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: /*------------------------------------------------------------*/
7: static PetscErrorCode TaoDestroy_TRON(Tao tao)
8: {
9: TAO_TRON *tron = (TAO_TRON *)tao->data;
11: PetscFunctionBegin;
12: PetscCall(VecDestroy(&tron->X_New));
13: PetscCall(VecDestroy(&tron->G_New));
14: PetscCall(VecDestroy(&tron->Work));
15: PetscCall(VecDestroy(&tron->DXFree));
16: PetscCall(VecDestroy(&tron->R));
17: PetscCall(VecDestroy(&tron->diag));
18: PetscCall(VecScatterDestroy(&tron->scatter));
19: PetscCall(ISDestroy(&tron->Free_Local));
20: PetscCall(MatDestroy(&tron->H_sub));
21: PetscCall(MatDestroy(&tron->Hpre_sub));
22: PetscCall(KSPDestroy(&tao->ksp));
23: PetscCall(PetscFree(tao->data));
24: PetscFunctionReturn(PETSC_SUCCESS);
25: }
27: /*------------------------------------------------------------*/
28: static PetscErrorCode TaoSetFromOptions_TRON(Tao tao, PetscOptionItems *PetscOptionsObject)
29: {
30: TAO_TRON *tron = (TAO_TRON *)tao->data;
31: PetscBool flg;
33: PetscFunctionBegin;
34: PetscOptionsHeadBegin(PetscOptionsObject, "Newton Trust Region Method for bound constrained optimization");
35: PetscCall(PetscOptionsInt("-tao_tron_maxgpits", "maximum number of gradient projections per TRON iterate", "TaoSetMaxGPIts", tron->maxgpits, &tron->maxgpits, &flg));
36: PetscOptionsHeadEnd();
37: PetscCall(KSPSetFromOptions(tao->ksp));
38: PetscFunctionReturn(PETSC_SUCCESS);
39: }
41: /*------------------------------------------------------------*/
42: static PetscErrorCode TaoView_TRON(Tao tao, PetscViewer viewer)
43: {
44: TAO_TRON *tron = (TAO_TRON *)tao->data;
45: PetscBool isascii;
47: PetscFunctionBegin;
48: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
49: if (isascii) {
50: PetscCall(PetscViewerASCIIPrintf(viewer, "Total PG its: %" PetscInt_FMT ",", tron->total_gp_its));
51: PetscCall(PetscViewerASCIIPrintf(viewer, "PG tolerance: %g \n", (double)tron->pg_ftol));
52: }
53: PetscFunctionReturn(PETSC_SUCCESS);
54: }
56: /* ---------------------------------------------------------- */
57: static PetscErrorCode TaoSetup_TRON(Tao tao)
58: {
59: TAO_TRON *tron = (TAO_TRON *)tao->data;
61: PetscFunctionBegin;
62: /* Allocate some arrays */
63: PetscCall(VecDuplicate(tao->solution, &tron->diag));
64: PetscCall(VecDuplicate(tao->solution, &tron->X_New));
65: PetscCall(VecDuplicate(tao->solution, &tron->G_New));
66: PetscCall(VecDuplicate(tao->solution, &tron->Work));
67: PetscCall(VecDuplicate(tao->solution, &tao->gradient));
68: PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));
69: PetscFunctionReturn(PETSC_SUCCESS);
70: }
72: static PetscErrorCode TaoSolve_TRON(Tao tao)
73: {
74: TAO_TRON *tron = (TAO_TRON *)tao->data;
75: PetscInt its;
76: TaoLineSearchConvergedReason ls_reason = TAOLINESEARCH_CONTINUE_ITERATING;
77: PetscReal prered, actred, delta, f, f_new, rhok, gdx, xdiff, stepsize;
79: PetscFunctionBegin;
80: tron->pgstepsize = 1.0;
81: tao->trust = tao->trust0;
82: /* Project the current point onto the feasible set */
83: PetscCall(TaoComputeVariableBounds(tao));
84: PetscCall(TaoLineSearchSetVariableBounds(tao->linesearch, tao->XL, tao->XU));
86: /* Project the initial point onto the feasible region */
87: PetscCall(VecMedian(tao->XL, tao->solution, tao->XU, tao->solution));
89: /* Compute the objective function and gradient */
90: PetscCall(TaoComputeObjectiveAndGradient(tao, tao->solution, &tron->f, tao->gradient));
91: PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));
92: PetscCheck(!PetscIsInfOrNanReal(tron->f) && !PetscIsInfOrNanReal(tron->gnorm), PetscObjectComm((PetscObject)tao), PETSC_ERR_USER, "User provided compute function generated Inf or NaN");
94: /* Project the gradient and calculate the norm */
95: PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, tao->gradient));
96: PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));
98: /* Initialize trust region radius */
99: tao->trust = tao->trust0;
100: if (tao->trust <= 0) tao->trust = PetscMax(tron->gnorm * tron->gnorm, 1.0);
102: /* Initialize step sizes for the line searches */
103: tron->pgstepsize = 1.0;
104: tron->stepsize = tao->trust;
106: tao->reason = TAO_CONTINUE_ITERATING;
107: PetscCall(TaoLogConvergenceHistory(tao, tron->f, tron->gnorm, 0.0, tao->ksp_its));
108: PetscCall(TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, tron->stepsize));
109: PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
110: while (tao->reason == TAO_CONTINUE_ITERATING) {
111: /* Call general purpose update function */
112: PetscTryTypeMethod(tao, update, tao->niter, tao->user_update);
114: /* Perform projected gradient iterations */
115: PetscCall(TronGradientProjections(tao, tron));
117: PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, tao->gradient));
118: PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));
120: tao->ksp_its = 0;
121: f = tron->f;
122: delta = tao->trust;
123: tron->n_free_last = tron->n_free;
124: PetscCall(TaoComputeHessian(tao, tao->solution, tao->hessian, tao->hessian_pre));
126: /* Generate index set (IS) of which bound constraints are active */
127: PetscCall(ISDestroy(&tron->Free_Local));
128: PetscCall(VecWhichInactive(tao->XL, tao->solution, tao->gradient, tao->XU, PETSC_TRUE, &tron->Free_Local));
129: PetscCall(ISGetSize(tron->Free_Local, &tron->n_free));
131: /* If no free variables */
132: if (tron->n_free == 0) {
133: PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));
134: PetscCall(TaoLogConvergenceHistory(tao, tron->f, tron->gnorm, 0.0, tao->ksp_its));
135: PetscCall(TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, delta));
136: PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
137: if (!tao->reason) tao->reason = TAO_CONVERGED_STEPTOL;
138: break;
139: }
140: /* use free_local to mask/submat gradient, hessian, stepdirection */
141: PetscCall(TaoVecGetSubVec(tao->gradient, tron->Free_Local, tao->subset_type, 0.0, &tron->R));
142: PetscCall(TaoVecGetSubVec(tao->gradient, tron->Free_Local, tao->subset_type, 0.0, &tron->DXFree));
143: PetscCall(VecSet(tron->DXFree, 0.0));
144: PetscCall(VecScale(tron->R, -1.0));
145: PetscCall(TaoMatGetSubMat(tao->hessian, tron->Free_Local, tron->diag, tao->subset_type, &tron->H_sub));
146: if (tao->hessian == tao->hessian_pre) {
147: PetscCall(MatDestroy(&tron->Hpre_sub));
148: PetscCall(PetscObjectReference((PetscObject)tron->H_sub));
149: tron->Hpre_sub = tron->H_sub;
150: } else {
151: PetscCall(TaoMatGetSubMat(tao->hessian_pre, tron->Free_Local, tron->diag, tao->subset_type, &tron->Hpre_sub));
152: }
153: PetscCall(KSPReset(tao->ksp));
154: PetscCall(KSPSetOperators(tao->ksp, tron->H_sub, tron->Hpre_sub));
155: while (1) {
156: /* Approximately solve the reduced linear system */
157: PetscCall(KSPCGSetRadius(tao->ksp, delta));
159: PetscCall(KSPSolve(tao->ksp, tron->R, tron->DXFree));
160: PetscCall(KSPGetIterationNumber(tao->ksp, &its));
161: tao->ksp_its += its;
162: tao->ksp_tot_its += its;
163: PetscCall(VecSet(tao->stepdirection, 0.0));
165: /* Add dxfree matrix to compute step direction vector */
166: PetscCall(VecISAXPY(tao->stepdirection, tron->Free_Local, 1.0, tron->DXFree));
168: PetscCall(VecDot(tao->gradient, tao->stepdirection, &gdx));
169: PetscCall(VecCopy(tao->solution, tron->X_New));
170: PetscCall(VecCopy(tao->gradient, tron->G_New));
172: stepsize = 1.0;
173: f_new = f;
175: PetscCall(TaoLineSearchSetInitialStepLength(tao->linesearch, 1.0));
176: PetscCall(TaoLineSearchApply(tao->linesearch, tron->X_New, &f_new, tron->G_New, tao->stepdirection, &stepsize, &ls_reason));
177: PetscCall(TaoAddLineSearchCounts(tao));
179: PetscCall(MatMult(tao->hessian, tao->stepdirection, tron->Work));
180: PetscCall(VecAYPX(tron->Work, 0.5, tao->gradient));
181: PetscCall(VecDot(tao->stepdirection, tron->Work, &prered));
182: actred = f_new - f;
183: if ((PetscAbsScalar(actred) <= 1e-6) && (PetscAbsScalar(prered) <= 1e-6)) {
184: rhok = 1.0;
185: } else if (actred < 0) {
186: rhok = PetscAbs(-actred / prered);
187: } else {
188: rhok = 0.0;
189: }
191: /* Compare actual improvement to the quadratic model */
192: if (rhok > tron->eta1) { /* Accept the point */
193: /* d = x_new - x */
194: PetscCall(VecCopy(tron->X_New, tao->stepdirection));
195: PetscCall(VecAXPY(tao->stepdirection, -1.0, tao->solution));
197: PetscCall(VecNorm(tao->stepdirection, NORM_2, &xdiff));
198: xdiff *= stepsize;
200: /* Adjust trust region size */
201: if (rhok < tron->eta2) {
202: delta = PetscMin(xdiff, delta) * tron->sigma1;
203: } else if (rhok > tron->eta4) {
204: delta = PetscMin(xdiff, delta) * tron->sigma3;
205: } else if (rhok > tron->eta3) {
206: delta = PetscMin(xdiff, delta) * tron->sigma2;
207: }
208: PetscCall(VecBoundGradientProjection(tron->G_New, tron->X_New, tao->XL, tao->XU, tao->gradient));
209: PetscCall(ISDestroy(&tron->Free_Local));
210: PetscCall(VecWhichInactive(tao->XL, tron->X_New, tao->gradient, tao->XU, PETSC_TRUE, &tron->Free_Local));
211: f = f_new;
212: PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));
213: PetscCall(VecCopy(tron->X_New, tao->solution));
214: PetscCall(VecCopy(tron->G_New, tao->gradient));
215: break;
216: } else if (delta <= 1e-30) {
217: break;
218: } else {
219: delta /= 4.0;
220: }
221: } /* end linear solve loop */
223: tron->f = f;
224: tron->actred = actred;
225: tao->trust = delta;
226: tao->niter++;
227: PetscCall(TaoLogConvergenceHistory(tao, tron->f, tron->gnorm, 0.0, tao->ksp_its));
228: PetscCall(TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, stepsize));
229: PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
230: } /* END MAIN LOOP */
231: PetscFunctionReturn(PETSC_SUCCESS);
232: }
234: static PetscErrorCode TronGradientProjections(Tao tao, TAO_TRON *tron)
235: {
236: PetscInt i;
237: TaoLineSearchConvergedReason ls_reason;
238: PetscReal actred = -1.0, actred_max = 0.0;
239: PetscReal f_new;
240: /*
241: The gradient and function value passed into and out of this
242: routine should be current and correct.
244: The free, active, and binding variables should be already identified
245: */
247: PetscFunctionBegin;
248: for (i = 0; i < tron->maxgpits; ++i) {
249: if (-actred <= (tron->pg_ftol) * actred_max) break;
251: ++tron->gp_iterates;
252: ++tron->total_gp_its;
253: f_new = tron->f;
255: PetscCall(VecCopy(tao->gradient, tao->stepdirection));
256: PetscCall(VecScale(tao->stepdirection, -1.0));
257: PetscCall(TaoLineSearchSetInitialStepLength(tao->linesearch, tron->pgstepsize));
258: PetscCall(TaoLineSearchApply(tao->linesearch, tao->solution, &f_new, tao->gradient, tao->stepdirection, &tron->pgstepsize, &ls_reason));
259: PetscCall(TaoAddLineSearchCounts(tao));
261: PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, tao->gradient));
262: PetscCall(VecNorm(tao->gradient, NORM_2, &tron->gnorm));
264: /* Update the iterate */
265: actred = f_new - tron->f;
266: actred_max = PetscMax(actred_max, -(f_new - tron->f));
267: tron->f = f_new;
268: }
269: PetscFunctionReturn(PETSC_SUCCESS);
270: }
272: static PetscErrorCode TaoComputeDual_TRON(Tao tao, Vec DXL, Vec DXU)
273: {
274: TAO_TRON *tron = (TAO_TRON *)tao->data;
276: PetscFunctionBegin;
280: PetscCheck(tron->Work && tao->gradient, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Dual variables don't exist yet or no longer exist.");
282: PetscCall(VecBoundGradientProjection(tao->gradient, tao->solution, tao->XL, tao->XU, tron->Work));
283: PetscCall(VecCopy(tron->Work, DXL));
284: PetscCall(VecAXPY(DXL, -1.0, tao->gradient));
285: PetscCall(VecSet(DXU, 0.0));
286: PetscCall(VecPointwiseMax(DXL, DXL, DXU));
288: PetscCall(VecCopy(tao->gradient, DXU));
289: PetscCall(VecAXPY(DXU, -1.0, tron->Work));
290: PetscCall(VecSet(tron->Work, 0.0));
291: PetscCall(VecPointwiseMin(DXU, tron->Work, DXU));
292: PetscFunctionReturn(PETSC_SUCCESS);
293: }
295: /*------------------------------------------------------------*/
296: /*MC
297: TAOTRON - The TRON algorithm is an active-set Newton trust region method
298: for bound-constrained minimization.
300: Options Database Keys:
301: + -tao_tron_maxgpits - maximum number of gradient projections per TRON iterate
302: - -tao_subset_type - "subvec","mask","matrix-free", strategies for handling active-sets
304: Level: beginner
305: M*/
306: PETSC_EXTERN PetscErrorCode TaoCreate_TRON(Tao tao)
307: {
308: TAO_TRON *tron;
309: const char *morethuente_type = TAOLINESEARCHMT;
311: PetscFunctionBegin;
312: tao->ops->setup = TaoSetup_TRON;
313: tao->ops->solve = TaoSolve_TRON;
314: tao->ops->view = TaoView_TRON;
315: tao->ops->setfromoptions = TaoSetFromOptions_TRON;
316: tao->ops->destroy = TaoDestroy_TRON;
317: tao->ops->computedual = TaoComputeDual_TRON;
319: PetscCall(PetscNew(&tron));
320: tao->data = (void *)tron;
322: /* Override default settings (unless already changed) */
323: if (!tao->max_it_changed) tao->max_it = 50;
324: if (!tao->trust0_changed) tao->trust0 = 1.0;
325: if (!tao->steptol_changed) tao->steptol = 0.0;
327: /* Initialize pointers and variables */
328: tron->n = 0;
329: tron->maxgpits = 3;
330: tron->pg_ftol = 0.001;
332: tron->eta1 = 1.0e-4;
333: tron->eta2 = 0.25;
334: tron->eta3 = 0.50;
335: tron->eta4 = 0.90;
337: tron->sigma1 = 0.5;
338: tron->sigma2 = 2.0;
339: tron->sigma3 = 4.0;
341: tron->gp_iterates = 0; /* Cumulative number */
342: tron->total_gp_its = 0;
343: tron->n_free = 0;
345: tron->DXFree = NULL;
346: tron->R = NULL;
347: tron->X_New = NULL;
348: tron->G_New = NULL;
349: tron->Work = NULL;
350: tron->Free_Local = NULL;
351: tron->H_sub = NULL;
352: tron->Hpre_sub = NULL;
353: tao->subset_type = TAO_SUBSET_SUBVEC;
355: PetscCall(TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch));
356: PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1));
357: PetscCall(TaoLineSearchSetType(tao->linesearch, morethuente_type));
358: PetscCall(TaoLineSearchUseTaoRoutines(tao->linesearch, tao));
359: PetscCall(TaoLineSearchSetOptionsPrefix(tao->linesearch, tao->hdr.prefix));
361: PetscCall(KSPCreate(((PetscObject)tao)->comm, &tao->ksp));
362: PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1));
363: PetscCall(KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix));
364: PetscCall(KSPSetType(tao->ksp, KSPSTCG));
365: PetscFunctionReturn(PETSC_SUCCESS);
366: }