Actual source code: bntl.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: 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.
12: x_0 = VecMedian(x_0)
13: f_0, g_0 = TaoComputeObjectiveAndGradient(x_0)
14: pg_0 = project(g_0)
15: check convergence at pg_0
16: needH = TaoBNKInitialize(default:BNK_INIT_INTERPOLATION)
17: niter = 0
18: step_accepted = true
20: while niter <= max_it
21: niter += 1
23: if needH
24: If max_cg_steps > 0
25: x_k, g_k, pg_k = TaoSolve(BNCG)
26: end
28: H_k = TaoComputeHessian(x_k)
29: if pc_type == BNK_PC_BFGS
30: add correction to BFGS approx
31: if scale_type == BNK_SCALE_AHESS
32: D = VecMedian(1e-6, abs(diag(H_k)), 1e6)
33: scale BFGS with VecReciprocal(D)
34: end
35: end
36: needH = False
37: end
39: if pc_type = BNK_PC_BFGS
40: B_k = BFGS
41: else
42: B_k = VecMedian(1e-6, abs(diag(H_k)), 1e6)
43: B_k = VecReciprocal(B_k)
44: end
45: w = x_k - VecMedian(x_k - 0.001*B_k*g_k)
46: eps = min(eps, norm2(w))
47: determine the active and inactive index sets such that
48: L = {i : (x_k)_i <= l_i + eps && (g_k)_i > 0}
49: U = {i : (x_k)_i >= u_i - eps && (g_k)_i < 0}
50: F = {i : l_i = (x_k)_i = u_i}
51: A = {L + U + F}
52: IA = {i : i not in A}
54: generate the reduced system Hr_k dr_k = -gr_k for variables in IA
55: if pc_type == BNK_PC_BFGS && scale_type == BNK_SCALE_PHESS
56: D = VecMedian(1e-6, abs(diag(Hr_k)), 1e6)
57: scale BFGS with VecReciprocal(D)
58: end
59: solve Hr_k dr_k = -gr_k
60: set d_k to (l - x) for variables in L, (u - x) for variables in U, and 0 for variables in F
62: x_{k+1} = VecMedian(x_k + d_k)
63: s = x_{k+1} - x_k
64: prered = dot(s, 0.5*gr_k - Hr_k*s)
65: f_{k+1} = TaoComputeObjective(x_{k+1})
66: actred = f_k - f_{k+1}
68: oldTrust = trust
69: step_accepted, trust = TaoBNKUpdateTrustRadius(default: BNK_UPDATE_REDUCTION)
70: if step_accepted
71: g_{k+1} = TaoComputeGradient(x_{k+1})
72: pg_{k+1} = project(g_{k+1})
73: count the accepted Newton step
74: else
75: if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
76: dr_k = -BFGS*gr_k for variables in I
77: if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
78: reset the BFGS preconditioner
79: calculate scale delta and apply it to BFGS
80: dr_k = -BFGS*gr_k for variables in I
81: if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
82: dr_k = -gr_k for variables in I
83: end
84: end
85: end
87: x_{k+1}, f_{k+1}, g_{k+1}, ls_failed = TaoBNKPerformLineSearch()
88: if ls_failed
89: f_{k+1} = f_k
90: x_{k+1} = x_k
91: g_{k+1} = g_k
92: pg_{k+1} = pg_k
93: terminate
94: else
95: pg_{k+1} = project(g_{k+1})
96: trust = oldTrust
97: trust = TaoBNKUpdateTrustRadius(BNK_UPDATE_STEP)
98: count the accepted step type (Newton, BFGS, scaled grad or grad)
99: end
100: end
102: check convergence at pg_{k+1}
103: end
104: */
106: PetscErrorCode TaoSolve_BNTL(Tao tao)
107: {
108: TAO_BNK *bnk = (TAO_BNK *)tao->data;
109: KSPConvergedReason ksp_reason;
110: TaoLineSearchConvergedReason ls_reason;
112: PetscReal oldTrust, prered, actred, steplen, resnorm;
113: PetscBool cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_FALSE;
114: PetscInt stepType, nDiff;
116: PetscFunctionBegin;
117: /* Initialize the preconditioner, KSP solver and trust radius/line search */
118: tao->reason = TAO_CONTINUE_ITERATING;
119: PetscCall(TaoBNKInitialize(tao, bnk->init_type, &needH));
120: if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(PETSC_SUCCESS);
122: /* Have not converged; continue with Newton method */
123: while (tao->reason == TAO_CONTINUE_ITERATING) {
124: /* Call general purpose update function */
125: if (tao->ops->update) {
126: PetscUseTypeMethod(tao, update, tao->niter, tao->user_update);
127: PetscCall(TaoComputeObjective(tao, tao->solution, &bnk->f));
128: }
130: if (needH && bnk->inactive_idx) {
131: /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
132: PetscCall(TaoBNKTakeCGSteps(tao, &cgTerminate));
133: if (cgTerminate) {
134: tao->reason = bnk->bncg->reason;
135: PetscFunctionReturn(PETSC_SUCCESS);
136: }
137: /* Compute the hessian and update the BFGS preconditioner at the new iterate */
138: PetscCall((*bnk->computehessian)(tao));
139: needH = PETSC_FALSE;
140: }
142: /* Use the common BNK kernel to compute the Newton step (for inactive variables only) */
143: PetscCall((*bnk->computestep)(tao, shift, &ksp_reason, &stepType));
145: /* Store current solution before it changes */
146: oldTrust = tao->trust;
147: bnk->fold = bnk->f;
148: PetscCall(VecCopy(tao->solution, bnk->Xold));
149: PetscCall(VecCopy(tao->gradient, bnk->Gold));
150: PetscCall(VecCopy(bnk->unprojected_gradient, bnk->unprojected_gradient_old));
152: /* Temporarily accept the step and project it into the bounds */
153: PetscCall(VecAXPY(tao->solution, 1.0, tao->stepdirection));
154: PetscCall(TaoBoundSolution(tao->solution, tao->XL, tao->XU, 0.0, &nDiff, tao->solution));
156: /* Check if the projection changed the step direction */
157: if (nDiff > 0) {
158: /* Projection changed the step, so we have to recompute the step and
159: the predicted reduction. Leave the trust radius unchanged. */
160: PetscCall(VecCopy(tao->solution, tao->stepdirection));
161: PetscCall(VecAXPY(tao->stepdirection, -1.0, bnk->Xold));
162: PetscCall(TaoBNKRecomputePred(tao, tao->stepdirection, &prered));
163: } else {
164: /* Step did not change, so we can just recover the pre-computed prediction */
165: PetscCall(KSPCGGetObjFcn(tao->ksp, &prered));
166: }
167: prered = -prered;
169: /* Compute the actual reduction and update the trust radius */
170: PetscCall(TaoComputeObjective(tao, tao->solution, &bnk->f));
171: PetscCheck(!PetscIsInfOrNanReal(bnk->f), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated infinity or NaN");
172: actred = bnk->fold - bnk->f;
173: PetscCall(TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted));
175: if (stepAccepted) {
176: /* Step is good, evaluate the gradient and the hessian */
177: steplen = 1.0;
178: needH = PETSC_TRUE;
179: ++bnk->newt;
180: PetscCall(TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient));
181: PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
182: PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient));
183: if (bnk->active_idx) PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
184: PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm));
185: } else {
186: /* Trust-region rejected the step. Revert the solution. */
187: bnk->f = bnk->fold;
188: PetscCall(VecCopy(bnk->Xold, tao->solution));
189: /* Trigger the line search */
190: PetscCall(TaoBNKSafeguardStep(tao, ksp_reason, &stepType));
191: PetscCall(TaoBNKPerformLineSearch(tao, &stepType, &steplen, &ls_reason));
192: if (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER) {
193: /* Line search failed, revert solution and terminate */
194: stepAccepted = PETSC_FALSE;
195: needH = PETSC_FALSE;
196: bnk->f = bnk->fold;
197: PetscCall(VecCopy(bnk->Xold, tao->solution));
198: PetscCall(VecCopy(bnk->Gold, tao->gradient));
199: PetscCall(VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient));
200: tao->trust = 0.0;
201: tao->reason = TAO_DIVERGED_LS_FAILURE;
202: } else {
203: /* new iterate so we need to recompute the Hessian */
204: needH = PETSC_TRUE;
205: /* compute the projected gradient */
206: PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
207: PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient));
208: if (bnk->active_idx) PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
209: PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm));
210: /* Line search succeeded so we should update the trust radius based on the LS step length */
211: tao->trust = oldTrust;
212: PetscCall(TaoBNKUpdateTrustRadius(tao, prered, actred, BNK_UPDATE_STEP, stepType, &stepAccepted));
213: /* count the accepted step type */
214: PetscCall(TaoBNKAddStepCounts(tao, stepType));
215: }
216: }
218: /* Check for termination */
219: PetscCall(VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W));
220: PetscCall(VecNorm(bnk->W, NORM_2, &resnorm));
221: PetscCheck(!PetscIsInfOrNanReal(resnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated infinity or NaN");
222: ++tao->niter;
223: PetscCall(TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its));
224: PetscCall(TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen));
225: PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
226: }
227: PetscFunctionReturn(PETSC_SUCCESS);
228: }
230: static PetscErrorCode TaoSetUp_BNTL(Tao tao)
231: {
232: KSP ksp;
233: PetscBool valid;
235: PetscFunctionBegin;
236: PetscCall(TaoSetUp_BNK(tao));
237: PetscCall(TaoGetKSP(tao, &ksp));
238: PetscCall(PetscObjectHasFunction((PetscObject)ksp, "KSPCGSetRadius_C", &valid));
239: 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);
240: PetscFunctionReturn(PETSC_SUCCESS);
241: }
243: static PetscErrorCode TaoSetFromOptions_BNTL(Tao tao, PetscOptionItems PetscOptionsObject)
244: {
245: TAO_BNK *bnk = (TAO_BNK *)tao->data;
247: PetscFunctionBegin;
248: PetscCall(TaoSetFromOptions_BNK(tao, PetscOptionsObject));
249: if (bnk->update_type == BNK_UPDATE_STEP) bnk->update_type = BNK_UPDATE_REDUCTION;
250: PetscFunctionReturn(PETSC_SUCCESS);
251: }
253: /*MC
254: TAOBNTL - Bounded Newton Trust Region method with line-search fall-back for nonlinear
255: minimization with bound constraints.
257: Options Database Keys:
258: + -tao_bnk_max_cg_its - maximum number of bounded conjugate-gradient iterations taken in each Newton loop
259: . -tao_bnk_init_type - trust radius initialization method ("constant", "direction", "interpolation")
260: . -tao_bnk_update_type - trust radius update method ("step", "direction", "interpolation")
261: - -tao_bnk_as_type - active-set estimation method ("none", "bertsekas")
263: Level: beginner
265: Developer Note:
266: One should control the maximum number of cg iterations through the standard pc_max_it option not with a special
267: ad hoc option
269: M*/
270: PETSC_EXTERN PetscErrorCode TaoCreate_BNTL(Tao tao)
271: {
272: TAO_BNK *bnk;
274: PetscFunctionBegin;
275: PetscCall(TaoCreate_BNK(tao));
276: tao->ops->solve = TaoSolve_BNTL;
277: tao->ops->setup = TaoSetUp_BNTL;
278: tao->ops->setfromoptions = TaoSetFromOptions_BNTL;
280: bnk = (TAO_BNK *)tao->data;
281: bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */
282: PetscFunctionReturn(PETSC_SUCCESS);
283: }