Actual source code: gpcg.c

  1: #include <petscksp.h>
  2: #include <../src/tao/quadratic/impls/gpcg/gpcg.h>

  4: static PetscErrorCode GPCGGradProjections(Tao tao);
  5: static PetscErrorCode GPCGObjectiveAndGradient(TaoLineSearch, Vec, PetscReal *, Vec, void *);

  7: /*------------------------------------------------------------*/
  8: static PetscErrorCode TaoDestroy_GPCG(Tao tao)
  9: {
 10:   TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;

 12:   /* Free allocated memory in GPCG structure */
 13:   PetscFunctionBegin;
 14:   PetscCall(VecDestroy(&gpcg->B));
 15:   PetscCall(VecDestroy(&gpcg->Work));
 16:   PetscCall(VecDestroy(&gpcg->X_New));
 17:   PetscCall(VecDestroy(&gpcg->G_New));
 18:   PetscCall(VecDestroy(&gpcg->DXFree));
 19:   PetscCall(VecDestroy(&gpcg->R));
 20:   PetscCall(VecDestroy(&gpcg->PG));
 21:   PetscCall(MatDestroy(&gpcg->Hsub));
 22:   PetscCall(MatDestroy(&gpcg->Hsub_pre));
 23:   PetscCall(ISDestroy(&gpcg->Free_Local));
 24:   PetscCall(KSPDestroy(&tao->ksp));
 25:   PetscCall(PetscFree(tao->data));
 26:   PetscFunctionReturn(PETSC_SUCCESS);
 27: }

 29: /*------------------------------------------------------------*/
 30: static PetscErrorCode TaoSetFromOptions_GPCG(Tao tao, PetscOptionItems *PetscOptionsObject)
 31: {
 32:   TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;
 33:   PetscBool flg;

 35:   PetscFunctionBegin;
 36:   PetscOptionsHeadBegin(PetscOptionsObject, "Gradient Projection, Conjugate Gradient method for bound constrained optimization");
 37:   PetscCall(PetscOptionsInt("-tao_gpcg_maxpgits", "maximum number of gradient projections per GPCG iterate", NULL, gpcg->maxgpits, &gpcg->maxgpits, &flg));
 38:   PetscOptionsHeadEnd();
 39:   PetscCall(KSPSetFromOptions(tao->ksp));
 40:   PetscCall(TaoLineSearchSetFromOptions(tao->linesearch));
 41:   PetscFunctionReturn(PETSC_SUCCESS);
 42: }

 44: /*------------------------------------------------------------*/
 45: static PetscErrorCode TaoView_GPCG(Tao tao, PetscViewer viewer)
 46: {
 47:   TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;
 48:   PetscBool isascii;

 50:   PetscFunctionBegin;
 51:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
 52:   if (isascii) {
 53:     PetscCall(PetscViewerASCIIPrintf(viewer, "Total PG its: %" PetscInt_FMT ",", gpcg->total_gp_its));
 54:     PetscCall(PetscViewerASCIIPrintf(viewer, "PG tolerance: %g \n", (double)gpcg->pg_ftol));
 55:   }
 56:   PetscCall(TaoLineSearchView(tao->linesearch, viewer));
 57:   PetscFunctionReturn(PETSC_SUCCESS);
 58: }

 60: /* GPCGObjectiveAndGradient()
 61:    Compute f=0.5 * x'Hx + b'x + c
 62:            g=Hx + b
 63: */
 64: static PetscErrorCode GPCGObjectiveAndGradient(TaoLineSearch ls, Vec X, PetscReal *f, Vec G, void *tptr)
 65: {
 66:   Tao       tao  = (Tao)tptr;
 67:   TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;
 68:   PetscReal f1, f2;

 70:   PetscFunctionBegin;
 71:   PetscCall(MatMult(tao->hessian, X, G));
 72:   PetscCall(VecDot(G, X, &f1));
 73:   PetscCall(VecDot(gpcg->B, X, &f2));
 74:   PetscCall(VecAXPY(G, 1.0, gpcg->B));
 75:   *f = f1 / 2.0 + f2 + gpcg->c;
 76:   PetscFunctionReturn(PETSC_SUCCESS);
 77: }

 79: /* ---------------------------------------------------------- */
 80: static PetscErrorCode TaoSetup_GPCG(Tao tao)
 81: {
 82:   TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;

 84:   PetscFunctionBegin;
 85:   /* Allocate some arrays */
 86:   if (!tao->gradient) PetscCall(VecDuplicate(tao->solution, &tao->gradient));
 87:   if (!tao->stepdirection) PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));

 89:   PetscCall(VecDuplicate(tao->solution, &gpcg->B));
 90:   PetscCall(VecDuplicate(tao->solution, &gpcg->Work));
 91:   PetscCall(VecDuplicate(tao->solution, &gpcg->X_New));
 92:   PetscCall(VecDuplicate(tao->solution, &gpcg->G_New));
 93:   PetscCall(VecDuplicate(tao->solution, &gpcg->DXFree));
 94:   PetscCall(VecDuplicate(tao->solution, &gpcg->R));
 95:   PetscCall(VecDuplicate(tao->solution, &gpcg->PG));
 96:   /*
 97:     if (gpcg->ksp_type == GPCG_KSP_NASH) {
 98:         PetscCall(KSPSetType(tao->ksp,KSPNASH));
 99:       } else if (gpcg->ksp_type == GPCG_KSP_STCG) {
100:         PetscCall(KSPSetType(tao->ksp,KSPSTCG));
101:       } else {
102:         PetscCall(KSPSetType(tao->ksp,KSPGLTR));
103:       }
104:       if (tao->ksp->ops->setfromoptions) {
105:         (*tao->ksp->ops->setfromoptions)(tao->ksp);
106:       }

108:     }
109:   */
110:   PetscFunctionReturn(PETSC_SUCCESS);
111: }

113: static PetscErrorCode TaoSolve_GPCG(Tao tao)
114: {
115:   TAO_GPCG                    *gpcg = (TAO_GPCG *)tao->data;
116:   PetscInt                     its;
117:   PetscReal                    actred, f, f_new, gnorm, gdx, stepsize, xtb;
118:   PetscReal                    xtHx;
119:   TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;

121:   PetscFunctionBegin;
122:   PetscCall(TaoComputeVariableBounds(tao));
123:   PetscCall(VecMedian(tao->XL, tao->solution, tao->XU, tao->solution));
124:   PetscCall(TaoLineSearchSetVariableBounds(tao->linesearch, tao->XL, tao->XU));

126:   /* Using f = .5*x'Hx + x'b + c and g=Hx + b,  compute b,c */
127:   PetscCall(TaoComputeHessian(tao, tao->solution, tao->hessian, tao->hessian_pre));
128:   PetscCall(TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient));
129:   PetscCall(VecCopy(tao->gradient, gpcg->B));
130:   PetscCall(MatMult(tao->hessian, tao->solution, gpcg->Work));
131:   PetscCall(VecDot(gpcg->Work, tao->solution, &xtHx));
132:   PetscCall(VecAXPY(gpcg->B, -1.0, gpcg->Work));
133:   PetscCall(VecDot(gpcg->B, tao->solution, &xtb));
134:   gpcg->c = f - xtHx / 2.0 - xtb;
135:   if (gpcg->Free_Local) PetscCall(ISDestroy(&gpcg->Free_Local));
136:   PetscCall(VecWhichInactive(tao->XL, tao->solution, tao->gradient, tao->XU, PETSC_TRUE, &gpcg->Free_Local));

138:   /* Project the gradient and calculate the norm */
139:   PetscCall(VecCopy(tao->gradient, gpcg->G_New));
140:   PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, gpcg->PG));
141:   PetscCall(VecNorm(gpcg->PG, NORM_2, &gpcg->gnorm));
142:   tao->step = 1.0;
143:   gpcg->f   = f;

145:   /* Check Stopping Condition      */
146:   tao->reason = TAO_CONTINUE_ITERATING;
147:   PetscCall(TaoLogConvergenceHistory(tao, f, gpcg->gnorm, 0.0, tao->ksp_its));
148:   PetscCall(TaoMonitor(tao, tao->niter, f, gpcg->gnorm, 0.0, tao->step));
149:   PetscUseTypeMethod(tao, convergencetest, tao->cnvP);

151:   while (tao->reason == TAO_CONTINUE_ITERATING) {
152:     /* Call general purpose update function */
153:     PetscTryTypeMethod(tao, update, tao->niter, tao->user_update);
154:     tao->ksp_its = 0;

156:     PetscCall(GPCGGradProjections(tao));
157:     PetscCall(ISGetSize(gpcg->Free_Local, &gpcg->n_free));

159:     f     = gpcg->f;
160:     gnorm = gpcg->gnorm;

162:     PetscCall(KSPReset(tao->ksp));

164:     if (gpcg->n_free > 0) {
165:       /* Create a reduced linear system */
166:       PetscCall(VecDestroy(&gpcg->R));
167:       PetscCall(VecDestroy(&gpcg->DXFree));
168:       PetscCall(TaoVecGetSubVec(tao->gradient, gpcg->Free_Local, tao->subset_type, 0.0, &gpcg->R));
169:       PetscCall(VecScale(gpcg->R, -1.0));
170:       PetscCall(TaoVecGetSubVec(tao->stepdirection, gpcg->Free_Local, tao->subset_type, 0.0, &gpcg->DXFree));
171:       PetscCall(VecSet(gpcg->DXFree, 0.0));

173:       PetscCall(TaoMatGetSubMat(tao->hessian, gpcg->Free_Local, gpcg->Work, tao->subset_type, &gpcg->Hsub));

175:       if (tao->hessian_pre == tao->hessian) {
176:         PetscCall(MatDestroy(&gpcg->Hsub_pre));
177:         PetscCall(PetscObjectReference((PetscObject)gpcg->Hsub));
178:         gpcg->Hsub_pre = gpcg->Hsub;
179:       } else {
180:         PetscCall(TaoMatGetSubMat(tao->hessian, gpcg->Free_Local, gpcg->Work, tao->subset_type, &gpcg->Hsub_pre));
181:       }

183:       PetscCall(KSPReset(tao->ksp));
184:       PetscCall(KSPSetOperators(tao->ksp, gpcg->Hsub, gpcg->Hsub_pre));

186:       PetscCall(KSPSolve(tao->ksp, gpcg->R, gpcg->DXFree));
187:       PetscCall(KSPGetIterationNumber(tao->ksp, &its));
188:       tao->ksp_its += its;
189:       tao->ksp_tot_its += its;
190:       PetscCall(VecSet(tao->stepdirection, 0.0));
191:       PetscCall(VecISAXPY(tao->stepdirection, gpcg->Free_Local, 1.0, gpcg->DXFree));

193:       PetscCall(VecDot(tao->stepdirection, tao->gradient, &gdx));
194:       PetscCall(TaoLineSearchSetInitialStepLength(tao->linesearch, 1.0));
195:       f_new = f;
196:       PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f_new, tao->gradient, tao->stepdirection, &stepsize, &ls_status));

198:       actred = f_new - f;

200:       /* Evaluate the function and gradient at the new point */
201:       PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, gpcg->PG));
202:       PetscCall(VecNorm(gpcg->PG, NORM_2, &gnorm));
203:       f = f_new;
204:       PetscCall(ISDestroy(&gpcg->Free_Local));
205:       PetscCall(VecWhichInactive(tao->XL, tao->solution, tao->gradient, tao->XU, PETSC_TRUE, &gpcg->Free_Local));
206:     } else {
207:       actred     = 0;
208:       gpcg->step = 1.0;
209:       /* if there were no free variables, no cg method */
210:     }

212:     tao->niter++;
213:     gpcg->f      = f;
214:     gpcg->gnorm  = gnorm;
215:     gpcg->actred = actred;
216:     PetscCall(TaoLogConvergenceHistory(tao, f, gpcg->gnorm, 0.0, tao->ksp_its));
217:     PetscCall(TaoMonitor(tao, tao->niter, f, gpcg->gnorm, 0.0, tao->step));
218:     PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
219:     if (tao->reason != TAO_CONTINUE_ITERATING) break;
220:   } /* END MAIN LOOP  */
221:   PetscFunctionReturn(PETSC_SUCCESS);
222: }

224: static PetscErrorCode GPCGGradProjections(Tao tao)
225: {
226:   TAO_GPCG                    *gpcg = (TAO_GPCG *)tao->data;
227:   PetscInt                     i;
228:   PetscReal                    actred = -1.0, actred_max = 0.0, gAg, gtg = gpcg->gnorm, alpha;
229:   PetscReal                    f_new, gdx, stepsize;
230:   Vec                          DX = tao->stepdirection, XL = tao->XL, XU = tao->XU, Work = gpcg->Work;
231:   Vec                          X = tao->solution, G = tao->gradient;
232:   TaoLineSearchConvergedReason lsflag = TAOLINESEARCH_CONTINUE_ITERATING;

234:   /*
235:      The free, active, and binding variables should be already identified
236:   */
237:   PetscFunctionBegin;
238:   for (i = 0; i < gpcg->maxgpits; i++) {
239:     if (-actred <= (gpcg->pg_ftol) * actred_max) break;
240:     PetscCall(VecBoundGradientProjection(G, X, XL, XU, DX));
241:     PetscCall(VecScale(DX, -1.0));
242:     PetscCall(VecDot(DX, G, &gdx));

244:     PetscCall(MatMult(tao->hessian, DX, Work));
245:     PetscCall(VecDot(DX, Work, &gAg));

247:     gpcg->gp_iterates++;
248:     gpcg->total_gp_its++;

250:     gtg = -gdx;
251:     if (PetscAbsReal(gAg) == 0.0) {
252:       alpha = 1.0;
253:     } else {
254:       alpha = PetscAbsReal(gtg / gAg);
255:     }
256:     PetscCall(TaoLineSearchSetInitialStepLength(tao->linesearch, alpha));
257:     f_new = gpcg->f;
258:     PetscCall(TaoLineSearchApply(tao->linesearch, X, &f_new, G, DX, &stepsize, &lsflag));

260:     /* Update the iterate */
261:     actred     = f_new - gpcg->f;
262:     actred_max = PetscMax(actred_max, -(f_new - gpcg->f));
263:     gpcg->f    = f_new;
264:     PetscCall(ISDestroy(&gpcg->Free_Local));
265:     PetscCall(VecWhichInactive(XL, X, tao->gradient, XU, PETSC_TRUE, &gpcg->Free_Local));
266:   }

268:   gpcg->gnorm = gtg;
269:   PetscFunctionReturn(PETSC_SUCCESS);
270: } /* End gradient projections */

272: static PetscErrorCode TaoComputeDual_GPCG(Tao tao, Vec DXL, Vec DXU)
273: {
274:   TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;

276:   PetscFunctionBegin;
277:   PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, gpcg->Work));
278:   PetscCall(VecCopy(gpcg->Work, DXL));
279:   PetscCall(VecAXPY(DXL, -1.0, tao->gradient));
280:   PetscCall(VecSet(DXU, 0.0));
281:   PetscCall(VecPointwiseMax(DXL, DXL, DXU));

283:   PetscCall(VecCopy(tao->gradient, DXU));
284:   PetscCall(VecAXPY(DXU, -1.0, gpcg->Work));
285:   PetscCall(VecSet(gpcg->Work, 0.0));
286:   PetscCall(VecPointwiseMin(DXU, gpcg->Work, DXU));
287:   PetscFunctionReturn(PETSC_SUCCESS);
288: }

290: /*------------------------------------------------------------*/
291: /*MC
292:   TAOGPCG - gradient projected conjugate gradient algorithm is an active-set
293:         conjugate-gradient based method for bound-constrained minimization

295:   Options Database Keys:
296: + -tao_gpcg_maxpgits - maximum number of gradient projections for GPCG iterate
297: - -tao_subset_type - "subvec","mask","matrix-free", strategies for handling active-sets

299:   Level: beginner
300: M*/
301: PETSC_EXTERN PetscErrorCode TaoCreate_GPCG(Tao tao)
302: {
303:   TAO_GPCG *gpcg;

305:   PetscFunctionBegin;
306:   tao->ops->setup          = TaoSetup_GPCG;
307:   tao->ops->solve          = TaoSolve_GPCG;
308:   tao->ops->view           = TaoView_GPCG;
309:   tao->ops->setfromoptions = TaoSetFromOptions_GPCG;
310:   tao->ops->destroy        = TaoDestroy_GPCG;
311:   tao->ops->computedual    = TaoComputeDual_GPCG;

313:   PetscCall(PetscNew(&gpcg));
314:   tao->data = (void *)gpcg;

316:   /* Override default settings (unless already changed) */
317:   PetscCall(TaoParametersInitialize(tao));
318:   PetscObjectParameterSetDefault(tao, max_it, 500);
319:   PetscObjectParameterSetDefault(tao, max_funcs, 100000);
320:   PetscObjectParameterSetDefault(tao, gatol, PetscDefined(USE_REAL_SINGLE) ? 1e-6 : 1e-12);
321:   PetscObjectParameterSetDefault(tao, grtol, PetscDefined(USE_REAL_SINGLE) ? 1e-6 : 1e-12);

323:   /* Initialize pointers and variables */
324:   gpcg->n        = 0;
325:   gpcg->maxgpits = 8;
326:   gpcg->pg_ftol  = 0.1;

328:   gpcg->gp_iterates  = 0; /* Cumulative number */
329:   gpcg->total_gp_its = 0;

331:   /* Initialize pointers and variables */
332:   gpcg->n_bind      = 0;
333:   gpcg->n_free      = 0;
334:   gpcg->n_upper     = 0;
335:   gpcg->n_lower     = 0;
336:   gpcg->subset_type = TAO_SUBSET_MASK;
337:   gpcg->Hsub        = NULL;
338:   gpcg->Hsub_pre    = NULL;

340:   PetscCall(KSPCreate(((PetscObject)tao)->comm, &tao->ksp));
341:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1));
342:   PetscCall(KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix));
343:   PetscCall(KSPSetType(tao->ksp, KSPNASH));

345:   PetscCall(TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch));
346:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1));
347:   PetscCall(TaoLineSearchSetType(tao->linesearch, TAOLINESEARCHGPCG));
348:   PetscCall(TaoLineSearchSetObjectiveAndGradientRoutine(tao->linesearch, GPCGObjectiveAndGradient, tao));
349:   PetscCall(TaoLineSearchSetOptionsPrefix(tao->linesearch, tao->hdr.prefix));
350:   PetscFunctionReturn(PETSC_SUCCESS);
351: }