Actual source code: bntl.c
petsc-3.11.4 2019-09-28
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.
7:
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.
11:
12: ------------------------------------------------------------
13:
14: x_0 = VecMedian(x_0)
15: f_0, g_0 = TaoComputeObjectiveAndGradient(x_0)
16: pg_0 = project(g_0)
17: check convergence at pg_0
18: needH = TaoBNKInitialize(default:BNK_INIT_INTERPOLATION)
19: niter = 0
20: step_accepted = true
22: while niter <= max_it
23: niter += 1
24:
25: if needH
26: If max_cg_steps > 0
27: x_k, g_k, pg_k = TaoSolve(BNCG)
28: end
30: H_k = TaoComputeHessian(x_k)
31: if pc_type == BNK_PC_BFGS
32: add correction to BFGS approx
33: if scale_type == BNK_SCALE_AHESS
34: D = VecMedian(1e-6, abs(diag(H_k)), 1e6)
35: scale BFGS with VecReciprocal(D)
36: end
37: end
38: needH = False
39: end
41: if pc_type = BNK_PC_BFGS
42: B_k = BFGS
43: else
44: B_k = VecMedian(1e-6, abs(diag(H_k)), 1e6)
45: B_k = VecReciprocal(B_k)
46: end
47: w = x_k - VecMedian(x_k - 0.001*B_k*g_k)
48: eps = min(eps, norm2(w))
49: determine the active and inactive index sets such that
50: L = {i : (x_k)_i <= l_i + eps && (g_k)_i > 0}
51: U = {i : (x_k)_i >= u_i - eps && (g_k)_i < 0}
52: F = {i : l_i = (x_k)_i = u_i}
53: A = {L + U + F}
54: IA = {i : i not in A}
56: generate the reduced system Hr_k dr_k = -gr_k for variables in IA
57: if pc_type == BNK_PC_BFGS && scale_type == BNK_SCALE_PHESS
58: D = VecMedian(1e-6, abs(diag(Hr_k)), 1e6)
59: scale BFGS with VecReciprocal(D)
60: end
61: solve Hr_k dr_k = -gr_k
62: set d_k to (l - x) for variables in L, (u - x) for variables in U, and 0 for variables in F
64: x_{k+1} = VecMedian(x_k + d_k)
65: s = x_{k+1} - x_k
66: prered = dot(s, 0.5*gr_k - Hr_k*s)
67: f_{k+1} = TaoComputeObjective(x_{k+1})
68: actred = f_k - f_{k+1}
70: oldTrust = trust
71: step_accepted, trust = TaoBNKUpdateTrustRadius(default: BNK_UPDATE_REDUCTION)
72: if step_accepted
73: g_{k+1} = TaoComputeGradient(x_{k+1})
74: pg_{k+1} = project(g_{k+1})
75: count the accepted Newton step
76: else
77: if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
78: dr_k = -BFGS*gr_k for variables in I
79: if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
80: reset the BFGS preconditioner
81: calculate scale delta and apply it to BFGS
82: dr_k = -BFGS*gr_k for variables in I
83: if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
84: dr_k = -gr_k for variables in I
85: end
86: end
87: end
88:
89: x_{k+1}, f_{k+1}, g_{k+1}, ls_failed = TaoBNKPerformLineSearch()
90: if ls_failed
91: f_{k+1} = f_k
92: x_{k+1} = x_k
93: g_{k+1} = g_k
94: pg_{k+1} = pg_k
95: terminate
96: else
97: pg_{k+1} = project(g_{k+1})
98: trust = oldTrust
99: trust = TaoBNKUpdateTrustRadius(BNK_UPDATE_STEP)
100: count the accepted step type (Newton, BFGS, scaled grad or grad)
101: end
102: end
104: check convergence at pg_{k+1}
105: end
106: */
108: PetscErrorCode TaoSolve_BNTL(Tao tao)
109: {
110: PetscErrorCode ierr;
111: TAO_BNK *bnk = (TAO_BNK *)tao->data;
112: KSPConvergedReason ksp_reason;
113: TaoLineSearchConvergedReason ls_reason;
115: PetscReal oldTrust, prered, actred, steplen, resnorm;
116: PetscBool cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_FALSE;
117: PetscInt stepType, nDiff;
118:
120: /* Initialize the preconditioner, KSP solver and trust radius/line search */
121: tao->reason = TAO_CONTINUE_ITERATING;
122: TaoBNKInitialize(tao, bnk->init_type, &needH);
123: if (tao->reason != TAO_CONTINUE_ITERATING) return(0);
125: /* Have not converged; continue with Newton method */
126: while (tao->reason == TAO_CONTINUE_ITERATING) {
127: /* Call general purpose update function */
128: if (tao->ops->update) {
129: (*tao->ops->update)(tao, tao->niter, tao->user_update);
130: }
131: ++tao->niter;
132:
133: if (needH && bnk->inactive_idx) {
134: /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
135: TaoBNKTakeCGSteps(tao, &cgTerminate);
136: if (cgTerminate) {
137: tao->reason = bnk->bncg->reason;
138: return(0);
139: }
140: /* Compute the hessian and update the BFGS preconditioner at the new iterate */
141: (*bnk->computehessian)(tao);
142: needH = PETSC_FALSE;
143: }
144:
145: /* Use the common BNK kernel to compute the Newton step (for inactive variables only) */
146: (*bnk->computestep)(tao, shift, &ksp_reason, &stepType);
148: /* Store current solution before it changes */
149: oldTrust = tao->trust;
150: bnk->fold = bnk->f;
151: VecCopy(tao->solution, bnk->Xold);
152: VecCopy(tao->gradient, bnk->Gold);
153: VecCopy(bnk->unprojected_gradient, bnk->unprojected_gradient_old);
154:
155: /* Temporarily accept the step and project it into the bounds */
156: VecAXPY(tao->solution, 1.0, tao->stepdirection);
157: TaoBoundSolution(tao->solution, tao->XL,tao->XU, 0.0, &nDiff, tao->solution);
158:
159: /* Check if the projection changed the step direction */
160: if (nDiff > 0) {
161: /* Projection changed the step, so we have to recompute the step and
162: the predicted reduction. Leave the trust radius unchanged. */
163: VecCopy(tao->solution, tao->stepdirection);
164: VecAXPY(tao->stepdirection, -1.0, bnk->Xold);
165: TaoBNKRecomputePred(tao, tao->stepdirection, &prered);
166: } else {
167: /* Step did not change, so we can just recover the pre-computed prediction */
168: KSPCGGetObjFcn(tao->ksp, &prered);
169: }
170: prered = -prered;
171:
172: /* Compute the actual reduction and update the trust radius */
173: TaoComputeObjective(tao, tao->solution, &bnk->f);
174: if (PetscIsInfOrNanReal(bnk->f)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
175: actred = bnk->fold - bnk->f;
176: TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted);
177:
178: if (stepAccepted) {
179: /* Step is good, evaluate the gradient and the hessian */
180: steplen = 1.0;
181: needH = PETSC_TRUE;
182: ++bnk->newt;
183: TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient);
184: TaoBNKEstimateActiveSet(tao, bnk->as_type);
185: VecCopy(bnk->unprojected_gradient, tao->gradient);
186: VecISSet(tao->gradient, bnk->active_idx, 0.0);
187: TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);
188: } else {
189: /* Trust-region rejected the step. Revert the solution. */
190: bnk->f = bnk->fold;
191: VecCopy(bnk->Xold, tao->solution);
192: /* Trigger the line search */
193: TaoBNKSafeguardStep(tao, ksp_reason, &stepType);
194: TaoBNKPerformLineSearch(tao, &stepType, &steplen, &ls_reason);
195: if (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER) {
196: /* Line search failed, revert solution and terminate */
197: stepAccepted = PETSC_FALSE;
198: needH = PETSC_FALSE;
199: bnk->f = bnk->fold;
200: VecCopy(bnk->Xold, tao->solution);
201: VecCopy(bnk->Gold, tao->gradient);
202: VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);
203: tao->trust = 0.0;
204: tao->reason = TAO_DIVERGED_LS_FAILURE;
205: } else {
206: /* new iterate so we need to recompute the Hessian */
207: needH = PETSC_TRUE;
208: /* compute the projected gradient */
209: TaoBNKEstimateActiveSet(tao, bnk->as_type);
210: VecCopy(bnk->unprojected_gradient, tao->gradient);
211: VecISSet(tao->gradient, bnk->active_idx, 0.0);
212: TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);
213: /* Line search succeeded so we should update the trust radius based on the LS step length */
214: tao->trust = oldTrust;
215: TaoBNKUpdateTrustRadius(tao, prered, actred, BNK_UPDATE_STEP, stepType, &stepAccepted);
216: /* count the accepted step type */
217: TaoBNKAddStepCounts(tao, stepType);
218: }
219: }
221: /* Check for termination */
222: VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W);
223: VecNorm(bnk->W, NORM_2, &resnorm);
224: if (PetscIsInfOrNanReal(resnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
225: TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its);
226: TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen);
227: (*tao->ops->convergencetest)(tao, tao->cnvP);
228: }
229: return(0);
230: }
232: /*------------------------------------------------------------*/
233: static PetscErrorCode TaoSetFromOptions_BNTL(PetscOptionItems *PetscOptionsObject,Tao tao)
234: {
235: TAO_BNK *bnk = (TAO_BNK *)tao->data;
239: TaoSetFromOptions_BNK(PetscOptionsObject, tao);
240: if (bnk->update_type == BNK_UPDATE_STEP) bnk->update_type = BNK_UPDATE_REDUCTION;
241: if (!bnk->is_nash && !bnk->is_stcg && !bnk->is_gltr) SETERRQ(PETSC_COMM_SELF,1,"Must use a trust-region CG method for KSP (KSPNASH, KSPSTCG, KSPGLTR)");
242: return(0);
243: }
245: /*------------------------------------------------------------*/
246: /*MC
247: TAOBNTL - Bounded Newton Trust Region method with line-search fall-back for nonlinear
248: minimization with bound constraints.
250: Options Database Keys:
251: + -tao_bnk_max_cg_its - maximum number of bounded conjugate-gradient iterations taken in each Newton loop
252: . -tao_bnk_init_type - trust radius initialization method ("constant", "direction", "interpolation")
253: . -tao_bnk_update_type - trust radius update method ("step", "direction", "interpolation")
254: - -tao_bnk_as_type - active-set estimation method ("none", "bertsekas")
256: Level: beginner
257: M*/
258: PETSC_EXTERN PetscErrorCode TaoCreate_BNTL(Tao tao)
259: {
260: TAO_BNK *bnk;
262:
264: TaoCreate_BNK(tao);
265: tao->ops->solve=TaoSolve_BNTL;
266: tao->ops->setfromoptions=TaoSetFromOptions_BNTL;
267:
268: bnk = (TAO_BNK *)tao->data;
269: bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */
270: return(0);
271: }