1 #include <../src/tao/bound/impls/bnk/bnk.h>
2 #include <petscksp.h>
3
4 /*
5 Implements Newton's Method with a trust region approach for solving
6 bound constrained minimization problems.
7
8 x_0 = VecMedian(x_0)
9 f_0, g_0= TaoComputeObjectiveAndGradient(x_0)
10 pg_0 = project(g_0)
11 check convergence at pg_0
12 needH = TaoBNKInitialize(default:BNK_INIT_INTERPOLATION)
13 niter = 0
14 step_accepted = false
15
16 while niter <= max_it
17
18 if needH
19 If max_cg_steps > 0
20 x_k, g_k, pg_k = TaoSolve(BNCG)
21 end
22
23 H_k = TaoComputeHessian(x_k)
24 if pc_type == BNK_PC_BFGS
25 add correction to BFGS approx
26 if scale_type == BNK_SCALE_AHESS
27 D = VecMedian(1e-6, abs(diag(H_k)), 1e6)
28 scale BFGS with VecReciprocal(D)
29 end
30 end
31 needH = False
32 end
33
34 if pc_type = BNK_PC_BFGS
35 B_k = BFGS
36 else
37 B_k = VecMedian(1e-6, abs(diag(H_k)), 1e6)
38 B_k = VecReciprocal(B_k)
39 end
40 w = x_k - VecMedian(x_k - 0.001*B_k*g_k)
41 eps = min(eps, norm2(w))
42 determine the active and inactive index sets such that
43 L = {i : (x_k)_i <= l_i + eps && (g_k)_i > 0}
44 U = {i : (x_k)_i >= u_i - eps && (g_k)_i < 0}
45 F = {i : l_i = (x_k)_i = u_i}
46 A = {L + U + F}
47 IA = {i : i not in A}
48
49 generate the reduced system Hr_k dr_k = -gr_k for variables in IA
50 if pc_type == BNK_PC_BFGS && scale_type == BNK_SCALE_PHESS
51 D = VecMedian(1e-6, abs(diag(Hr_k)), 1e6)
52 scale BFGS with VecReciprocal(D)
53 end
54
55 while !stepAccepted
56 solve Hr_k dr_k = -gr_k
57 set d_k to (l - x) for variables in L, (u - x) for variables in U, and 0 for variables in F
58
59 x_{k+1} = VecMedian(x_k + d_k)
60 s = x_{k+1} - x_k
61 prered = dot(s, 0.5*gr_k - Hr_k*s)
62 f_{k+1} = TaoComputeObjective(x_{k+1})
63 actred = f_k - f_{k+1}
64
65 oldTrust = trust
66 step_accepted, trust = TaoBNKUpdateTrustRadius(default: BNK_UPDATE_REDUCTION)
67 if step_accepted
68 g_{k+1} = TaoComputeGradient(x_{k+1})
69 pg_{k+1} = project(g_{k+1})
70 count the accepted Newton step
71 needH = True
72 else
73 f_{k+1} = f_k
74 x_{k+1} = x_k
75 g_{k+1} = g_k
76 pg_{k+1} = pg_k
77 if trust == oldTrust
78 terminate because we cannot shrink the radius any further
79 end
80 end
81
82 end
83 check convergence at pg_{k+1}
84 niter += 1
85
86 end
87 */
88
TaoSolve_BNTR(Tao tao)89 PetscErrorCode TaoSolve_BNTR(Tao tao)
90 {
91 TAO_BNK *bnk = (TAO_BNK *)tao->data;
92 KSPConvergedReason ksp_reason;
93
94 PetscReal oldTrust, prered, actred, steplen = 0.0, resnorm;
95 PetscBool cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_FALSE;
96 PetscInt stepType, nDiff;
97
98 PetscFunctionBegin;
99 /* Initialize the preconditioner, KSP solver and trust radius/line search */
100 tao->reason = TAO_CONTINUE_ITERATING;
101 PetscCall(TaoBNKInitialize(tao, bnk->init_type, &needH));
102 if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(PETSC_SUCCESS);
103
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 PetscUseTypeMethod(tao, update, tao->niter, tao->user_update);
109 PetscCall(TaoComputeObjective(tao, tao->solution, &bnk->f));
110 }
111
112 if (needH && bnk->inactive_idx) {
113 /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
114 PetscCall(TaoBNKTakeCGSteps(tao, &cgTerminate));
115 if (cgTerminate) {
116 tao->reason = bnk->bncg->reason;
117 PetscFunctionReturn(PETSC_SUCCESS);
118 }
119 /* Compute the hessian and update the BFGS preconditioner at the new iterate */
120 PetscCall((*bnk->computehessian)(tao));
121 needH = PETSC_FALSE;
122 }
123
124 /* Store current solution before it changes */
125 bnk->fold = bnk->f;
126 PetscCall(VecCopy(tao->solution, bnk->Xold));
127 PetscCall(VecCopy(tao->gradient, bnk->Gold));
128 PetscCall(VecCopy(bnk->unprojected_gradient, bnk->unprojected_gradient_old));
129
130 /* Enter into trust region loops */
131 stepAccepted = PETSC_FALSE;
132 while (!stepAccepted && tao->reason == TAO_CONTINUE_ITERATING) {
133 tao->ksp_its = 0;
134
135 /* Use the common BNK kernel to compute the Newton step (for inactive variables only) */
136 PetscCall((*bnk->computestep)(tao, shift, &ksp_reason, &stepType));
137
138 /* Temporarily accept the step and project it into the bounds */
139 PetscCall(VecAXPY(tao->solution, 1.0, tao->stepdirection));
140 PetscCall(TaoBoundSolution(tao->solution, tao->XL, tao->XU, 0.0, &nDiff, tao->solution));
141
142 /* Check if the projection changed the step direction */
143 if (nDiff > 0) {
144 /* Projection changed the step, so we have to recompute the step and
145 the predicted reduction. Leave the trust radius unchanged. */
146 PetscCall(VecCopy(tao->solution, tao->stepdirection));
147 PetscCall(VecAXPY(tao->stepdirection, -1.0, bnk->Xold));
148 PetscCall(TaoBNKRecomputePred(tao, tao->stepdirection, &prered));
149 } else {
150 /* Step did not change, so we can just recover the pre-computed prediction */
151 PetscCall(KSPCGGetObjFcn(tao->ksp, &prered));
152 }
153 prered = -prered;
154
155 /* Compute the actual reduction and update the trust radius */
156 PetscCall(TaoComputeObjective(tao, tao->solution, &bnk->f));
157 PetscCheck(!PetscIsInfOrNanReal(bnk->f), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated infinity or NaN");
158 actred = bnk->fold - bnk->f;
159 oldTrust = tao->trust;
160 PetscCall(TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted));
161
162 if (stepAccepted) {
163 /* Step is good, evaluate the gradient and flip the need-Hessian switch */
164 steplen = 1.0;
165 needH = PETSC_TRUE;
166 ++bnk->newt;
167 PetscCall(TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient));
168 PetscCall(TaoBNKEstimateActiveSet(tao, bnk->as_type));
169 PetscCall(VecCopy(bnk->unprojected_gradient, tao->gradient));
170 if (bnk->active_idx) PetscCall(VecISSet(tao->gradient, bnk->active_idx, 0.0));
171 PetscCall(TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm));
172 } else {
173 /* Step is bad, revert old solution and re-solve with new radius*/
174 steplen = 0.0;
175 needH = PETSC_FALSE;
176 bnk->f = bnk->fold;
177 PetscCall(VecCopy(bnk->Xold, tao->solution));
178 PetscCall(VecCopy(bnk->Gold, tao->gradient));
179 PetscCall(VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient));
180 if (oldTrust == tao->trust) {
181 /* Can't change the radius anymore so just terminate */
182 tao->reason = TAO_DIVERGED_TR_REDUCTION;
183 }
184 }
185 }
186 /* Check for termination */
187 PetscCall(VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W));
188 PetscCall(VecNorm(bnk->W, NORM_2, &resnorm));
189 PetscCheck(!PetscIsInfOrNanReal(resnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated infinity or NaN");
190 ++tao->niter;
191 PetscCall(TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its));
192 PetscCall(TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen));
193 PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
194 }
195 PetscFunctionReturn(PETSC_SUCCESS);
196 }
197
TaoSetUp_BNTR(Tao tao)198 static PetscErrorCode TaoSetUp_BNTR(Tao tao)
199 {
200 KSP ksp;
201 PetscBool valid;
202
203 PetscFunctionBegin;
204 PetscCall(TaoSetUp_BNK(tao));
205 PetscCall(TaoGetKSP(tao, &ksp));
206 PetscCall(PetscObjectHasFunction((PetscObject)ksp, "KSPCGSetRadius_C", &valid));
207 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);
208 PetscFunctionReturn(PETSC_SUCCESS);
209 }
210
TaoSetFromOptions_BNTR(Tao tao,PetscOptionItems PetscOptionsObject)211 static PetscErrorCode TaoSetFromOptions_BNTR(Tao tao, PetscOptionItems PetscOptionsObject)
212 {
213 TAO_BNK *bnk = (TAO_BNK *)tao->data;
214
215 PetscFunctionBegin;
216 PetscCall(TaoSetFromOptions_BNK(tao, PetscOptionsObject));
217 if (bnk->update_type == BNK_UPDATE_STEP) bnk->update_type = BNK_UPDATE_REDUCTION;
218 PetscFunctionReturn(PETSC_SUCCESS);
219 }
220
221 /*MC
222 TAOBNTR - Bounded Newton Trust Region for nonlinear minimization with bound constraints.
223
224 Options Database Keys:
225 + -tao_bnk_max_cg_its - maximum number of bounded conjugate-gradient iterations taken in each Newton loop
226 . -tao_bnk_init_type - trust radius initialization method ("constant", "direction", "interpolation")
227 . -tao_bnk_update_type - trust radius update method ("step", "direction", "interpolation")
228 - -tao_bnk_as_type - active-set estimation method ("none", "bertsekas")
229
230 Level: beginner
231 M*/
TaoCreate_BNTR(Tao tao)232 PETSC_EXTERN PetscErrorCode TaoCreate_BNTR(Tao tao)
233 {
234 TAO_BNK *bnk;
235
236 PetscFunctionBegin;
237 PetscCall(TaoCreate_BNK(tao));
238 tao->ops->solve = TaoSolve_BNTR;
239 tao->ops->setup = TaoSetUp_BNTR;
240 tao->ops->setfromoptions = TaoSetFromOptions_BNTR;
241
242 bnk = (TAO_BNK *)tao->data;
243 bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */
244 PetscFunctionReturn(PETSC_SUCCESS);
245 }
246