Actual source code: bnls.c
1: #include <../src/tao/bound/impls/bnk/bnk.h>
2: #include <petscksp.h>
4: /*
5: Implements Newton's Method with a line search approach for
6: solving 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_DIRECTION)
15: niter = 0
16: step_accepted = true
18: while niter < max_it
19: if needH
20: If max_cg_steps > 0
21: x_k, g_k, pg_k = TaoSolve(BNCG)
22: end
24: H_k = TaoComputeHessian(x_k)
25: if pc_type == BNK_PC_BFGS
26: add correction to BFGS approx
27: if scale_type == BNK_SCALE_AHESS
28: D = VecMedian(1e-6, abs(diag(H_k)), 1e6)
29: scale BFGS with VecReciprocal(D)
30: end
31: end
32: needH = False
33: end
35: if pc_type = BNK_PC_BFGS
36: B_k = BFGS
37: else
38: B_k = VecMedian(1e-6, abs(diag(H_k)), 1e6)
39: B_k = VecReciprocal(B_k)
40: end
41: w = x_k - VecMedian(x_k - 0.001*B_k*g_k)
42: eps = min(eps, norm2(w))
43: determine the active and inactive index sets such that
44: L = {i : (x_k)_i <= l_i + eps && (g_k)_i > 0}
45: U = {i : (x_k)_i >= u_i - eps && (g_k)_i < 0}
46: F = {i : l_i = (x_k)_i = u_i}
47: A = {L + U + F}
48: IA = {i : i not in A}
50: generate the reduced system Hr_k dr_k = -gr_k for variables in IA
51: if p > 0
52: Hr_k += p*
53: end
54: if pc_type == BNK_PC_BFGS && scale_type == BNK_SCALE_PHESS
55: D = VecMedian(1e-6, abs(diag(Hr_k)), 1e6)
56: scale BFGS with VecReciprocal(D)
57: end
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: if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
62: dr_k = -BFGS*gr_k for variables in I
63: if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
64: reset the BFGS preconditioner
65: calculate scale delta and apply it to BFGS
66: dr_k = -BFGS*gr_k for variables in I
67: if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
68: dr_k = -gr_k for variables in I
69: end
70: end
71: end
73: x_{k+1}, f_{k+1}, g_{k+1}, ls_failed = TaoBNKPerformLineSearch()
74: if ls_failed
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: terminate
80: else
81: pg_{k+1} = project(g_{k+1})
82: count the accepted step type (Newton, BFGS, scaled grad or grad)
83: end
85: niter += 1
86: check convergence at pg_{k+1}
87: end
88: */
90: PetscErrorCode TaoSolve_BNLS(Tao tao)
91: {
92: TAO_BNK *bnk = (TAO_BNK *)tao->data;
93: KSPConvergedReason ksp_reason;
94: TaoLineSearchConvergedReason ls_reason;
95: PetscReal steplen = 1.0, resnorm;
96: PetscBool cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_TRUE;
97: PetscInt stepType;
99: /* Initialize the preconditioner, KSP solver and trust radius/line search */
100: tao->reason = TAO_CONTINUE_ITERATING;
101: TaoBNKInitialize(tao, bnk->init_type, &needH);
102: if (tao->reason != TAO_CONTINUE_ITERATING) return 0;
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: (*tao->ops->update)(tao, tao->niter, tao->user_update);
109: }
111: if (needH && bnk->inactive_idx) {
112: /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
113: TaoBNKTakeCGSteps(tao, &cgTerminate);
114: if (cgTerminate) {
115: tao->reason = bnk->bncg->reason;
116: return 0;
117: }
118: /* Compute the hessian and update the BFGS preconditioner at the new iterate */
119: (*bnk->computehessian)(tao);
120: needH = PETSC_FALSE;
121: }
123: /* Use the common BNK kernel to compute the safeguarded Newton step (for inactive variables only) */
124: (*bnk->computestep)(tao, shift, &ksp_reason, &stepType);
125: TaoBNKSafeguardStep(tao, ksp_reason, &stepType);
127: /* Store current solution before it changes */
128: bnk->fold = bnk->f;
129: VecCopy(tao->solution, bnk->Xold);
130: VecCopy(tao->gradient, bnk->Gold);
131: VecCopy(bnk->unprojected_gradient, bnk->unprojected_gradient_old);
133: /* Trigger the line search */
134: TaoBNKPerformLineSearch(tao, &stepType, &steplen, &ls_reason);
136: if (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER) {
137: /* Failed to find an improving point */
138: needH = PETSC_FALSE;
139: bnk->f = bnk->fold;
140: VecCopy(bnk->Xold, tao->solution);
141: VecCopy(bnk->Gold, tao->gradient);
142: VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);
143: steplen = 0.0;
144: tao->reason = TAO_DIVERGED_LS_FAILURE;
145: } else {
146: /* new iterate so we need to recompute the Hessian */
147: needH = PETSC_TRUE;
148: /* compute the projected gradient */
149: TaoBNKEstimateActiveSet(tao, bnk->as_type);
150: VecCopy(bnk->unprojected_gradient, tao->gradient);
151: VecISSet(tao->gradient, bnk->active_idx, 0.0);
152: TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);
153: /* update the trust radius based on the step length */
154: TaoBNKUpdateTrustRadius(tao, 0.0, 0.0, BNK_UPDATE_STEP, stepType, &stepAccepted);
155: /* count the accepted step type */
156: TaoBNKAddStepCounts(tao, stepType);
157: /* active BNCG recycling for next iteration */
158: TaoSetRecycleHistory(bnk->bncg, PETSC_TRUE);
159: }
161: /* Check for termination */
162: VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W);
163: VecNorm(bnk->W, NORM_2, &resnorm);
165: ++tao->niter;
166: TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its);
167: TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen);
168: (*tao->ops->convergencetest)(tao, tao->cnvP);
169: }
170: return 0;
171: }
173: /*------------------------------------------------------------*/
174: /*MC
175: TAOBNLS - Bounded Newton Line Search for nonlinear minimization with bound constraints.
177: Options Database Keys:
178: + -tao_bnk_max_cg_its - maximum number of bounded conjugate-gradient iterations taken in each Newton loop
179: . -tao_bnk_init_type - trust radius initialization method ("constant", "direction", "interpolation")
180: . -tao_bnk_update_type - trust radius update method ("step", "direction", "interpolation")
181: - -tao_bnk_as_type - active-set estimation method ("none", "bertsekas")
183: Level: beginner
184: M*/
185: PETSC_EXTERN PetscErrorCode TaoCreate_BNLS(Tao tao)
186: {
187: TAO_BNK *bnk;
189: TaoCreate_BNK(tao);
190: tao->ops->solve = TaoSolve_BNLS;
192: bnk = (TAO_BNK *)tao->data;
193: bnk->init_type = BNK_INIT_DIRECTION;
194: bnk->update_type = BNK_UPDATE_STEP; /* trust region updates based on line search step length */
195: return 0;
196: }