Actual source code: almm.c

  1: #include <../src/tao/constrained/impls/almm/almm.h>
  2: #include <petsctao.h>
  3: #include <petsc/private/petscimpl.h>
  4: #include <petsc/private/vecimpl.h>

  6: static PetscErrorCode TaoALMMCombinePrimal_Private(Tao,Vec,Vec,Vec);
  7: static PetscErrorCode TaoALMMCombineDual_Private(Tao,Vec,Vec,Vec);
  8: static PetscErrorCode TaoALMMSplitPrimal_Private(Tao,Vec,Vec,Vec);
  9: static PetscErrorCode TaoALMMComputeOptimalityNorms_Private(Tao);
 10: static PetscErrorCode TaoALMMComputeAugLagAndGradient_Private(Tao);
 11: static PetscErrorCode TaoALMMComputePHRLagAndGradient_Private(Tao);

 13: static PetscErrorCode TaoSolve_ALMM(Tao tao)
 14: {
 15:   TAO_ALMM           *auglag = (TAO_ALMM*)tao->data;
 16:   TaoConvergedReason reason;
 17:   PetscReal          updated;

 19:   /* reset initial multiplier/slack guess */
 20:   if (!tao->recycle) {
 21:     if (tao->ineq_constrained) {
 22:       VecZeroEntries(auglag->Ps);
 23:       TaoALMMCombinePrimal_Private(tao, auglag->Px, auglag->Ps, auglag->P);
 24:       VecZeroEntries(auglag->Yi);
 25:     }
 26:     if (tao->eq_constrained) {
 27:       VecZeroEntries(auglag->Ye);
 28:     }
 29:   }

 31:   /* compute initial nonlinear Lagrangian and its derivatives */
 32:   (*auglag->sub_obj)(tao);
 33:   TaoALMMComputeOptimalityNorms_Private(tao);
 34:   /* print initial step and check convergence */
 35:   PetscInfo(tao,"Solving with %s formulation\n",TaoALMMTypes[auglag->type]);
 36:   TaoLogConvergenceHistory(tao, auglag->Lval, auglag->gnorm, auglag->cnorm, tao->ksp_its);
 37:   TaoMonitor(tao, tao->niter, auglag->fval, auglag->gnorm, auglag->cnorm, 0.0);
 38:   (*tao->ops->convergencetest)(tao, tao->cnvP);
 39:   /* set initial penalty factor and inner solver tolerance */
 40:   switch (auglag->type) {
 41:     case TAO_ALMM_CLASSIC:
 42:       auglag->mu = auglag->mu0;
 43:       break;
 44:     case TAO_ALMM_PHR:
 45:       auglag->cenorm = 0.0;
 46:       if (tao->eq_constrained) {
 47:         VecDot(auglag->Ce, auglag->Ce, &auglag->cenorm);
 48:       }
 49:       auglag->cinorm = 0.0;
 50:       if (tao->ineq_constrained) {
 51:         VecCopy(auglag->Ci, auglag->Ciwork);
 52:         VecScale(auglag->Ciwork, -1.0);
 53:         VecPointwiseMax(auglag->Ciwork, auglag->Cizero, auglag->Ciwork);
 54:         VecDot(auglag->Ciwork, auglag->Ciwork, &auglag->cinorm);
 55:       }
 56:       /* determine initial penalty factor based on the balance of constraint violation and objective function value */
 57:       auglag->mu = PetscMax(1.e-6, PetscMin(10.0, 2.0*PetscAbsReal(auglag->fval)/(auglag->cenorm + auglag->cinorm)));
 58:       break;
 59:     default:
 60:       break;
 61:   }
 62:   auglag->gtol = auglag->gtol0;
 63:   PetscInfo(tao,"Initial penalty: %.2f\n",auglag->mu);

 65:   /* start aug-lag outer loop */
 66:   while (tao->reason == TAO_CONTINUE_ITERATING) {
 67:     ++tao->niter;
 68:     /* update subsolver tolerance */
 69:     PetscInfo(tao,"Subsolver tolerance: ||G|| <= %e\n",auglag->gtol);
 70:     TaoSetTolerances(auglag->subsolver, auglag->gtol, 0.0, 0.0);
 71:     /* solve the bound-constrained or unconstrained subproblem */
 72:     TaoSolve(auglag->subsolver);
 73:     TaoGetConvergedReason(auglag->subsolver, &reason);
 74:     tao->ksp_its += auglag->subsolver->ksp_its;
 75:     if (reason != TAO_CONVERGED_GATOL) {
 76:       PetscInfo(tao,"Subsolver failed to converge, reason: %s\n",TaoConvergedReasons[reason]);
 77:     }
 78:     /* evaluate solution and test convergence */
 79:     (*auglag->sub_obj)(tao);
 80:     TaoALMMComputeOptimalityNorms_Private(tao);
 81:     /* decide whether to update multipliers or not */
 82:     updated = 0.0;
 83:     if (auglag->cnorm <= auglag->ytol) {
 84:       PetscInfo(tao,"Multipliers updated: ||C|| <= %e\n",auglag->ytol);
 85:       /* constraints are good, update multipliers and convergence tolerances */
 86:       if (tao->eq_constrained) {
 87:         VecAXPY(auglag->Ye, auglag->mu, auglag->Ce);
 88:         VecSet(auglag->Cework, auglag->ye_max);
 89:         VecPointwiseMin(auglag->Ye, auglag->Cework, auglag->Ye);
 90:         VecSet(auglag->Cework, auglag->ye_min);
 91:         VecPointwiseMax(auglag->Ye, auglag->Cework, auglag->Ye);
 92:       }
 93:       if (tao->ineq_constrained) {
 94:         VecAXPY(auglag->Yi, auglag->mu, auglag->Ci);
 95:         VecSet(auglag->Ciwork, auglag->yi_max);
 96:         VecPointwiseMin(auglag->Yi, auglag->Ciwork, auglag->Yi);
 97:         VecSet(auglag->Ciwork, auglag->yi_min);
 98:         VecPointwiseMax(auglag->Yi, auglag->Ciwork, auglag->Yi);
 99:       }
100:       /* tolerances are updated only for non-PHR methods */
101:       if (auglag->type != TAO_ALMM_PHR) {
102:         auglag->ytol = PetscMax(tao->catol, auglag->ytol/PetscPowReal(auglag->mu, auglag->mu_pow_good));
103:         auglag->gtol = PetscMax(tao->gatol, auglag->gtol/auglag->mu);
104:       }
105:       updated = 1.0;
106:     } else {
107:       /* constraints are bad, update penalty factor */
108:       auglag->mu = PetscMin(auglag->mu_max, auglag->mu_fac*auglag->mu);
109:       /* tolerances are reset only for non-PHR methods */
110:       if (auglag->type != TAO_ALMM_PHR) {
111:         auglag->ytol = PetscMax(tao->catol, 0.1/PetscPowReal(auglag->mu, auglag->mu_pow_bad));
112:         auglag->gtol = PetscMax(tao->gatol, 1.0/auglag->mu);
113:       }
114:       PetscInfo(tao,"Penalty increased: mu = %.2f\n",auglag->mu);
115:     }
116:     TaoLogConvergenceHistory(tao, auglag->fval, auglag->gnorm, auglag->cnorm, tao->ksp_its);
117:     TaoMonitor(tao, tao->niter, auglag->fval, auglag->gnorm, auglag->cnorm, updated);
118:     (*tao->ops->convergencetest)(tao, tao->cnvP);
119:   }

121:   return 0;
122: }

124: static PetscErrorCode TaoView_ALMM(Tao tao,PetscViewer viewer)
125: {
126:   TAO_ALMM       *auglag = (TAO_ALMM*)tao->data;
127:   PetscBool      isascii;

129:   PetscViewerASCIIPushTab(viewer);
130:   TaoView(auglag->subsolver,viewer);
131:   PetscViewerASCIIPopTab(viewer);
132:   PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii);
133:   if (isascii) {
134:     PetscViewerASCIIPushTab(viewer);
135:     PetscViewerASCIIPrintf(viewer, "ALMM Formulation Type: %s\n", TaoALMMTypes[auglag->type]);
136:     PetscViewerASCIIPopTab(viewer);
137:   }
138:   return 0;
139: }

141: static PetscErrorCode TaoSetUp_ALMM(Tao tao)
142: {
143:   TAO_ALMM       *auglag = (TAO_ALMM*)tao->data;
144:   VecType        vec_type;
145:   Vec            SL, SU;
146:   PetscBool      is_cg = PETSC_FALSE, is_lmvm = PETSC_FALSE;

150:   TaoComputeVariableBounds(tao);
151:   /* alias base vectors and create extras */
152:   VecGetType(tao->solution, &vec_type);
153:   auglag->Px = tao->solution;
154:   if (!tao->gradient) { /* base gradient */
155:     VecDuplicate(tao->solution, &tao->gradient);
156:   }
157:   auglag->LgradX = tao->gradient;
158:   if (!auglag->Xwork) { /* opt var work vector */
159:     VecDuplicate(tao->solution, &auglag->Xwork);
160:   }
161:   if (tao->eq_constrained) {
162:     auglag->Ce = tao->constraints_equality;
163:     auglag->Ae = tao->jacobian_equality;
164:     if (!auglag->Ye) { /* equality multipliers */
165:       VecDuplicate(auglag->Ce, &auglag->Ye);
166:     }
167:     if (!auglag->Cework) {
168:       VecDuplicate(auglag->Ce, &auglag->Cework);
169:     }
170:   }
171:   if (tao->ineq_constrained) {
172:     auglag->Ci = tao->constraints_inequality;
173:     auglag->Ai = tao->jacobian_inequality;
174:     if (!auglag->Yi) { /* inequality multipliers */
175:       VecDuplicate(auglag->Ci, &auglag->Yi);
176:     }
177:     if (!auglag->Ciwork) {
178:       VecDuplicate(auglag->Ci, &auglag->Ciwork);
179:     }
180:     if (!auglag->Cizero) {
181:       VecDuplicate(auglag->Ci, &auglag->Cizero);
182:       VecZeroEntries(auglag->Cizero);
183:     }
184:     if (!auglag->Ps) { /* slack vars */
185:       VecDuplicate(auglag->Ci, &auglag->Ps);
186:     }
187:     if (!auglag->LgradS) { /* slack component of Lagrangian gradient */
188:       VecDuplicate(auglag->Ci, &auglag->LgradS);
189:     }
190:     /* create vector for combined primal space and the associated communication objects */
191:     if (!auglag->P) {
192:       PetscMalloc1(2, &auglag->Parr);
193:       auglag->Parr[0] = auglag->Px; auglag->Parr[1] = auglag->Ps;
194:       VecConcatenate(2, auglag->Parr, &auglag->P, &auglag->Pis);
195:       PetscMalloc1(2, &auglag->Pscatter);
196:       VecScatterCreate(auglag->P, auglag->Pis[0], auglag->Px, NULL, &auglag->Pscatter[0]);
197:       VecScatterCreate(auglag->P, auglag->Pis[1], auglag->Ps, NULL, &auglag->Pscatter[1]);
198:     }
199:     if (tao->eq_constrained) {
200:       /* create vector for combined dual space and the associated communication objects */
201:       if (!auglag->Y) {
202:         PetscMalloc1(2, &auglag->Yarr);
203:         auglag->Yarr[0] = auglag->Ye; auglag->Yarr[1] = auglag->Yi;
204:         VecConcatenate(2, auglag->Yarr, &auglag->Y, &auglag->Yis);
205:         PetscMalloc1(2, &auglag->Yscatter);
206:         VecScatterCreate(auglag->Y, auglag->Yis[0], auglag->Ye, NULL, &auglag->Yscatter[0]);
207:         VecScatterCreate(auglag->Y, auglag->Yis[1], auglag->Yi, NULL, &auglag->Yscatter[1]);
208:       }
209:       if (!auglag->C) {
210:         VecDuplicate(auglag->Y, &auglag->C);
211:       }
212:     } else {
213:       if (!auglag->C) {
214:         auglag->C = auglag->Ci;
215:       }
216:       if (!auglag->Y) {
217:         auglag->Y = auglag->Yi;
218:       }
219:     }
220:   } else {
221:     if (!auglag->P) {
222:       auglag->P = auglag->Px;
223:     }
224:     if (!auglag->G) {
225:       auglag->G = auglag->LgradX;
226:     }
227:     if (!auglag->C) {
228:       auglag->C = auglag->Ce;
229:     }
230:     if (!auglag->Y) {
231:       auglag->Y = auglag->Ye;
232:     }
233:   }
234:   /* initialize parameters */
235:   if (auglag->type == TAO_ALMM_PHR) {
236:     auglag->mu_fac = 10.0;
237:     auglag->yi_min = 0.0;
238:     auglag->ytol0 = 0.5;
239:     auglag->gtol0 = tao->gatol;
240:     if (tao->gatol_changed && tao->catol_changed) {
241:       PetscInfo(tao,"TAOALMM with PHR: different gradient and constraint tolerances are not supported, setting catol = gatol\n");
242:       tao->catol = tao->gatol;
243:     }
244:   }
245:   /* set the Lagrangian formulation type for the subsolver */
246:   switch (auglag->type) {
247:     case TAO_ALMM_CLASSIC:
248:       auglag->sub_obj = TaoALMMComputeAugLagAndGradient_Private;
249:       break;
250:     case TAO_ALMM_PHR:
251:       auglag->sub_obj = TaoALMMComputePHRLagAndGradient_Private;
252:       break;
253:     default:
254:       break;
255:   }
256:   /* set up the subsolver */
257:   TaoSetSolution(auglag->subsolver, auglag->P);
258:   TaoSetObjective(auglag->subsolver, TaoALMMSubsolverObjective_Private, (void*)auglag);
259:   TaoSetObjectiveAndGradient(auglag->subsolver, NULL, TaoALMMSubsolverObjectiveAndGradient_Private, (void*)auglag);
260:   if (tao->bounded) {
261:     /* make sure that the subsolver is a bound-constrained method */
262:     PetscObjectTypeCompare((PetscObject)auglag->subsolver, TAOCG, &is_cg);
263:     PetscObjectTypeCompare((PetscObject)auglag->subsolver, TAOLMVM, &is_lmvm);
264:     if (is_cg) {
265:       TaoSetType(auglag->subsolver, TAOBNCG);
266:       PetscInfo(tao,"TAOCG detected for bound-constrained problem, switching to TAOBNCG instead.");
267:     }
268:     if (is_lmvm) {
269:       TaoSetType(auglag->subsolver, TAOBQNLS);
270:       PetscInfo(tao,"TAOLMVM detected for bound-constrained problem, switching to TAOBQNLS instead.");
271:     }
272:     /* create lower and upper bound clone vectors for subsolver */
273:     if (!auglag->PL) {
274:       VecDuplicate(auglag->P, &auglag->PL);
275:     }
276:     if (!auglag->PU) {
277:       VecDuplicate(auglag->P, &auglag->PU);
278:     }
279:     if (tao->ineq_constrained) {
280:       /* create lower and upper bounds for slack, set lower to 0 */
281:       VecDuplicate(auglag->Ci, &SL);
282:       VecSet(SL, 0.0);
283:       VecDuplicate(auglag->Ci, &SU);
284:       VecSet(SU, PETSC_INFINITY);
285:       /* combine opt var bounds with slack bounds */
286:       TaoALMMCombinePrimal_Private(tao, tao->XL, SL, auglag->PL);
287:       TaoALMMCombinePrimal_Private(tao, tao->XU, SU, auglag->PU);
288:       /* destroy work vectors */
289:       VecDestroy(&SL);
290:       VecDestroy(&SU);
291:     } else {
292:       /* no inequality constraints, just copy bounds into the subsolver */
293:       VecCopy(tao->XL, auglag->PL);
294:       VecCopy(tao->XU, auglag->PU);
295:     }
296:     TaoSetVariableBounds(auglag->subsolver, auglag->PL, auglag->PU);
297:   }
298:   TaoSetUp(auglag->subsolver);
299:   auglag->G = auglag->subsolver->gradient;

301:   return 0;
302: }

304: static PetscErrorCode TaoDestroy_ALMM(Tao tao)
305: {
306:   TAO_ALMM       *auglag = (TAO_ALMM*)tao->data;

308:   TaoDestroy(&auglag->subsolver);
309:   if (tao->setupcalled) {
310:     VecDestroy(&auglag->Xwork);              /* opt work */
311:     if (tao->eq_constrained) {
312:       VecDestroy(&auglag->Ye);               /* equality multipliers */
313:       VecDestroy(&auglag->Cework);           /* equality work vector */
314:     }
315:     if (tao->ineq_constrained) {
316:       VecDestroy(&auglag->Ps);               /* slack vars */
317:       auglag->Parr[0] = NULL;                                     /* clear pointer to tao->solution, will be destroyed by TaoDestroy() shell */
318:       PetscFree(auglag->Parr);               /* array of primal vectors */
319:       VecDestroy(&auglag->LgradS);           /* slack grad */
320:       VecDestroy(&auglag->Cizero);           /* zero vector for pointwise max */
321:       VecDestroy(&auglag->Yi);               /* inequality multipliers */
322:       VecDestroy(&auglag->Ciwork);           /* inequality work vector */
323:       VecDestroy(&auglag->P);                /* combo primal */
324:       ISDestroy(&auglag->Pis[0]);            /* index set for X inside P */
325:       ISDestroy(&auglag->Pis[1]);            /* index set for S inside P */
326:       PetscFree(auglag->Pis);                /* array of P index sets */
327:       VecScatterDestroy(&auglag->Pscatter[0]);
328:       VecScatterDestroy(&auglag->Pscatter[1]);
329:       PetscFree(auglag->Pscatter);
330:       if (tao->eq_constrained) {
331:         VecDestroy(&auglag->Y);              /* combo multipliers */
332:         PetscFree(auglag->Yarr);             /* array of dual vectors */
333:         VecDestroy(&auglag->C);              /* combo constraints */
334:         ISDestroy(&auglag->Yis[0]);          /* index set for Ye inside Y */
335:         ISDestroy(&auglag->Yis[1]);          /* index set for Yi inside Y */
336:         PetscFree(auglag->Yis);
337:         VecScatterDestroy(&auglag->Yscatter[0]);
338:         VecScatterDestroy(&auglag->Yscatter[1]);
339:         PetscFree(auglag->Yscatter);
340:       }
341:     }
342:     if (tao->bounded) {
343:       VecDestroy(&auglag->PL);                /* lower bounds for subsolver */
344:       VecDestroy(&auglag->PU);                /* upper bounds for subsolver */
345:     }
346:   }
347:   PetscFree(tao->data);
348:   return 0;
349: }

351: static PetscErrorCode TaoSetFromOptions_ALMM(PetscOptionItems *PetscOptionsObject,Tao tao)
352: {
353:   TAO_ALMM       *auglag = (TAO_ALMM*)tao->data;
354:   PetscInt       i;

356:   PetscOptionsHead(PetscOptionsObject,"Augmented Lagrangian multiplier method solves problems with general constraints by converting them into a sequence of unconstrained problems.");
357:   PetscOptionsReal("-tao_almm_mu_init","initial penalty parameter","",auglag->mu0,&auglag->mu0,NULL);
358:   PetscOptionsReal("-tao_almm_mu_factor","increase factor for the penalty parameter","",auglag->mu_fac,&auglag->mu_fac,NULL);
359:   PetscOptionsReal("-tao_almm_mu_power_good","exponential for penalty parameter when multiplier update is accepted","",auglag->mu_pow_good,&auglag->mu_pow_good,NULL);
360:   PetscOptionsReal("-tao_almm_mu_power_bad","exponential for penalty parameter when multiplier update is rejected","",auglag->mu_pow_bad,&auglag->mu_pow_bad,NULL);
361:   PetscOptionsReal("-tao_almm_mu_max","maximum safeguard for penalty parameter updates","",auglag->mu_max,&auglag->mu_max,NULL);
362:   PetscOptionsReal("-tao_almm_ye_min","minimum safeguard for equality multiplier updates","",auglag->ye_min,&auglag->ye_min,NULL);
363:   PetscOptionsReal("-tao_almm_ye_max","maximum safeguard for equality multipliers updates","",auglag->ye_max,&auglag->ye_max,NULL);
364:   PetscOptionsReal("-tao_almm_yi_min","minimum safeguard for inequality multipliers updates","",auglag->yi_min,&auglag->yi_min,NULL);
365:   PetscOptionsReal("-tao_almm_yi_max","maximum safeguard for inequality multipliers updates","",auglag->yi_max,&auglag->yi_max,NULL);
366:   PetscOptionsEnum("-tao_almm_type","augmented Lagrangian formulation type for the subproblem","TaoALMMType",TaoALMMTypes,(PetscEnum)auglag->type,(PetscEnum*)&auglag->type,NULL);
367:   PetscOptionsTail();
368:   TaoSetOptionsPrefix(auglag->subsolver,((PetscObject)tao)->prefix);
369:   TaoAppendOptionsPrefix(auglag->subsolver,"tao_almm_subsolver_");
370:   TaoSetFromOptions(auglag->subsolver);
371:   for (i=0; i<tao->numbermonitors; i++) {
372:     PetscObjectReference((PetscObject)tao->monitorcontext[i]);
373:     TaoSetMonitor(auglag->subsolver, tao->monitor[i], tao->monitorcontext[i], tao->monitordestroy[i]);
374:     if (tao->monitor[i] == TaoMonitorDefault || tao->monitor[i] == TaoDefaultCMonitor || tao->monitor[i] == TaoDefaultGMonitor || tao->monitor[i] == TaoDefaultSMonitor) {
375:       auglag->info = PETSC_TRUE;
376:     }
377:   }
378:   return 0;
379: }

381: /* -------------------------------------------------------- */

383: /*MC
384:   TaoALMM - Augmented Lagrangian multiplier method for solving nonlinear optimization problems with general constraints.

386:   Options Database Keys:
387: + -tao_almm_mu_init <real>       - initial penalty parameter (default: 10.)
388: . -tao_almm_mu_factor <real>     - increase factor for the penalty parameter (default: 100.)
389: . -tao_almm_mu_max <real>        - maximum safeguard for penalty parameter updates (default: 1.e20)
390: . -tao_almm_mu_power_good <real> - exponential for penalty parameter when multiplier update is accepted (default: 0.9)
391: . -tao_almm_mu_power_bad <real>  - exponential for penalty parameter when multiplier update is rejected (default: 0.1)
392: . -tao_almm_ye_min <real>        - minimum safeguard for equality multiplier updates (default: -1.e20)
393: . -tao_almm_ye_max <real>        - maximum safeguard for equality multiplier updates (default: 1.e20)
394: . -tao_almm_yi_min <real>        - minimum safeguard for inequality multiplier updates (default: -1.e20)
395: . -tao_almm_yi_max <real>        - maximum safeguard for inequality multiplier updates (default: 1.e20)
396: - -tao_almm_type <classic,phr>   - change formulation of the augmented Lagrangian merit function for the subproblem (default: classic)

398:   Level: beginner

400:   Notes:
401:   This method converts a constrained problem into a sequence of unconstrained problems via the augmented
402:   Lagrangian merit function. Bound constraints are pushed down to the subproblem without any modifications.

404:   Two formulations are offered for the subproblem: canonical Hestenes-Powell augmented Lagrangian with slack
405:   variables for inequality constraints, and a slack-less Powell-Hestenes-Rockafellar (PHR) formulation utilizing a
406:   pointwise max() penalty on inequality constraints. The canonical augmented Lagrangian formulation typically
407:   converges faster for most problems. However, PHR may be desirable for problems featuring a large number
408:   of inequality constraints because it avoids inflating the size of the subproblem with slack variables.

410:   The subproblem is solved using a nested first-order TAO solver. The user can retrieve a pointer to
411:   the subsolver via TaoALMMGetSubsolver() or pass command line arguments to it using the
412:   "-tao_almm_subsolver_" prefix. Currently, TaoALMM does not support second-order methods for the
413:   subproblem. It is also highly recommended that the subsolver chosen by the user utilize a trust-region
414:   strategy for globalization (default: TAOBQNKTR) especially if the outer problem features bound constraints.

416: .vb
417:   while unconverged
418:     solve argmin_x L(x) s.t. l <= x <= u
419:     if ||c|| <= y_tol
420:       if ||c|| <= c_tol && ||Lgrad|| <= g_tol:
421:         problem converged, return solution
422:       else
423:         constraints sufficiently improved
424:         update multipliers and tighten tolerances
425:       endif
426:     else
427:       constraints did not improve
428:       update penalty and loosen tolerances
429:     endif
430:   endwhile
431: .ve

433: .seealso: TaoALMMGetType(), TaoALMMSetType(), TaoALMMSetSubsolver(), TaoALMMGetSubsolver(),
434:           TaoALMMGetMultipliers(), TaoALMMSetMultipliers(), TaoALMMGetPrimalIS(), TaoALMMGetDualIS()
435: M*/
436: PETSC_EXTERN PetscErrorCode TaoCreate_ALMM(Tao tao)
437: {
438:   TAO_ALMM       *auglag;

440:   PetscNewLog(tao, &auglag);

442:   tao->ops->destroy        = TaoDestroy_ALMM;
443:   tao->ops->setup          = TaoSetUp_ALMM;
444:   tao->ops->setfromoptions = TaoSetFromOptions_ALMM;
445:   tao->ops->view           = TaoView_ALMM;
446:   tao->ops->solve          = TaoSolve_ALMM;

448:   tao->gatol = 1.e-5;
449:   tao->grtol = 0.0;
450:   tao->gttol = 0.0;
451:   tao->catol = 1.e-5;
452:   tao->crtol = 0.0;

454:   tao->data           = (void*)auglag;
455:   auglag->parent      = tao;
456:   auglag->mu0         = 10.0;
457:   auglag->mu          = auglag->mu0;
458:   auglag->mu_fac      = 10.0;
459:   auglag->mu_max      = PETSC_INFINITY;
460:   auglag->mu_pow_good = 0.9;
461:   auglag->mu_pow_bad  = 0.1;
462:   auglag->ye_min      = PETSC_NINFINITY;
463:   auglag->ye_max      = PETSC_INFINITY;
464:   auglag->yi_min      = PETSC_NINFINITY;
465:   auglag->yi_max      = PETSC_INFINITY;
466:   auglag->ytol0       = 0.1/PetscPowReal(auglag->mu0, auglag->mu_pow_bad);
467:   auglag->ytol        = auglag->ytol0;
468:   auglag->gtol0       = 1.0/auglag->mu0;
469:   auglag->gtol        = auglag->gtol0;

471:   auglag->sub_obj     = TaoALMMComputeAugLagAndGradient_Private;
472:   auglag->type        = TAO_ALMM_CLASSIC;
473:   auglag->info        = PETSC_FALSE;

475:   TaoCreate(PetscObjectComm((PetscObject)tao),&auglag->subsolver);
476:   TaoSetType(auglag->subsolver, TAOBQNKTR);
477:   TaoSetTolerances(auglag->subsolver, auglag->gtol, 0.0, 0.0);
478:   TaoSetMaximumIterations(auglag->subsolver, 1000);
479:   TaoSetMaximumFunctionEvaluations(auglag->subsolver, 10000);
480:   TaoSetFunctionLowerBound(auglag->subsolver, PETSC_NINFINITY);
481:   PetscObjectIncrementTabLevel((PetscObject)auglag->subsolver,(PetscObject)tao,1);

483:   PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetType_C", TaoALMMGetType_Private);
484:   PetscObjectComposeFunction((PetscObject)tao, "TaoALMMSetType_C", TaoALMMSetType_Private);
485:   PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetSubsolver_C", TaoALMMGetSubsolver_Private);
486:   PetscObjectComposeFunction((PetscObject)tao, "TaoALMMSetSubsolver_C", TaoALMMSetSubsolver_Private);
487:   PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetMultipliers_C", TaoALMMGetMultipliers_Private);
488:   PetscObjectComposeFunction((PetscObject)tao, "TaoALMMSetMultipliers_C", TaoALMMSetMultipliers_Private);
489:   PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetPrimalIS_C", TaoALMMGetPrimalIS_Private);
490:   PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetDualIS_C", TaoALMMGetDualIS_Private);
491:   return 0;
492: }

494: static PetscErrorCode TaoALMMCombinePrimal_Private(Tao tao, Vec X, Vec S, Vec P)
495: {
496:   TAO_ALMM     *auglag = (TAO_ALMM*)tao->data;

498:   if (tao->ineq_constrained) {
499:     VecScatterBegin(auglag->Pscatter[0], X, P, INSERT_VALUES, SCATTER_REVERSE);
500:     VecScatterEnd(auglag->Pscatter[0], X, P, INSERT_VALUES, SCATTER_REVERSE);
501:     VecScatterBegin(auglag->Pscatter[1], S, P, INSERT_VALUES, SCATTER_REVERSE);
502:     VecScatterEnd(auglag->Pscatter[1], S, P, INSERT_VALUES, SCATTER_REVERSE);
503:   } else {
504:     VecCopy(X, P);
505:   }
506:   return 0;
507: }

509: static PetscErrorCode TaoALMMCombineDual_Private(Tao tao, Vec EQ, Vec IN, Vec Y)
510: {
511:   TAO_ALMM     *auglag = (TAO_ALMM*)tao->data;

513:   if (tao->eq_constrained) {
514:     if (tao->ineq_constrained) {
515:       VecScatterBegin(auglag->Yscatter[0], EQ, Y, INSERT_VALUES, SCATTER_REVERSE);
516:       VecScatterEnd(auglag->Yscatter[0], EQ, Y, INSERT_VALUES, SCATTER_REVERSE);
517:       VecScatterBegin(auglag->Yscatter[1], IN, Y, INSERT_VALUES, SCATTER_REVERSE);
518:       VecScatterEnd(auglag->Yscatter[1], IN, Y, INSERT_VALUES, SCATTER_REVERSE);
519:     } else {
520:       VecCopy(EQ, Y);
521:     }
522:   } else {
523:     VecCopy(IN, Y);
524:   }
525:   return 0;
526: }

528: static PetscErrorCode TaoALMMSplitPrimal_Private(Tao tao, Vec P, Vec X, Vec S)
529: {
530:   TAO_ALMM     *auglag = (TAO_ALMM*)tao->data;

532:   if (tao->ineq_constrained) {
533:     VecScatterBegin(auglag->Pscatter[0], P, X, INSERT_VALUES, SCATTER_FORWARD);
534:     VecScatterEnd(auglag->Pscatter[0], P, X, INSERT_VALUES, SCATTER_FORWARD);
535:     VecScatterBegin(auglag->Pscatter[1], P, S, INSERT_VALUES, SCATTER_FORWARD);
536:     VecScatterEnd(auglag->Pscatter[1], P, S, INSERT_VALUES, SCATTER_FORWARD);
537:   } else {
538:     VecCopy(P, X);
539:   }
540:   return 0;
541: }

543: /* this assumes that the latest constraints are stored in Ce and Ci, and also combined in C */
544: static PetscErrorCode TaoALMMComputeOptimalityNorms_Private(Tao tao)
545: {
546:   TAO_ALMM     *auglag = (TAO_ALMM*)tao->data;

548:   /* if bounded, project the gradient */
549:   if (tao->bounded) {
550:     VecBoundGradientProjection(auglag->LgradX, auglag->Px, tao->XL, tao->XU, auglag->LgradX);
551:   }
552:   if (auglag->type == TAO_ALMM_PHR) {
553:     VecNorm(auglag->LgradX, NORM_INFINITY, &auglag->gnorm);
554:     auglag->cenorm = 0.0;
555:     if (tao->eq_constrained) {
556:       VecNorm(auglag->Ce, NORM_INFINITY, &auglag->cenorm);
557:     }
558:     auglag->cinorm = 0.0;
559:     if (tao->ineq_constrained) {
560:       VecCopy(auglag->Yi, auglag->Ciwork);
561:       VecScale(auglag->Ciwork, -1.0/auglag->mu);
562:       VecPointwiseMax(auglag->Ciwork, auglag->Ci, auglag->Ciwork);
563:       VecNorm(auglag->Ciwork, NORM_INFINITY, &auglag->cinorm);
564:     }
565:     auglag->cnorm_old = auglag->cnorm;
566:     auglag->cnorm = PetscMax(auglag->cenorm, auglag->cinorm);
567:     auglag->ytol = auglag->ytol0 * auglag->cnorm_old;
568:   } else {
569:     VecNorm(auglag->LgradX, NORM_2, &auglag->gnorm);
570:     VecNorm(auglag->C, NORM_2, &auglag->cnorm);
571:   }
572:   return 0;
573: }

575: static PetscErrorCode TaoALMMEvaluateIterate_Private(Tao tao, Vec P)
576: {
577:   TAO_ALMM       *auglag = (TAO_ALMM*)tao->data;

579:   /* split solution into primal and slack components */
580:   TaoALMMSplitPrimal_Private(tao, auglag->P, auglag->Px, auglag->Ps);

582:   /* compute f, df/dx and the constraints */
583:   TaoComputeObjectiveAndGradient(tao, auglag->Px, &auglag->fval, auglag->LgradX);
584:   if (tao->eq_constrained) {
585:     TaoComputeEqualityConstraints(tao, auglag->Px, auglag->Ce);
586:     TaoComputeJacobianEquality(tao, auglag->Px, auglag->Ae, auglag->Ae);
587:   }
588:   if (tao->ineq_constrained) {
589:     TaoComputeInequalityConstraints(tao, auglag->Px, auglag->Ci);
590:     TaoComputeJacobianInequality(tao, auglag->Px, auglag->Ai, auglag->Ai);
591:     switch (auglag->type) {
592:       case TAO_ALMM_CLASSIC:
593:         /* classic formulation converts inequality to equality constraints via slack variables */
594:         VecAXPY(auglag->Ci, -1.0, auglag->Ps);
595:         break;
596:       case TAO_ALMM_PHR:
597:         /* PHR is based on Ci <= 0 while TAO defines Ci >= 0 so we hit it with a negative sign */
598:         VecScale(auglag->Ci, -1.0);
599:         MatScale(auglag->Ai, -1.0);
600:         break;
601:       default:
602:         break;
603:     }
604:   }
605:   /* combine constraints into one vector */
606:   TaoALMMCombineDual_Private(tao, auglag->Ce, auglag->Ci, auglag->C);
607:   return 0;
608: }

610: /*
611: Lphr = f + 0.5*mu*[ (Ce + Ye/mu)^T (Ce + Ye/mu) + pmin(0, Ci + Yi/mu)^T pmin(0, Ci + Yi/mu)]

613: dLphr/dX = dF/dX + mu*[ (Ce + Ye/mu)^T Ae + pmin(0, Ci + Yi/mu)^T Ai]

615: dLphr/dS = 0
616: */
617: static PetscErrorCode TaoALMMComputePHRLagAndGradient_Private(Tao tao)
618: {
619:   TAO_ALMM       *auglag = (TAO_ALMM*)tao->data;
620:   PetscReal      eq_norm=0.0, ineq_norm=0.0;

622:   TaoALMMEvaluateIterate_Private(tao, auglag->P);
623:   if (tao->eq_constrained) {
624:     /* Ce_work = mu*(Ce + Ye/mu) */
625:     VecWAXPY(auglag->Cework, 1.0/auglag->mu, auglag->Ye, auglag->Ce);
626:     VecDot(auglag->Cework, auglag->Cework, &eq_norm); /* contribution to scalar Lagrangian */
627:     VecScale(auglag->Cework, auglag->mu);
628:     /* dL/dX += mu*(Ce + Ye/mu)^T Ae */
629:     MatMultTransposeAdd(auglag->Ae, auglag->Cework, auglag->LgradX, auglag->LgradX);
630:   }
631:   if (tao->ineq_constrained) {
632:     /* Ci_work = mu * pmax(0, Ci + Yi/mu) where pmax() is pointwise max() */
633:     VecWAXPY(auglag->Ciwork, 1.0/auglag->mu, auglag->Yi, auglag->Ci);
634:     VecPointwiseMax(auglag->Ciwork, auglag->Cizero, auglag->Ciwork);
635:     VecDot(auglag->Ciwork, auglag->Ciwork, &ineq_norm); /* contribution to scalar Lagrangian */
636:     /* dL/dX += mu * pmax(0, Ci + Yi/mu)^T Ai */
637:     VecScale(auglag->Ciwork, auglag->mu);
638:     MatMultTransposeAdd(auglag->Ai, auglag->Ciwork, auglag->LgradX, auglag->LgradX);
639:     /* dL/dS = 0 because there are no slacks in PHR */
640:     VecZeroEntries(auglag->LgradS);
641:   }
642:   /* combine gradient together */
643:   TaoALMMCombinePrimal_Private(tao, auglag->LgradX, auglag->LgradS, auglag->G);
644:   /* compute L = f + 0.5 * mu * [(Ce + Ye/mu)^T (Ce + Ye/mu) + pmax(0, Ci + Yi/mu)^T pmax(0, Ci + Yi/mu)] */
645:   auglag->Lval = auglag->fval + 0.5*auglag->mu*(eq_norm + ineq_norm);
646:   return 0;
647: }

649: /*
650: Lc = F + Ye^TCe + Yi^T(Ci - S) + 0.5*mu*[Ce^TCe + (Ci - S)^T(Ci - S)]

652: dLc/dX = dF/dX + Ye^TAe + Yi^TAi + 0.5*mu*[Ce^TAe + (Ci - S)^TAi]

654: dLc/dS = -[Yi + mu*(Ci - S)]
655: */
656: static PetscErrorCode TaoALMMComputeAugLagAndGradient_Private(Tao tao)
657: {
658:   TAO_ALMM       *auglag = (TAO_ALMM*)tao->data;
659:   PetscReal      yeTce=0.0, yiTcims=0.0, ceTce=0.0, cimsTcims=0.0;

661:   TaoALMMEvaluateIterate_Private(tao, auglag->P);
662:   if (tao->eq_constrained) {
663:     /* compute scalar contributions */
664:     VecDot(auglag->Ye, auglag->Ce, &yeTce);
665:     VecDot(auglag->Ce, auglag->Ce, &ceTce);
666:     /* dL/dX += ye^T Ae */
667:     MatMultTransposeAdd(auglag->Ae, auglag->Ye, auglag->LgradX, auglag->LgradX);
668:     /* dL/dX += mu * ce^T Ae */
669:     MatMultTranspose(auglag->Ae, auglag->Ce, auglag->Xwork);
670:     VecAXPY(auglag->LgradX, auglag->mu, auglag->Xwork);
671:   }
672:   if (tao->ineq_constrained) {
673:     /* compute scalar contributions */
674:     VecDot(auglag->Yi, auglag->Ci, &yiTcims);
675:     VecDot(auglag->Ci, auglag->Ci, &cimsTcims);
676:     /* dL/dX += yi^T Ai */
677:     MatMultTransposeAdd(auglag->Ai, auglag->Yi, auglag->LgradX, auglag->LgradX);
678:     /* dL/dX += mu * (ci - s)^T Ai */
679:     MatMultTranspose(auglag->Ai, auglag->Ci, auglag->Xwork);
680:     VecAXPY(auglag->LgradX, auglag->mu, auglag->Xwork);
681:     /* dL/dS = -[yi + mu*(ci - s)] */
682:     VecWAXPY(auglag->LgradS, auglag->mu, auglag->Ci, auglag->Yi);
683:     VecScale(auglag->LgradS, -1.0);
684:   }
685:   /* combine gradient together */
686:   TaoALMMCombinePrimal_Private(tao, auglag->LgradX, auglag->LgradS, auglag->G);
687:   /* compute L = f + ye^T ce + yi^T (ci - s) + 0.5*mu*||ce||^2 + 0.5*mu*||ci - s||^2 */
688:   auglag->Lval = auglag->fval + yeTce + yiTcims + 0.5*auglag->mu*(ceTce + cimsTcims);
689:   return 0;
690: }

692: PetscErrorCode TaoALMMSubsolverObjective_Private(Tao tao, Vec P, PetscReal *Lval, void *ctx)
693: {
694:   TAO_ALMM       *auglag = (TAO_ALMM*)ctx;

696:   VecCopy(P, auglag->P);
697:   (*auglag->sub_obj)(auglag->parent);
698:   *Lval = auglag->Lval;
699:   return 0;
700: }

702: PetscErrorCode TaoALMMSubsolverObjectiveAndGradient_Private(Tao tao, Vec P, PetscReal *Lval, Vec G, void *ctx)
703: {
704:   TAO_ALMM       *auglag = (TAO_ALMM*)ctx;

706:   VecCopy(P, auglag->P);
707:   (*auglag->sub_obj)(auglag->parent);
708:   VecCopy(auglag->G, G);
709:   *Lval = auglag->Lval;
710:   return 0;
711: }