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 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
21
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
29
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
40
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}
55
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
63
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}
69
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
103
104 check convergence at pg_{k+1}
105 end
106 */
107
TaoSolve_BNTL(Tao tao)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;
114
115 PetscReal oldTrust, prered, actred, steplen, resnorm;
116 PetscBool cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_FALSE;
117 PetscInt stepType, nDiff;
118
119 PetscFunctionBegin;
120 /* Initialize the preconditioner, KSP solver and trust radius/line search */
121 tao->reason = TAO_CONTINUE_ITERATING;
122 ierr = TaoBNKInitialize(tao, bnk->init_type, &needH);CHKERRQ(ierr);
123 if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
124
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 ierr = (*tao->ops->update)(tao, tao->niter, tao->user_update);CHKERRQ(ierr);
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 ierr = TaoBNKTakeCGSteps(tao, &cgTerminate);CHKERRQ(ierr);
136 if (cgTerminate) {
137 tao->reason = bnk->bncg->reason;
138 PetscFunctionReturn(0);
139 }
140 /* Compute the hessian and update the BFGS preconditioner at the new iterate */
141 ierr = (*bnk->computehessian)(tao);CHKERRQ(ierr);
142 needH = PETSC_FALSE;
143 }
144
145 /* Use the common BNK kernel to compute the Newton step (for inactive variables only) */
146 ierr = (*bnk->computestep)(tao, shift, &ksp_reason, &stepType);CHKERRQ(ierr);
147
148 /* Store current solution before it changes */
149 oldTrust = tao->trust;
150 bnk->fold = bnk->f;
151 ierr = VecCopy(tao->solution, bnk->Xold);CHKERRQ(ierr);
152 ierr = VecCopy(tao->gradient, bnk->Gold);CHKERRQ(ierr);
153 ierr = VecCopy(bnk->unprojected_gradient, bnk->unprojected_gradient_old);CHKERRQ(ierr);
154
155 /* Temporarily accept the step and project it into the bounds */
156 ierr = VecAXPY(tao->solution, 1.0, tao->stepdirection);CHKERRQ(ierr);
157 ierr = TaoBoundSolution(tao->solution, tao->XL,tao->XU, 0.0, &nDiff, tao->solution);CHKERRQ(ierr);
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 ierr = VecCopy(tao->solution, tao->stepdirection);CHKERRQ(ierr);
164 ierr = VecAXPY(tao->stepdirection, -1.0, bnk->Xold);CHKERRQ(ierr);
165 ierr = TaoBNKRecomputePred(tao, tao->stepdirection, &prered);CHKERRQ(ierr);
166 } else {
167 /* Step did not change, so we can just recover the pre-computed prediction */
168 ierr = KSPCGGetObjFcn(tao->ksp, &prered);CHKERRQ(ierr);
169 }
170 prered = -prered;
171
172 /* Compute the actual reduction and update the trust radius */
173 ierr = TaoComputeObjective(tao, tao->solution, &bnk->f);CHKERRQ(ierr);
174 if (PetscIsInfOrNanReal(bnk->f)) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
175 actred = bnk->fold - bnk->f;
176 ierr = TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted);CHKERRQ(ierr);
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 ierr = TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
184 ierr = TaoBNKEstimateActiveSet(tao, bnk->as_type);CHKERRQ(ierr);
185 ierr = VecCopy(bnk->unprojected_gradient, tao->gradient);CHKERRQ(ierr);
186 ierr = VecISSet(tao->gradient, bnk->active_idx, 0.0);CHKERRQ(ierr);
187 ierr = TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);CHKERRQ(ierr);
188 } else {
189 /* Trust-region rejected the step. Revert the solution. */
190 bnk->f = bnk->fold;
191 ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr);
192 /* Trigger the line search */
193 ierr = TaoBNKSafeguardStep(tao, ksp_reason, &stepType);CHKERRQ(ierr);
194 ierr = TaoBNKPerformLineSearch(tao, &stepType, &steplen, &ls_reason);CHKERRQ(ierr);
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 ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr);
201 ierr = VecCopy(bnk->Gold, tao->gradient);CHKERRQ(ierr);
202 ierr = VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);CHKERRQ(ierr);
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 ierr = TaoBNKEstimateActiveSet(tao, bnk->as_type);CHKERRQ(ierr);
210 ierr = VecCopy(bnk->unprojected_gradient, tao->gradient);CHKERRQ(ierr);
211 ierr = VecISSet(tao->gradient, bnk->active_idx, 0.0);CHKERRQ(ierr);
212 ierr = TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);CHKERRQ(ierr);
213 /* Line search succeeded so we should update the trust radius based on the LS step length */
214 tao->trust = oldTrust;
215 ierr = TaoBNKUpdateTrustRadius(tao, prered, actred, BNK_UPDATE_STEP, stepType, &stepAccepted);CHKERRQ(ierr);
216 /* count the accepted step type */
217 ierr = TaoBNKAddStepCounts(tao, stepType);CHKERRQ(ierr);
218 }
219 }
220
221 /* Check for termination */
222 ierr = VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W);CHKERRQ(ierr);
223 ierr = VecNorm(bnk->W, NORM_2, &resnorm);CHKERRQ(ierr);
224 if (PetscIsInfOrNanReal(resnorm)) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
225 ierr = TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its);CHKERRQ(ierr);
226 ierr = TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen);CHKERRQ(ierr);
227 ierr = (*tao->ops->convergencetest)(tao, tao->cnvP);CHKERRQ(ierr);
228 }
229 PetscFunctionReturn(0);
230 }
231
232 /*------------------------------------------------------------*/
TaoSetFromOptions_BNTL(PetscOptionItems * PetscOptionsObject,Tao tao)233 static PetscErrorCode TaoSetFromOptions_BNTL(PetscOptionItems *PetscOptionsObject,Tao tao)
234 {
235 TAO_BNK *bnk = (TAO_BNK *)tao->data;
236 PetscErrorCode ierr;
237
238 PetscFunctionBegin;
239 ierr = TaoSetFromOptions_BNK(PetscOptionsObject, tao);CHKERRQ(ierr);
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(PetscObjectComm((PetscObject)tao),PETSC_ERR_SUP,"Must use a trust-region CG method for KSP (KSPNASH, KSPSTCG, KSPGLTR)");
242 PetscFunctionReturn(0);
243 }
244
245 /*------------------------------------------------------------*/
246 /*MC
247 TAOBNTL - Bounded Newton Trust Region method with line-search fall-back for nonlinear
248 minimization with bound constraints.
249
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")
255
256 Level: beginner
257 M*/
TaoCreate_BNTL(Tao tao)258 PETSC_EXTERN PetscErrorCode TaoCreate_BNTL(Tao tao)
259 {
260 TAO_BNK *bnk;
261 PetscErrorCode ierr;
262
263 PetscFunctionBegin;
264 ierr = TaoCreate_BNK(tao);CHKERRQ(ierr);
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 PetscFunctionReturn(0);
271 }
272