Actual source code: tron.c

  1: #include <../src/tao/bound/impls/tron/tron.h>
  2: #include <../src/tao/matrix/submatfree.h>

  4: /* TRON Routines */
  5: static PetscErrorCode TronGradientProjections(Tao, TAO_TRON *);
  6: static PetscErrorCode TaoDestroy_TRON(Tao tao)
  7: {
  8:   TAO_TRON *tron = (TAO_TRON *)tao->data;

 10:   PetscFunctionBegin;
 11:   PetscCall(VecDestroy(&tron->X_New));
 12:   PetscCall(VecDestroy(&tron->G_New));
 13:   PetscCall(VecDestroy(&tron->Work));
 14:   PetscCall(VecDestroy(&tron->DXFree));
 15:   PetscCall(VecDestroy(&tron->R));
 16:   PetscCall(VecDestroy(&tron->diag));
 17:   PetscCall(VecScatterDestroy(&tron->scatter));
 18:   PetscCall(ISDestroy(&tron->Free_Local));
 19:   PetscCall(MatDestroy(&tron->H_sub));
 20:   PetscCall(MatDestroy(&tron->Hpre_sub));
 21:   PetscCall(KSPDestroy(&tao->ksp));
 22:   PetscCall(PetscFree(tao->data));
 23:   PetscFunctionReturn(PETSC_SUCCESS);
 24: }

 26: static PetscErrorCode TaoSetFromOptions_TRON(Tao tao, PetscOptionItems PetscOptionsObject)
 27: {
 28:   TAO_TRON *tron = (TAO_TRON *)tao->data;
 29:   PetscBool flg;

 31:   PetscFunctionBegin;
 32:   PetscOptionsHeadBegin(PetscOptionsObject, "Newton Trust Region Method for bound constrained optimization");
 33:   PetscCall(PetscOptionsInt("-tao_tron_maxgpits", "maximum number of gradient projections per TRON iterate", "TaoSetMaxGPIts", tron->maxgpits, &tron->maxgpits, &flg));
 34:   PetscOptionsHeadEnd();
 35:   PetscCall(KSPSetFromOptions(tao->ksp));
 36:   PetscFunctionReturn(PETSC_SUCCESS);
 37: }

 39: static PetscErrorCode TaoView_TRON(Tao tao, PetscViewer viewer)
 40: {
 41:   TAO_TRON *tron = (TAO_TRON *)tao->data;
 42:   PetscBool isascii;

 44:   PetscFunctionBegin;
 45:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
 46:   if (isascii) {
 47:     PetscCall(PetscViewerASCIIPrintf(viewer, "Total PG its: %" PetscInt_FMT ",", tron->total_gp_its));
 48:     PetscCall(PetscViewerASCIIPrintf(viewer, "PG tolerance: %g \n", (double)tron->pg_ftol));
 49:   }
 50:   PetscFunctionReturn(PETSC_SUCCESS);
 51: }

 53: static PetscErrorCode TaoSetup_TRON(Tao tao)
 54: {
 55:   TAO_TRON *tron = (TAO_TRON *)tao->data;

 57:   PetscFunctionBegin;
 58:   /* Allocate some arrays */
 59:   PetscCall(VecDuplicate(tao->solution, &tron->diag));
 60:   PetscCall(VecDuplicate(tao->solution, &tron->X_New));
 61:   PetscCall(VecDuplicate(tao->solution, &tron->G_New));
 62:   PetscCall(VecDuplicate(tao->solution, &tron->Work));
 63:   PetscCall(VecDuplicate(tao->solution, &tao->gradient));
 64:   PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));
 65:   PetscFunctionReturn(PETSC_SUCCESS);
 66: }

 68: static PetscErrorCode TaoSolve_TRON(Tao tao)
 69: {
 70:   TAO_TRON                    *tron = (TAO_TRON *)tao->data;
 71:   PetscInt                     its;
 72:   TaoLineSearchConvergedReason ls_reason = TAOLINESEARCH_CONTINUE_ITERATING;
 73:   PetscReal                    prered, actred, delta, f, f_new, rhok, gdx, xdiff, stepsize;

 75:   PetscFunctionBegin;
 76:   tron->pgstepsize = 1.0;
 77:   tao->trust       = tao->trust0;
 78:   /*   Project the current point onto the feasible set */
 79:   PetscCall(TaoComputeVariableBounds(tao));
 80:   PetscCall(TaoLineSearchSetVariableBounds(tao->linesearch, tao->XL, tao->XU));

 82:   /* Project the initial point onto the feasible region */
 83:   PetscCall(VecMedian(tao->XL, tao->solution, tao->XU, tao->solution));

 85:   /* Compute the objective function and gradient */
 86:   PetscCall(TaoComputeObjectiveAndGradient(tao, tao->solution, &tron->f, tao->gradient));
 87:   PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));
 88:   PetscCheck(!PetscIsInfOrNanReal(tron->f) && !PetscIsInfOrNanReal(tron->gnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated infinity or NaN");

 90:   /* Project the gradient and calculate the norm */
 91:   PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, tao->gradient));
 92:   PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));

 94:   /* Initialize trust region radius */
 95:   tao->trust = tao->trust0;
 96:   if (tao->trust <= 0) tao->trust = PetscMax(tron->gnorm * tron->gnorm, 1.0);

 98:   /* Initialize step sizes for the line searches */
 99:   tron->pgstepsize = 1.0;
100:   tron->stepsize   = tao->trust;

102:   tao->reason = TAO_CONTINUE_ITERATING;
103:   PetscCall(TaoLogConvergenceHistory(tao, tron->f, tron->gnorm, 0.0, tao->ksp_its));
104:   PetscCall(TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, tron->stepsize));
105:   PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
106:   while (tao->reason == TAO_CONTINUE_ITERATING) {
107:     /* Call general purpose update function */
108:     if (tao->ops->update) {
109:       PetscUseTypeMethod(tao, update, tao->niter, tao->user_update);
110:       PetscCall(TaoComputeObjective(tao, tao->solution, &tron->f));
111:     }

113:     /* Perform projected gradient iterations */
114:     PetscCall(TronGradientProjections(tao, tron));

116:     PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, tao->gradient));
117:     PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));

119:     tao->ksp_its      = 0;
120:     f                 = tron->f;
121:     delta             = tao->trust;
122:     tron->n_free_last = tron->n_free;
123:     PetscCall(TaoComputeHessian(tao, tao->solution, tao->hessian, tao->hessian_pre));

125:     /* Generate index set (IS) of which bound constraints are active */
126:     PetscCall(ISDestroy(&tron->Free_Local));
127:     PetscCall(VecWhichInactive(tao->XL, tao->solution, tao->gradient, tao->XU, PETSC_TRUE, &tron->Free_Local));
128:     PetscCall(ISGetSize(tron->Free_Local, &tron->n_free));

130:     /* If no free variables */
131:     if (tron->n_free == 0) {
132:       PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));
133:       PetscCall(TaoLogConvergenceHistory(tao, tron->f, tron->gnorm, 0.0, tao->ksp_its));
134:       PetscCall(TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, delta));
135:       PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
136:       if (!tao->reason) tao->reason = TAO_CONVERGED_STEPTOL;
137:       break;
138:     }
139:     /* use free_local to mask/submat gradient, hessian, stepdirection */
140:     PetscCall(TaoVecGetSubVec(tao->gradient, tron->Free_Local, tao->subset_type, 0.0, &tron->R));
141:     PetscCall(TaoVecGetSubVec(tao->gradient, tron->Free_Local, tao->subset_type, 0.0, &tron->DXFree));
142:     PetscCall(VecSet(tron->DXFree, 0.0));
143:     PetscCall(VecScale(tron->R, -1.0));
144:     PetscCall(TaoMatGetSubMat(tao->hessian, tron->Free_Local, tron->diag, tao->subset_type, &tron->H_sub));
145:     if (tao->hessian == tao->hessian_pre) {
146:       PetscCall(MatDestroy(&tron->Hpre_sub));
147:       PetscCall(PetscObjectReference((PetscObject)tron->H_sub));
148:       tron->Hpre_sub = tron->H_sub;
149:     } else {
150:       PetscCall(TaoMatGetSubMat(tao->hessian_pre, tron->Free_Local, tron->diag, tao->subset_type, &tron->Hpre_sub));
151:     }
152:     PetscCall(KSPReset(tao->ksp));
153:     PetscCall(KSPSetOperators(tao->ksp, tron->H_sub, tron->Hpre_sub));
154:     while (1) {
155:       /* Approximately solve the reduced linear system */
156:       PetscCall(KSPCGSetRadius(tao->ksp, delta));

158:       PetscCall(KSPSolve(tao->ksp, tron->R, tron->DXFree));
159:       PetscCall(KSPGetIterationNumber(tao->ksp, &its));
160:       tao->ksp_its += its;
161:       tao->ksp_tot_its += its;
162:       PetscCall(VecSet(tao->stepdirection, 0.0));

164:       /* Add dxfree matrix to compute step direction vector */
165:       PetscCall(VecISAXPY(tao->stepdirection, tron->Free_Local, 1.0, tron->DXFree));

167:       PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx));
168:       PetscCall(VecCopy(tao->solution, tron->X_New));
169:       PetscCall(VecCopy(tao->gradient, tron->G_New));

171:       stepsize = 1.0;
172:       f_new    = f;

174:       PetscCall(TaoLineSearchSetInitialStepLength(tao->linesearch, 1.0));
175:       PetscCall(TaoLineSearchApply(tao->linesearch, tron->X_New, &f_new, tron->G_New, tao->stepdirection, &stepsize, &ls_reason));
176:       PetscCall(TaoAddLineSearchCounts(tao));

178:       PetscCall(MatMult(tao->hessian, tao->stepdirection, tron->Work));
179:       PetscCall(VecAYPX(tron->Work, 0.5, tao->gradient));
180:       PetscCall(VecDot(tao->stepdirection, tron->Work, &prered));
181:       actred = f_new - f;
182:       if ((PetscAbsScalar(actred) <= 1e-6) && (PetscAbsScalar(prered) <= 1e-6)) {
183:         rhok = 1.0;
184:       } else if (actred < 0) {
185:         rhok = PetscAbs(-actred / prered);
186:       } else {
187:         rhok = 0.0;
188:       }

190:       /* Compare actual improvement to the quadratic model */
191:       if (rhok > tron->eta1) { /* Accept the point */
192:         /* d = x_new - x */
193:         PetscCall(VecCopy(tron->X_New, tao->stepdirection));
194:         PetscCall(VecAXPY(tao->stepdirection, -1.0, tao->solution));

196:         PetscCall(VecNorm(tao->stepdirection, NORM_2, &xdiff));
197:         xdiff *= stepsize;

199:         /* Adjust trust region size */
200:         if (rhok < tron->eta2) {
201:           delta = PetscMin(xdiff, delta) * tron->sigma1;
202:         } else if (rhok > tron->eta4) {
203:           delta = PetscMin(xdiff, delta) * tron->sigma3;
204:         } else if (rhok > tron->eta3) {
205:           delta = PetscMin(xdiff, delta) * tron->sigma2;
206:         }
207:         PetscCall(VecBoundGradientProjection(tron->G_New, tron->X_New, tao->XL, tao->XU, tao->gradient));
208:         PetscCall(ISDestroy(&tron->Free_Local));
209:         PetscCall(VecWhichInactive(tao->XL, tron->X_New, tao->gradient, tao->XU, PETSC_TRUE, &tron->Free_Local));
210:         f = f_new;
211:         PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));
212:         PetscCall(VecCopy(tron->X_New, tao->solution));
213:         PetscCall(VecCopy(tron->G_New, tao->gradient));
214:         break;
215:       } else if (delta <= 1e-30) {
216:         break;
217:       } else {
218:         delta /= 4.0;
219:       }
220:     } /* end linear solve loop */

222:     tron->f      = f;
223:     tron->actred = actred;
224:     tao->trust   = delta;
225:     tao->niter++;
226:     PetscCall(TaoLogConvergenceHistory(tao, tron->f, tron->gnorm, 0.0, tao->ksp_its));
227:     PetscCall(TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, stepsize));
228:     PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
229:   } /* END MAIN LOOP  */
230:   PetscFunctionReturn(PETSC_SUCCESS);
231: }

233: static PetscErrorCode TronGradientProjections(Tao tao, TAO_TRON *tron)
234: {
235:   PetscInt                     i;
236:   TaoLineSearchConvergedReason ls_reason;
237:   PetscReal                    actred = -1.0, actred_max = 0.0;
238:   PetscReal                    f_new;
239:   /*
240:      The gradient and function value passed into and out of this
241:      routine should be current and correct.

243:      The free, active, and binding variables should be already identified
244:   */

246:   PetscFunctionBegin;
247:   for (i = 0; i < tron->maxgpits; ++i) {
248:     if (-actred <= (tron->pg_ftol) * actred_max) break;

250:     ++tron->gp_iterates;
251:     ++tron->total_gp_its;
252:     f_new = tron->f;

254:     PetscCall(VecCopy(tao->gradient, tao->stepdirection));
255:     PetscCall(VecScale(tao->stepdirection, -1.0));
256:     PetscCall(TaoLineSearchSetInitialStepLength(tao->linesearch, tron->pgstepsize));
257:     PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f_new, tao->gradient, tao->stepdirection, &tron->pgstepsize, &ls_reason));
258:     PetscCall(TaoAddLineSearchCounts(tao));

260:     PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, tao->gradient));
261:     PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));

263:     /* Update the iterate */
264:     actred     = f_new - tron->f;
265:     actred_max = PetscMax(actred_max, -(f_new - tron->f));
266:     tron->f    = f_new;
267:   }
268:   PetscFunctionReturn(PETSC_SUCCESS);
269: }

271: static PetscErrorCode TaoComputeDual_TRON(Tao tao, Vec DXL, Vec DXU)
272: {
273:   TAO_TRON *tron = (TAO_TRON *)tao->data;

275:   PetscFunctionBegin;
279:   PetscCheck(tron->Work && tao->gradient, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Dual variables don't exist yet or no longer exist.");

281:   PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, tron->Work));
282:   PetscCall(VecCopy(tron->Work, DXL));
283:   PetscCall(VecAXPY(DXL, -1.0, tao->gradient));
284:   PetscCall(VecSet(DXU, 0.0));
285:   PetscCall(VecPointwiseMax(DXL, DXL, DXU));

287:   PetscCall(VecCopy(tao->gradient, DXU));
288:   PetscCall(VecAXPY(DXU, -1.0, tron->Work));
289:   PetscCall(VecSet(tron->Work, 0.0));
290:   PetscCall(VecPointwiseMin(DXU, tron->Work, DXU));
291:   PetscFunctionReturn(PETSC_SUCCESS);
292: }

294: /*MC
295:   TAOTRON - The TRON algorithm is an active-set Newton trust region method
296:   for bound-constrained minimization.

298:   Options Database Keys:
299: + -tao_tron_maxgpits - maximum number of gradient projections per TRON iterate
300: - -tao_subset_type - "subvec","mask","matrix-free", strategies for handling active-sets

302:   Level: beginner
303: M*/
304: PETSC_EXTERN PetscErrorCode TaoCreate_TRON(Tao tao)
305: {
306:   TAO_TRON   *tron;
307:   const char *morethuente_type = TAOLINESEARCHMT;

309:   PetscFunctionBegin;
310:   tao->ops->setup          = TaoSetup_TRON;
311:   tao->ops->solve          = TaoSolve_TRON;
312:   tao->ops->view           = TaoView_TRON;
313:   tao->ops->setfromoptions = TaoSetFromOptions_TRON;
314:   tao->ops->destroy        = TaoDestroy_TRON;
315:   tao->ops->computedual    = TaoComputeDual_TRON;

317:   PetscCall(PetscNew(&tron));
318:   tao->data = (void *)tron;

320:   /* Override default settings (unless already changed) */
321:   PetscCall(TaoParametersInitialize(tao));
322:   PetscObjectParameterSetDefault(tao, max_it, 50);
323:   PetscObjectParameterSetDefault(tao, trust0, 1.0);
324:   PetscObjectParameterSetDefault(tao, steptol, 0.0);

326:   /* Initialize pointers and variables */
327:   tron->n        = 0;
328:   tron->maxgpits = 3;
329:   tron->pg_ftol  = 0.001;

331:   tron->eta1 = 1.0e-4;
332:   tron->eta2 = 0.25;
333:   tron->eta3 = 0.50;
334:   tron->eta4 = 0.90;

336:   tron->sigma1 = 0.5;
337:   tron->sigma2 = 2.0;
338:   tron->sigma3 = 4.0;

340:   tron->gp_iterates  = 0; /* Cumulative number */
341:   tron->total_gp_its = 0;
342:   tron->n_free       = 0;

344:   tron->DXFree     = NULL;
345:   tron->R          = NULL;
346:   tron->X_New      = NULL;
347:   tron->G_New      = NULL;
348:   tron->Work       = NULL;
349:   tron->Free_Local = NULL;
350:   tron->H_sub      = NULL;
351:   tron->Hpre_sub   = NULL;
352:   tao->subset_type = TAO_SUBSET_SUBVEC;

354:   PetscCall(TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch));
355:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1));
356:   PetscCall(TaoLineSearchSetType(tao->linesearch, morethuente_type));
357:   PetscCall(TaoLineSearchUseTaoRoutines(tao->linesearch, tao));
358:   PetscCall(TaoLineSearchSetOptionsPrefix(tao->linesearch, tao->hdr.prefix));

360:   PetscCall(KSPCreate(((PetscObject)tao)->comm, &tao->ksp));
361:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1));
362:   PetscCall(KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix));
363:   PetscCall(KSPSetType(tao->ksp, KSPSTCG));
364:   PetscFunctionReturn(PETSC_SUCCESS);
365: }