ITERATING;
102: TaoBNKInitialize(tao, bnk->init_type, &needH);
103: if (tao->reason != TAO_CONTINUE_ITERATING) return 0;
105: /* Have not converged; continue with Newton method */
106: while (tao->reason == TAO_CONTINUE_ITERATING) {
107: /* Call general purpose update function */
108: if (tao->ops->update) {
109: PetscUseTypeMethod(tao, update, tao->niter, tao->user_update);
110: TaoComputeObjectiveAndGradient(tao, tao->solution, &bnk->f, bnk->unprojected_gradient);
111: }
113: if (needH && bnk->inactive_idx) {
114: /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
115: TaoBNKTakeCGSteps(tao, &cgTerminate);
116: if (cgTerminate) {
117: tao->reason = bnk->bncg->reason;
118: return 0;
119: }
120: /* Compute the hessian and update the BFGS preconditioner at the new iterate */
121: (*bnk->computehessian)(tao);
122: needH = PETSC_FALSE;
123: }
125: /* Store current solution before it changes */
126: bnk->fold = bnk->f;
127: VecCopy(tao->solution, bnk->Xold);
128: VecCopy(tao->gradient, bnk->Gold);
129: VecCopy(bnk->unprojected_gradient, bnk->unprojected_gradient_old);
131: /* Enter into trust region loops */
132: stepAccepted = PETSC_FALSE;
133: while (!stepAccepted && tao->reason == TAO_CONTINUE_ITERATING) {
134: tao->ksp_its = 0;
136: /* Use the common BNK kernel to compute the Newton step (for inactive variables only) */
137: (*bnk->computestep)(tao, shift, &ksp_reason, &stepType);
139: /* Temporarily accept the step and project it into the bounds */
140: VecAXPY(tao->solution, 1.0, tao->stepdirection);
141: TaoBoundSolution(tao->solution, tao->XL, tao->XU, 0.0, &nDiff, tao->solution);
143: /* Check if the projection changed the step direction */
144: if (nDiff > 0) {
145: /* Projection changed the step, so we have to recompute the step and
146: the predicted reduction. Leave the trust radius unchanged. */
147: VecCopy(tao->solution, tao->stepdirection);
148: VecAXPY(tao->stepdirection, -1.0, bnk->Xold);
149: TaoBNKRecomputePred(tao, tao->stepdirection, &prered);
150: } else {
151: /* Step did not change, so we can just recover the pre-computed prediction */
152: KSPCGGetObjFcn(tao->ksp, &prered);
153: }
154: prered = -prered;
156: /* Compute the actual reduction and update the trust radius */
157: TaoComputeObjective(tao, tao->solution, &bnk->f);
159: actred = bnk->fold - bnk->f;
160: oldTrust = tao->trust;
161: TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted);
163: if (stepAccepted) {
164: /* Step is good, evaluate the gradient and flip the need-Hessian switch */
165: steplen = 1.0;
166: needH = PETSC_TRUE;
167: ++bnk->newt;
168: TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient);
169: TaoBNKEstimateActiveSet(tao, bnk->as_type);
170: VecCopy(bnk->unprojected_gradient, tao->gradient);
171: VecISSet(tao->gradient, bnk->active_idx, 0.0);
172: TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);
173: } else {
174: /* Step is bad, revert old solution and re-solve with new radius*/
175: steplen = 0.0;
176: needH = PETSC_FALSE;
177: bnk->f = bnk->fold;
178: VecCopy(bnk->Xold, tao->solution);
179: VecCopy(bnk->Gold, tao->gradient);
180: VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);
181: if (oldTrust == tao->trust) {
182: /* Can't change the radius anymore so just terminate */
183: tao->reason = TAO_DIVERGED_TR_REDUCTION;
184: }
185: }
186: }
187: /* Check for termination */
188: VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W);
189: VecNorm(bnk->W, NORM_2, &resnorm);
191: ++tao->niter;
192: TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its);
193: TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen);
194: PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
195: }
196: return 0;
197: }
199: /*------------------------------------------------------------*/
200: static PetscErrorCode TaoSetUp_BNTR(Tao tao)
201: {
202: KSP ksp;
203: PetscVoidFunction valid;
205: TaoSetUp_BNK(tao);
206: TaoGetKSP(tao, &ksp);
207: PetscObjectQueryFunction((PetscObject)ksp, "KSPCGSetRadius_C", &valid);
209: return 0;
210: }
212: /*------------------------------------------------------------*/
214: static PetscErrorCode TaoSetFromOptions_BNTR(Tao tao, PetscOptionItems *PetscOptionsObject)
215: {
216: TAO_BNK *bnk = (TAO_BNK *)tao->data;
218: TaoSetFromOptions_BNK(tao, PetscOptionsObject);
219: if (bnk->update_type == BNK_UPDATE_STEP) bnk->update_type = BNK_UPDATE_REDUCTION;
220: return 0;
221: }
223: /*------------------------------------------------------------*/
224: /*MC
225: TAOBNTR - Bounded Newton Trust Region for nonlinear minimization with bound constraints.
227: Options Database Keys:
228: + -tao_bnk_max_cg_its - maximum number of bounded conjugate-gradient iterations taken in each Newton loop
229: . -tao_bnk_init_type - trust radius initialization method ("constant", "direction", "interpolation")
230: . -tao_bnk_update_type - trust radius update method ("step", "direction", "interpolation")
231: - -tao_bnk_as_type - active-set estimation method ("none", "bertsekas")
233: Level: beginner
234: M*/
235: PETSC_EXTERN PetscErrorCode TaoCreate_BNTR(Tao tao)
236: {
237: TAO_BNK *bnk;
239: TaoCreate_BNK(tao);
240: tao->ops->solve = TaoSolve_BNTR;
241: tao->ops->setup = TaoSetUp_BNTR;
242: tao->ops->setfromoptions = TaoSetFromOptions_BNTR;
244: bnk = (TAO_BNK *)tao->data;
245: bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */
246: return 0;
247: }