Actual source code: bntr.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: ------------------------------------------------------------
9:
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
17:
18: while niter <= max_it
19: niter += 1
20:
21: if needH
22: If max_cg_steps > 0
23: x_k, g_k, pg_k = TaoSolve(BNCG)
24: end
25:
26: H_k = TaoComputeHessian(x_k)
27: if pc_type == BNK_PC_BFGS
28: add correction to BFGS approx
29: if scale_type == BNK_SCALE_AHESS
30: D = VecMedian(1e-6, abs(diag(H_k)), 1e6)
31: scale BFGS with VecReciprocal(D)
32: end
33: end
34: needH = False
35: end
37: if pc_type = BNK_PC_BFGS
38: B_k = BFGS
39: else
40: B_k = VecMedian(1e-6, abs(diag(H_k)), 1e6)
41: B_k = VecReciprocal(B_k)
42: end
43: w = x_k - VecMedian(x_k - 0.001*B_k*g_k)
44: eps = min(eps, norm2(w))
45: determine the active and inactive index sets such that
46: L = {i : (x_k)_i <= l_i + eps && (g_k)_i > 0}
47: U = {i : (x_k)_i >= u_i - eps && (g_k)_i < 0}
48: F = {i : l_i = (x_k)_i = u_i}
49: A = {L + U + F}
50: IA = {i : i not in A}
51:
52: generate the reduced system Hr_k dr_k = -gr_k for variables in IA
53: if pc_type == BNK_PC_BFGS && scale_type == BNK_SCALE_PHESS
54: D = VecMedian(1e-6, abs(diag(Hr_k)), 1e6)
55: scale BFGS with VecReciprocal(D)
56: end
57:
58: while !stepAccepted
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
61:
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: needH = True
75: else
76: f_{k+1} = f_k
77: x_{k+1} = x_k
78: g_{k+1} = g_k
79: pg_{k+1} = pg_k
80: if trust == oldTrust
81: terminate because we cannot shrink the radius any further
82: end
83: end
84:
85: check convergence at pg_{k+1}
86: end
87:
88: end
89: */
91: PetscErrorCode TaoSolve_BNTR(Tao tao)
92: {
93: PetscErrorCode ierr;
94: TAO_BNK *bnk = (TAO_BNK *)tao->data;
95: KSPConvergedReason ksp_reason;
97: PetscReal oldTrust, prered, actred, steplen, resnorm;
98: PetscBool cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_FALSE;
99: PetscInt stepType, nDiff;
100:
102: /* Initialize the preconditioner, KSP solver and trust radius/line search */
103: tao->reason = TAO_CONTINUE_ITERATING;
104: TaoBNKInitialize(tao, bnk->init_type, &needH);
105: if (tao->reason != TAO_CONTINUE_ITERATING) return(0);
107: /* Have not converged; continue with Newton method */
108: while (tao->reason == TAO_CONTINUE_ITERATING) {
109: /* Call general purpose update function */
110: if (tao->ops->update) {
111: (*tao->ops->update)(tao, tao->niter, tao->user_update);
112: }
113: ++tao->niter;
114:
115: if (needH && bnk->inactive_idx) {
116: /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
117: TaoBNKTakeCGSteps(tao, &cgTerminate);
118: if (cgTerminate) {
119: tao->reason = bnk->bncg->reason;
120: return(0);
121: }
122: /* Compute the hessian and update the BFGS preconditioner at the new iterate */
123: (*bnk->computehessian)(tao);
124: needH = PETSC_FALSE;
125: }
126:
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);
132:
133: /* Enter into trust region loops */
134: stepAccepted = PETSC_FALSE;
135: while (!stepAccepted && tao->reason == TAO_CONTINUE_ITERATING) {
136: tao->ksp_its=0;
137:
138: /* Use the common BNK kernel to compute the Newton step (for inactive variables only) */
139: (*bnk->computestep)(tao, shift, &ksp_reason, &stepType);
141: /* Temporarily accept the step and project it into the bounds */
142: VecAXPY(tao->solution, 1.0, tao->stepdirection);
143: TaoBoundSolution(tao->solution, tao->XL,tao->XU, 0.0, &nDiff, tao->solution);
145: /* Check if the projection changed the step direction */
146: if (nDiff > 0) {
147: /* Projection changed the step, so we have to recompute the step and
148: the predicted reduction. Leave the trust radius unchanged. */
149: VecCopy(tao->solution, tao->stepdirection);
150: VecAXPY(tao->stepdirection, -1.0, bnk->Xold);
151: TaoBNKRecomputePred(tao, tao->stepdirection, &prered);
152: } else {
153: /* Step did not change, so we can just recover the pre-computed prediction */
154: KSPCGGetObjFcn(tao->ksp, &prered);
155: }
156: prered = -prered;
158: /* Compute the actual reduction and update the trust radius */
159: TaoComputeObjective(tao, tao->solution, &bnk->f);
160: if (PetscIsInfOrNanReal(bnk->f)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
161: actred = bnk->fold - bnk->f;
162: oldTrust = tao->trust;
163: TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted);
165: if (stepAccepted) {
166: /* Step is good, evaluate the gradient and flip the need-Hessian switch */
167: steplen = 1.0;
168: needH = PETSC_TRUE;
169: ++bnk->newt;
170: TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient);
171: TaoBNKEstimateActiveSet(tao, bnk->as_type);
172: VecCopy(bnk->unprojected_gradient, tao->gradient);
173: VecISSet(tao->gradient, bnk->active_idx, 0.0);
174: TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);
175: } else {
176: /* Step is bad, revert old solution and re-solve with new radius*/
177: steplen = 0.0;
178: needH = PETSC_FALSE;
179: bnk->f = bnk->fold;
180: VecCopy(bnk->Xold, tao->solution);
181: VecCopy(bnk->Gold, tao->gradient);
182: VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);
183: if (oldTrust == tao->trust) {
184: /* Can't change the radius anymore so just terminate */
185: tao->reason = TAO_DIVERGED_TR_REDUCTION;
186: }
187: }
189: /* Check for termination */
190: VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W);
191: VecNorm(bnk->W, NORM_2, &resnorm);
192: if (PetscIsInfOrNanReal(resnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
193: TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its);
194: TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen);
195: (*tao->ops->convergencetest)(tao, tao->cnvP);
196: }
197: }
198: return(0);
199: }
201: /*------------------------------------------------------------*/
203: static PetscErrorCode TaoSetFromOptions_BNTR(PetscOptionItems *PetscOptionsObject,Tao tao)
204: {
205: TAO_BNK *bnk = (TAO_BNK *)tao->data;
209: TaoSetFromOptions_BNK(PetscOptionsObject, tao);
210: if (bnk->update_type == BNK_UPDATE_STEP) bnk->update_type = BNK_UPDATE_REDUCTION;
211: 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)");
212: return(0);
213: }
215: /*------------------------------------------------------------*/
216: /*MC
217: TAOBNTR - Bounded Newton Trust Region for nonlinear minimization with bound constraints.
219: Options Database Keys:
220: + -tao_bnk_max_cg_its - maximum number of bounded conjugate-gradient iterations taken in each Newton loop
221: . -tao_bnk_init_type - trust radius initialization method ("constant", "direction", "interpolation")
222: . -tao_bnk_update_type - trust radius update method ("step", "direction", "interpolation")
223: - -tao_bnk_as_type - active-set estimation method ("none", "bertsekas")
225: Level: beginner
226: M*/
227: PETSC_EXTERN PetscErrorCode TaoCreate_BNTR(Tao tao)
228: {
229: TAO_BNK *bnk;
231:
233: TaoCreate_BNK(tao);
234: tao->ops->solve=TaoSolve_BNTR;
235: tao->ops->setfromoptions=TaoSetFromOptions_BNTR;
236:
237: bnk = (TAO_BNK *)tao->data;
238: bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */
239: return(0);
240: }