1 #include <petscksp.h> 2 #include <../src/tao/quadratic/impls/gpcg/gpcg.h> /*I "gpcg.h" I*/ 3 4 static PetscErrorCode GPCGGradProjections(Tao tao); 5 static PetscErrorCode GPCGObjectiveAndGradient(TaoLineSearch, Vec, PetscReal *, Vec, void *); 6 7 /*------------------------------------------------------------*/ 8 static PetscErrorCode TaoDestroy_GPCG(Tao tao) 9 { 10 TAO_GPCG *gpcg = (TAO_GPCG *)tao->data; 11 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(0); 27 } 28 29 /*------------------------------------------------------------*/ 30 static PetscErrorCode TaoSetFromOptions_GPCG(Tao tao, PetscOptionItems *PetscOptionsObject) 31 { 32 TAO_GPCG *gpcg = (TAO_GPCG *)tao->data; 33 PetscBool flg; 34 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(0); 42 } 43 44 /*------------------------------------------------------------*/ 45 static PetscErrorCode TaoView_GPCG(Tao tao, PetscViewer viewer) 46 { 47 TAO_GPCG *gpcg = (TAO_GPCG *)tao->data; 48 PetscBool isascii; 49 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(0); 58 } 59 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; 69 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(0); 77 } 78 79 /* ---------------------------------------------------------- */ 80 static PetscErrorCode TaoSetup_GPCG(Tao tao) 81 { 82 TAO_GPCG *gpcg = (TAO_GPCG *)tao->data; 83 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)); 88 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 } 107 108 } 109 */ 110 PetscFunctionReturn(0); 111 } 112 113 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; 120 121 PetscFunctionBegin; 122 123 PetscCall(TaoComputeVariableBounds(tao)); 124 PetscCall(VecMedian(tao->XL, tao->solution, tao->XU, tao->solution)); 125 PetscCall(TaoLineSearchSetVariableBounds(tao->linesearch, tao->XL, tao->XU)); 126 127 /* Using f = .5*x'Hx + x'b + c and g=Hx + b, compute b,c */ 128 PetscCall(TaoComputeHessian(tao, tao->solution, tao->hessian, tao->hessian_pre)); 129 PetscCall(TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient)); 130 PetscCall(VecCopy(tao->gradient, gpcg->B)); 131 PetscCall(MatMult(tao->hessian, tao->solution, gpcg->Work)); 132 PetscCall(VecDot(gpcg->Work, tao->solution, &xtHx)); 133 PetscCall(VecAXPY(gpcg->B, -1.0, gpcg->Work)); 134 PetscCall(VecDot(gpcg->B, tao->solution, &xtb)); 135 gpcg->c = f - xtHx / 2.0 - xtb; 136 if (gpcg->Free_Local) PetscCall(ISDestroy(&gpcg->Free_Local)); 137 PetscCall(VecWhichInactive(tao->XL, tao->solution, tao->gradient, tao->XU, PETSC_TRUE, &gpcg->Free_Local)); 138 139 /* Project the gradient and calculate the norm */ 140 PetscCall(VecCopy(tao->gradient, gpcg->G_New)); 141 PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, gpcg->PG)); 142 PetscCall(VecNorm(gpcg->PG, NORM_2, &gpcg->gnorm)); 143 tao->step = 1.0; 144 gpcg->f = f; 145 146 /* Check Stopping Condition */ 147 tao->reason = TAO_CONTINUE_ITERATING; 148 PetscCall(TaoLogConvergenceHistory(tao, f, gpcg->gnorm, 0.0, tao->ksp_its)); 149 PetscCall(TaoMonitor(tao, tao->niter, f, gpcg->gnorm, 0.0, tao->step)); 150 PetscUseTypeMethod(tao, convergencetest, tao->cnvP); 151 152 while (tao->reason == TAO_CONTINUE_ITERATING) { 153 /* Call general purpose update function */ 154 PetscTryTypeMethod(tao, update, tao->niter, tao->user_update); 155 tao->ksp_its = 0; 156 157 PetscCall(GPCGGradProjections(tao)); 158 PetscCall(ISGetSize(gpcg->Free_Local, &gpcg->n_free)); 159 160 f = gpcg->f; 161 gnorm = gpcg->gnorm; 162 163 PetscCall(KSPReset(tao->ksp)); 164 165 if (gpcg->n_free > 0) { 166 /* Create a reduced linear system */ 167 PetscCall(VecDestroy(&gpcg->R)); 168 PetscCall(VecDestroy(&gpcg->DXFree)); 169 PetscCall(TaoVecGetSubVec(tao->gradient, gpcg->Free_Local, tao->subset_type, 0.0, &gpcg->R)); 170 PetscCall(VecScale(gpcg->R, -1.0)); 171 PetscCall(TaoVecGetSubVec(tao->stepdirection, gpcg->Free_Local, tao->subset_type, 0.0, &gpcg->DXFree)); 172 PetscCall(VecSet(gpcg->DXFree, 0.0)); 173 174 PetscCall(TaoMatGetSubMat(tao->hessian, gpcg->Free_Local, gpcg->Work, tao->subset_type, &gpcg->Hsub)); 175 176 if (tao->hessian_pre == tao->hessian) { 177 PetscCall(MatDestroy(&gpcg->Hsub_pre)); 178 PetscCall(PetscObjectReference((PetscObject)gpcg->Hsub)); 179 gpcg->Hsub_pre = gpcg->Hsub; 180 } else { 181 PetscCall(TaoMatGetSubMat(tao->hessian, gpcg->Free_Local, gpcg->Work, tao->subset_type, &gpcg->Hsub_pre)); 182 } 183 184 PetscCall(KSPReset(tao->ksp)); 185 PetscCall(KSPSetOperators(tao->ksp, gpcg->Hsub, gpcg->Hsub_pre)); 186 187 PetscCall(KSPSolve(tao->ksp, gpcg->R, gpcg->DXFree)); 188 PetscCall(KSPGetIterationNumber(tao->ksp, &its)); 189 tao->ksp_its += its; 190 tao->ksp_tot_its += its; 191 PetscCall(VecSet(tao->stepdirection, 0.0)); 192 PetscCall(VecISAXPY(tao->stepdirection, gpcg->Free_Local, 1.0, gpcg->DXFree)); 193 194 PetscCall(VecDot(tao->stepdirection, tao->gradient, &gdx)); 195 PetscCall(TaoLineSearchSetInitialStepLength(tao->linesearch, 1.0)); 196 f_new = f; 197 PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f_new, tao->gradient, tao->stepdirection, &stepsize, &ls_status)); 198 199 actred = f_new - f; 200 201 /* Evaluate the function and gradient at the new point */ 202 PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, gpcg->PG)); 203 PetscCall(VecNorm(gpcg->PG, NORM_2, &gnorm)); 204 f = f_new; 205 PetscCall(ISDestroy(&gpcg->Free_Local)); 206 PetscCall(VecWhichInactive(tao->XL, tao->solution, tao->gradient, tao->XU, PETSC_TRUE, &gpcg->Free_Local)); 207 } else { 208 actred = 0; 209 gpcg->step = 1.0; 210 /* if there were no free variables, no cg method */ 211 } 212 213 tao->niter++; 214 gpcg->f = f; 215 gpcg->gnorm = gnorm; 216 gpcg->actred = actred; 217 PetscCall(TaoLogConvergenceHistory(tao, f, gpcg->gnorm, 0.0, tao->ksp_its)); 218 PetscCall(TaoMonitor(tao, tao->niter, f, gpcg->gnorm, 0.0, tao->step)); 219 PetscUseTypeMethod(tao, convergencetest, tao->cnvP); 220 if (tao->reason != TAO_CONTINUE_ITERATING) break; 221 } /* END MAIN LOOP */ 222 223 PetscFunctionReturn(0); 224 } 225 226 static PetscErrorCode GPCGGradProjections(Tao tao) 227 { 228 TAO_GPCG *gpcg = (TAO_GPCG *)tao->data; 229 PetscInt i; 230 PetscReal actred = -1.0, actred_max = 0.0, gAg, gtg = gpcg->gnorm, alpha; 231 PetscReal f_new, gdx, stepsize; 232 Vec DX = tao->stepdirection, XL = tao->XL, XU = tao->XU, Work = gpcg->Work; 233 Vec X = tao->solution, G = tao->gradient; 234 TaoLineSearchConvergedReason lsflag = TAOLINESEARCH_CONTINUE_ITERATING; 235 236 /* 237 The free, active, and binding variables should be already identified 238 */ 239 PetscFunctionBegin; 240 for (i = 0; i < gpcg->maxgpits; i++) { 241 if (-actred <= (gpcg->pg_ftol) * actred_max) break; 242 PetscCall(VecBoundGradientProjection(G, X, XL, XU, DX)); 243 PetscCall(VecScale(DX, -1.0)); 244 PetscCall(VecDot(DX, G, &gdx)); 245 246 PetscCall(MatMult(tao->hessian, DX, Work)); 247 PetscCall(VecDot(DX, Work, &gAg)); 248 249 gpcg->gp_iterates++; 250 gpcg->total_gp_its++; 251 252 gtg = -gdx; 253 if (PetscAbsReal(gAg) == 0.0) { 254 alpha = 1.0; 255 } else { 256 alpha = PetscAbsReal(gtg / gAg); 257 } 258 PetscCall(TaoLineSearchSetInitialStepLength(tao->linesearch, alpha)); 259 f_new = gpcg->f; 260 PetscCall(TaoLineSearchApply(tao->linesearch, X, &f_new, G, DX, &stepsize, &lsflag)); 261 262 /* Update the iterate */ 263 actred = f_new - gpcg->f; 264 actred_max = PetscMax(actred_max, -(f_new - gpcg->f)); 265 gpcg->f = f_new; 266 PetscCall(ISDestroy(&gpcg->Free_Local)); 267 PetscCall(VecWhichInactive(XL, X, tao->gradient, XU, PETSC_TRUE, &gpcg->Free_Local)); 268 } 269 270 gpcg->gnorm = gtg; 271 PetscFunctionReturn(0); 272 } /* End gradient projections */ 273 274 static PetscErrorCode TaoComputeDual_GPCG(Tao tao, Vec DXL, Vec DXU) 275 { 276 TAO_GPCG *gpcg = (TAO_GPCG *)tao->data; 277 278 PetscFunctionBegin; 279 PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, gpcg->Work)); 280 PetscCall(VecCopy(gpcg->Work, DXL)); 281 PetscCall(VecAXPY(DXL, -1.0, tao->gradient)); 282 PetscCall(VecSet(DXU, 0.0)); 283 PetscCall(VecPointwiseMax(DXL, DXL, DXU)); 284 285 PetscCall(VecCopy(tao->gradient, DXU)); 286 PetscCall(VecAXPY(DXU, -1.0, gpcg->Work)); 287 PetscCall(VecSet(gpcg->Work, 0.0)); 288 PetscCall(VecPointwiseMin(DXU, gpcg->Work, DXU)); 289 PetscFunctionReturn(0); 290 } 291 292 /*------------------------------------------------------------*/ 293 /*MC 294 TAOGPCG - gradient projected conjugate gradient algorithm is an active-set 295 conjugate-gradient based method for bound-constrained minimization 296 297 Options Database Keys: 298 + -tao_gpcg_maxpgits - maximum number of gradient projections for GPCG iterate 299 - -tao_subset_type - "subvec","mask","matrix-free", strategies for handling active-sets 300 301 Level: beginner 302 M*/ 303 PETSC_EXTERN PetscErrorCode TaoCreate_GPCG(Tao tao) 304 { 305 TAO_GPCG *gpcg; 306 307 PetscFunctionBegin; 308 tao->ops->setup = TaoSetup_GPCG; 309 tao->ops->solve = TaoSolve_GPCG; 310 tao->ops->view = TaoView_GPCG; 311 tao->ops->setfromoptions = TaoSetFromOptions_GPCG; 312 tao->ops->destroy = TaoDestroy_GPCG; 313 tao->ops->computedual = TaoComputeDual_GPCG; 314 315 PetscCall(PetscNew(&gpcg)); 316 tao->data = (void *)gpcg; 317 318 /* Override default settings (unless already changed) */ 319 if (!tao->max_it_changed) tao->max_it = 500; 320 if (!tao->max_funcs_changed) tao->max_funcs = 100000; 321 #if defined(PETSC_USE_REAL_SINGLE) 322 if (!tao->gatol_changed) tao->gatol = 1e-6; 323 if (!tao->grtol_changed) tao->grtol = 1e-6; 324 #else 325 if (!tao->gatol_changed) tao->gatol = 1e-12; 326 if (!tao->grtol_changed) tao->grtol = 1e-12; 327 #endif 328 329 /* Initialize pointers and variables */ 330 gpcg->n = 0; 331 gpcg->maxgpits = 8; 332 gpcg->pg_ftol = 0.1; 333 334 gpcg->gp_iterates = 0; /* Cumulative number */ 335 gpcg->total_gp_its = 0; 336 337 /* Initialize pointers and variables */ 338 gpcg->n_bind = 0; 339 gpcg->n_free = 0; 340 gpcg->n_upper = 0; 341 gpcg->n_lower = 0; 342 gpcg->subset_type = TAO_SUBSET_MASK; 343 gpcg->Hsub = NULL; 344 gpcg->Hsub_pre = NULL; 345 346 PetscCall(KSPCreate(((PetscObject)tao)->comm, &tao->ksp)); 347 PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1)); 348 PetscCall(KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix)); 349 PetscCall(KSPSetType(tao->ksp, KSPNASH)); 350 351 PetscCall(TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch)); 352 PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1)); 353 PetscCall(TaoLineSearchSetType(tao->linesearch, TAOLINESEARCHGPCG)); 354 PetscCall(TaoLineSearchSetObjectiveAndGradientRoutine(tao->linesearch, GPCGObjectiveAndGradient, tao)); 355 PetscCall(TaoLineSearchSetOptionsPrefix(tao->linesearch, tao->hdr.prefix)); 356 PetscFunctionReturn(0); 357 } 358