Actual source code: bmrm.c
petsc-3.7.7 2017-09-25
1: #include <../src/tao/unconstrained/impls/bmrm/bmrm.h>
3: static PetscErrorCode init_df_solver(TAO_DF*);
4: static PetscErrorCode ensure_df_space(PetscInt, TAO_DF*);
5: static PetscErrorCode destroy_df_solver(TAO_DF*);
6: static PetscReal phi(PetscReal*,PetscInt,PetscReal,PetscReal*,PetscReal,PetscReal*,PetscReal*,PetscReal*);
7: static PetscInt project(PetscInt,PetscReal*,PetscReal,PetscReal*,PetscReal*,PetscReal*,PetscReal*,PetscReal*,TAO_DF*);
8: static PetscErrorCode solve(TAO_DF*);
11: /*------------------------------------------------------------*/
12: /* The main solver function
14: f = Remp(W) This is what the user provides us from the application layer
15: So the ComputeGradient function for instance should get us back the subgradient of Remp(W)
17: Regularizer assumed to be L2 norm = lambda*0.5*W'W ()
18: */
22: static PetscErrorCode make_grad_node(Vec X, Vec_Chain **p)
23: {
27: PetscNew(p);
28: VecDuplicate(X, &(*p)->V);
29: VecCopy(X, (*p)->V);
30: (*p)->next = NULL;
31: return(0);
32: }
36: static PetscErrorCode destroy_grad_list(Vec_Chain *head)
37: {
39: Vec_Chain *p = head->next, *q;
42: while(p) {
43: q = p->next;
44: VecDestroy(&p->V);
45: PetscFree(p);
46: p = q;
47: }
48: head->next = NULL;
49: return(0);
50: }
55: static PetscErrorCode TaoSolve_BMRM(Tao tao)
56: {
57: PetscErrorCode ierr;
58: TaoConvergedReason reason;
59: TAO_DF df;
60: TAO_BMRM *bmrm = (TAO_BMRM*)tao->data;
62: /* Values and pointers to parts of the optimization problem */
63: PetscReal f = 0.0;
64: Vec W = tao->solution;
65: Vec G = tao->gradient;
66: PetscReal lambda;
67: PetscReal bt;
68: Vec_Chain grad_list, *tail_glist, *pgrad;
69: PetscInt i;
70: PetscMPIInt rank;
72: /* Used in converged criteria check */
73: PetscReal reg;
74: PetscReal jtwt, max_jtwt, pre_epsilon, epsilon, jw, min_jw;
75: PetscReal innerSolverTol;
76: MPI_Comm comm;
79: PetscObjectGetComm((PetscObject)tao,&comm);
80: MPI_Comm_rank(comm, &rank);
81: lambda = bmrm->lambda;
83: /* Check Stopping Condition */
84: tao->step = 1.0;
85: max_jtwt = -BMRM_INFTY;
86: min_jw = BMRM_INFTY;
87: innerSolverTol = 1.0;
88: epsilon = 0.0;
90: if (!rank) {
91: init_df_solver(&df);
92: grad_list.next = NULL;
93: tail_glist = &grad_list;
94: }
96: df.tol = 1e-6;
97: reason = TAO_CONTINUE_ITERATING;
99: /*-----------------Algorithm Begins------------------------*/
100: /* make the scatter */
101: VecScatterCreateToZero(W, &bmrm->scatter, &bmrm->local_w);
102: VecAssemblyBegin(bmrm->local_w);
103: VecAssemblyEnd(bmrm->local_w);
105: /* NOTE: In application pass the sub-gradient of Remp(W) */
106: TaoComputeObjectiveAndGradient(tao, W, &f, G);
107: TaoMonitor(tao,tao->niter,f,1.0,0.0,tao->step,&reason);
108: while (reason == TAO_CONTINUE_ITERATING) {
109: /* compute bt = Remp(Wt-1) - <Wt-1, At> */
110: VecDot(W, G, &bt);
111: bt = f - bt;
113: /* First gather the gradient to the master node */
114: VecScatterBegin(bmrm->scatter, G, bmrm->local_w, INSERT_VALUES, SCATTER_FORWARD);
115: VecScatterEnd(bmrm->scatter, G, bmrm->local_w, INSERT_VALUES, SCATTER_FORWARD);
117: /* Bring up the inner solver */
118: if (!rank) {
119: ensure_df_space(tao->niter+1, &df);
120: make_grad_node(bmrm->local_w, &pgrad);
121: tail_glist->next = pgrad;
122: tail_glist = pgrad;
124: df.a[tao->niter] = 1.0;
125: df.f[tao->niter] = -bt;
126: df.u[tao->niter] = 1.0;
127: df.l[tao->niter] = 0.0;
129: /* set up the Q */
130: pgrad = grad_list.next;
131: for (i=0; i<=tao->niter; i++) {
132: VecDot(pgrad->V, bmrm->local_w, ®);
133: df.Q[i][tao->niter] = df.Q[tao->niter][i] = reg / lambda;
134: pgrad = pgrad->next;
135: }
137: if (tao->niter > 0) {
138: df.x[tao->niter] = 0.0;
139: solve(&df);
140: } else
141: df.x[0] = 1.0;
143: /* now computing Jt*(alpha_t) which should be = Jt(wt) to check convergence */
144: jtwt = 0.0;
145: VecSet(bmrm->local_w, 0.0);
146: pgrad = grad_list.next;
147: for (i=0; i<=tao->niter; i++) {
148: jtwt -= df.x[i] * df.f[i];
149: VecAXPY(bmrm->local_w, -df.x[i] / lambda, pgrad->V);
150: pgrad = pgrad->next;
151: }
153: VecNorm(bmrm->local_w, NORM_2, ®);
154: reg = 0.5*lambda*reg*reg;
155: jtwt -= reg;
156: } /* end if rank == 0 */
158: /* scatter the new W to all nodes */
159: VecScatterBegin(bmrm->scatter,bmrm->local_w,W,INSERT_VALUES,SCATTER_REVERSE);
160: VecScatterEnd(bmrm->scatter,bmrm->local_w,W,INSERT_VALUES,SCATTER_REVERSE);
162: TaoComputeObjectiveAndGradient(tao, W, &f, G);
164: MPI_Bcast(&jtwt,1,MPIU_REAL,0,comm);
165: MPI_Bcast(®,1,MPIU_REAL,0,comm);
167: jw = reg + f; /* J(w) = regularizer + Remp(w) */
168: if (jw < min_jw) min_jw = jw;
169: if (jtwt > max_jtwt) max_jtwt = jtwt;
171: pre_epsilon = epsilon;
172: epsilon = min_jw - jtwt;
174: if (!rank) {
175: if (innerSolverTol > epsilon) innerSolverTol = epsilon;
176: else if (innerSolverTol < 1e-7) innerSolverTol = 1e-7;
178: /* if the annealing doesn't work well, lower the inner solver tolerance */
179: if(pre_epsilon < epsilon) innerSolverTol *= 0.2;
181: df.tol = innerSolverTol*0.5;
182: }
184: tao->niter++;
185: TaoMonitor(tao,tao->niter,min_jw,epsilon,0.0,tao->step,&reason);
186: }
188: /* free all the memory */
189: if (!rank) {
190: destroy_grad_list(&grad_list);
191: destroy_df_solver(&df);
192: }
194: VecDestroy(&bmrm->local_w);
195: VecScatterDestroy(&bmrm->scatter);
196: return(0);
197: }
200: /* ---------------------------------------------------------- */
204: static PetscErrorCode TaoSetup_BMRM(Tao tao)
205: {
210: /* Allocate some arrays */
211: if (!tao->gradient) {
212: VecDuplicate(tao->solution, &tao->gradient);
213: }
214: return(0);
215: }
217: /*------------------------------------------------------------*/
220: static PetscErrorCode TaoDestroy_BMRM(Tao tao)
221: {
225: PetscFree(tao->data);
226: return(0);
227: }
231: static PetscErrorCode TaoSetFromOptions_BMRM(PetscOptionItems *PetscOptionsObject,Tao tao)
232: {
234: TAO_BMRM* bmrm = (TAO_BMRM*)tao->data;
237: PetscOptionsHead(PetscOptionsObject,"BMRM for regularized risk minimization");
238: PetscOptionsReal("-tao_bmrm_lambda", "regulariser weight","", 100,&bmrm->lambda,NULL);
239: PetscOptionsTail();
240: return(0);
241: }
243: /*------------------------------------------------------------*/
246: static PetscErrorCode TaoView_BMRM(Tao tao, PetscViewer viewer)
247: {
248: PetscBool isascii;
252: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
253: if (isascii) {
254: PetscViewerASCIIPushTab(viewer);
255: PetscViewerASCIIPopTab(viewer);
256: }
257: return(0);
258: }
260: /*------------------------------------------------------------*/
261: /*MC
262: TAOBMRM - bundle method for regularized risk minimization
264: Options Database Keys:
265: . - tao_bmrm_lambda - regulariser weight
267: Level: beginner
268: M*/
272: PETSC_EXTERN PetscErrorCode TaoCreate_BMRM(Tao tao)
273: {
274: TAO_BMRM *bmrm;
278: tao->ops->setup = TaoSetup_BMRM;
279: tao->ops->solve = TaoSolve_BMRM;
280: tao->ops->view = TaoView_BMRM;
281: tao->ops->setfromoptions = TaoSetFromOptions_BMRM;
282: tao->ops->destroy = TaoDestroy_BMRM;
284: PetscNewLog(tao,&bmrm);
285: bmrm->lambda = 1.0;
286: tao->data = (void*)bmrm;
288: /* Override default settings (unless already changed) */
289: if (!tao->max_it_changed) tao->max_it = 2000;
290: if (!tao->max_funcs_changed) tao->max_funcs = 4000;
291: if (!tao->gatol_changed) tao->gatol = 1.0e-12;
292: if (!tao->grtol_changed) tao->grtol = 1.0e-12;
294: return(0);
295: }
299: PetscErrorCode init_df_solver(TAO_DF *df)
300: {
301: PetscInt i, n = INCRE_DIM;
305: /* default values */
306: df->maxProjIter = 200;
307: df->maxPGMIter = 300000;
308: df->b = 1.0;
310: /* memory space required by Dai-Fletcher */
311: df->cur_num_cp = n;
312: PetscMalloc1(n, &df->f);
313: PetscMalloc1(n, &df->a);
314: PetscMalloc1(n, &df->l);
315: PetscMalloc1(n, &df->u);
316: PetscMalloc1(n, &df->x);
317: PetscMalloc1(n, &df->Q);
319: for (i = 0; i < n; i ++) {
320: PetscMalloc1(n, &df->Q[i]);
321: }
323: PetscMalloc1(n, &df->g);
324: PetscMalloc1(n, &df->y);
325: PetscMalloc1(n, &df->tempv);
326: PetscMalloc1(n, &df->d);
327: PetscMalloc1(n, &df->Qd);
328: PetscMalloc1(n, &df->t);
329: PetscMalloc1(n, &df->xplus);
330: PetscMalloc1(n, &df->tplus);
331: PetscMalloc1(n, &df->sk);
332: PetscMalloc1(n, &df->yk);
334: PetscMalloc1(n, &df->ipt);
335: PetscMalloc1(n, &df->ipt2);
336: PetscMalloc1(n, &df->uv);
337: return(0);
338: }
342: PetscErrorCode ensure_df_space(PetscInt dim, TAO_DF *df)
343: {
345: PetscReal *tmp, **tmp_Q;
346: PetscInt i, n, old_n;
349: df->dim = dim;
350: if (dim <= df->cur_num_cp) return(0);
352: old_n = df->cur_num_cp;
353: df->cur_num_cp += INCRE_DIM;
354: n = df->cur_num_cp;
356: /* memory space required by dai-fletcher */
357: PetscMalloc1(n, &tmp);
358: PetscMemcpy(tmp, df->f, sizeof(PetscReal)*old_n);
359: PetscFree(df->f);
360: df->f = tmp;
362: PetscMalloc1(n, &tmp);
363: PetscMemcpy(tmp, df->a, sizeof(PetscReal)*old_n);
364: PetscFree(df->a);
365: df->a = tmp;
367: PetscMalloc1(n, &tmp);
368: PetscMemcpy(tmp, df->l, sizeof(PetscReal)*old_n);
369: PetscFree(df->l);
370: df->l = tmp;
372: PetscMalloc1(n, &tmp);
373: PetscMemcpy(tmp, df->u, sizeof(PetscReal)*old_n);
374: PetscFree(df->u);
375: df->u = tmp;
377: PetscMalloc1(n, &tmp);
378: PetscMemcpy(tmp, df->x, sizeof(PetscReal)*old_n);
379: PetscFree(df->x);
380: df->x = tmp;
382: PetscMalloc1(n, &tmp_Q);
383: for (i = 0; i < n; i ++) {
384: PetscMalloc1(n, &tmp_Q[i]);
385: if (i < old_n) {
386: PetscMemcpy(tmp_Q[i], df->Q[i], sizeof(PetscReal)*old_n);
387: PetscFree(df->Q[i]);
388: }
389: }
391: PetscFree(df->Q);
392: df->Q = tmp_Q;
394: PetscFree(df->g);
395: PetscMalloc1(n, &df->g);
397: PetscFree(df->y);
398: PetscMalloc1(n, &df->y);
400: PetscFree(df->tempv);
401: PetscMalloc1(n, &df->tempv);
403: PetscFree(df->d);
404: PetscMalloc1(n, &df->d);
406: PetscFree(df->Qd);
407: PetscMalloc1(n, &df->Qd);
409: PetscFree(df->t);
410: PetscMalloc1(n, &df->t);
412: PetscFree(df->xplus);
413: PetscMalloc1(n, &df->xplus);
415: PetscFree(df->tplus);
416: PetscMalloc1(n, &df->tplus);
418: PetscFree(df->sk);
419: PetscMalloc1(n, &df->sk);
421: PetscFree(df->yk);
422: PetscMalloc1(n, &df->yk);
424: PetscFree(df->ipt);
425: PetscMalloc1(n, &df->ipt);
427: PetscFree(df->ipt2);
428: PetscMalloc1(n, &df->ipt2);
430: PetscFree(df->uv);
431: PetscMalloc1(n, &df->uv);
432: return(0);
433: }
437: PetscErrorCode destroy_df_solver(TAO_DF *df)
438: {
440: PetscInt i;
443: PetscFree(df->f);
444: PetscFree(df->a);
445: PetscFree(df->l);
446: PetscFree(df->u);
447: PetscFree(df->x);
449: for (i = 0; i < df->cur_num_cp; i ++) {
450: PetscFree(df->Q[i]);
451: }
452: PetscFree(df->Q);
453: PetscFree(df->ipt);
454: PetscFree(df->ipt2);
455: PetscFree(df->uv);
456: PetscFree(df->g);
457: PetscFree(df->y);
458: PetscFree(df->tempv);
459: PetscFree(df->d);
460: PetscFree(df->Qd);
461: PetscFree(df->t);
462: PetscFree(df->xplus);
463: PetscFree(df->tplus);
464: PetscFree(df->sk);
465: PetscFree(df->yk);
466: return(0);
467: }
469: /* Piecewise linear monotone target function for the Dai-Fletcher projector */
472: PetscReal phi(PetscReal *x,PetscInt n,PetscReal lambda,PetscReal *a,PetscReal b,PetscReal *c,PetscReal *l,PetscReal *u)
473: {
474: PetscReal r = 0.0;
475: PetscInt i;
477: for (i = 0; i < n; i++){
478: x[i] = -c[i] + lambda*a[i];
479: if (x[i] > u[i]) x[i] = u[i];
480: else if(x[i] < l[i]) x[i] = l[i];
481: r += a[i]*x[i];
482: }
483: return r - b;
484: }
486: /** Modified Dai-Fletcher QP projector solves the problem:
487: *
488: * minimise 0.5*x'*x - c'*x
489: * subj to a'*x = b
490: * l \leq x \leq u
491: *
492: * \param c The point to be projected onto feasible set
493: */
496: PetscInt project(PetscInt n,PetscReal *a,PetscReal b,PetscReal *c,PetscReal *l,PetscReal *u,PetscReal *x,PetscReal *lam_ext,TAO_DF *df)
497: {
498: PetscReal lambda, lambdal, lambdau, dlambda, lambda_new;
499: PetscReal r, rl, ru, s;
500: PetscInt innerIter;
501: PetscBool nonNegativeSlack = PETSC_FALSE;
504: *lam_ext = 0;
505: lambda = 0;
506: dlambda = 0.5;
507: innerIter = 1;
509: /* \phi(x;lambda) := 0.5*x'*x + c'*x - lambda*(a'*x-b)
510: *
511: * Optimality conditions for \phi:
512: *
513: * 1. lambda <= 0
514: * 2. r <= 0
515: * 3. r*lambda == 0
516: */
518: /* Bracketing Phase */
519: r = phi(x, n, lambda, a, b, c, l, u);
521: if(nonNegativeSlack) {
522: /* inequality constraint, i.e., with \xi >= 0 constraint */
523: if (r < TOL_R) return 0;
524: } else {
525: /* equality constraint ,i.e., without \xi >= 0 constraint */
526: if (fabs(r) < TOL_R) return 0;
527: }
529: if (r < 0.0){
530: lambdal = lambda;
531: rl = r;
532: lambda = lambda + dlambda;
533: r = phi(x, n, lambda, a, b, c, l, u);
534: while (r < 0.0 && dlambda < BMRM_INFTY) {
535: lambdal = lambda;
536: s = rl/r - 1.0;
537: if (s < 0.1) s = 0.1;
538: dlambda = dlambda + dlambda/s;
539: lambda = lambda + dlambda;
540: rl = r;
541: r = phi(x, n, lambda, a, b, c, l, u);
542: }
543: lambdau = lambda;
544: ru = r;
545: } else {
546: lambdau = lambda;
547: ru = r;
548: lambda = lambda - dlambda;
549: r = phi(x, n, lambda, a, b, c, l, u);
550: while (r > 0.0 && dlambda > -BMRM_INFTY) {
551: lambdau = lambda;
552: s = ru/r - 1.0;
553: if (s < 0.1) s = 0.1;
554: dlambda = dlambda + dlambda/s;
555: lambda = lambda - dlambda;
556: ru = r;
557: r = phi(x, n, lambda, a, b, c, l, u);
558: }
559: lambdal = lambda;
560: rl = r;
561: }
563: if(fabs(dlambda) > BMRM_INFTY) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"L2N2_DaiFletcherPGM detected Infeasible QP problem!");
565: if(ru == 0){
566: return innerIter;
567: }
569: /* Secant Phase */
570: s = 1.0 - rl/ru;
571: dlambda = dlambda/s;
572: lambda = lambdau - dlambda;
573: r = phi(x, n, lambda, a, b, c, l, u);
575: while (fabs(r) > TOL_R
576: && dlambda > TOL_LAM * (1.0 + fabs(lambda))
577: && innerIter < df->maxProjIter){
578: innerIter++;
579: if (r > 0.0){
580: if (s <= 2.0){
581: lambdau = lambda;
582: ru = r;
583: s = 1.0 - rl/ru;
584: dlambda = (lambdau - lambdal) / s;
585: lambda = lambdau - dlambda;
586: } else {
587: s = ru/r-1.0;
588: if (s < 0.1) s = 0.1;
589: dlambda = (lambdau - lambda) / s;
590: lambda_new = 0.75*lambdal + 0.25*lambda;
591: if (lambda_new < (lambda - dlambda))
592: lambda_new = lambda - dlambda;
593: lambdau = lambda;
594: ru = r;
595: lambda = lambda_new;
596: s = (lambdau - lambdal) / (lambdau - lambda);
597: }
598: } else {
599: if (s >= 2.0){
600: lambdal = lambda;
601: rl = r;
602: s = 1.0 - rl/ru;
603: dlambda = (lambdau - lambdal) / s;
604: lambda = lambdau - dlambda;
605: } else {
606: s = rl/r - 1.0;
607: if (s < 0.1) s = 0.1;
608: dlambda = (lambda-lambdal) / s;
609: lambda_new = 0.75*lambdau + 0.25*lambda;
610: if (lambda_new > (lambda + dlambda))
611: lambda_new = lambda + dlambda;
612: lambdal = lambda;
613: rl = r;
614: lambda = lambda_new;
615: s = (lambdau - lambdal) / (lambdau-lambda);
616: }
617: }
618: r = phi(x, n, lambda, a, b, c, l, u);
619: }
621: *lam_ext = lambda;
622: if(innerIter >= df->maxProjIter) {
623: PetscPrintf(PETSC_COMM_SELF, "WARNING: DaiFletcher max iterations\n");
624: }
625: return innerIter;
626: }
631: PetscErrorCode solve(TAO_DF *df)
632: {
634: PetscInt i, j, innerIter, it, it2, luv, info, lscount = 0, projcount = 0;
635: PetscReal gd, max, ak, bk, akold, bkold, lamnew, alpha, kktlam=0.0, lam_ext;
636: PetscReal DELTAsv, ProdDELTAsv;
637: PetscReal c, *tempQ;
638: PetscReal *x = df->x, *a = df->a, b = df->b, *l = df->l, *u = df->u, tol = df->tol;
639: PetscReal *tempv = df->tempv, *y = df->y, *g = df->g, *d = df->d, *Qd = df->Qd;
640: PetscReal *xplus = df->xplus, *tplus = df->tplus, *sk = df->sk, *yk = df->yk;
641: PetscReal **Q = df->Q, *f = df->f, *t = df->t;
642: PetscInt dim = df->dim, *ipt = df->ipt, *ipt2 = df->ipt2, *uv = df->uv;
644: /*** variables for the adaptive nonmonotone linesearch ***/
645: PetscInt L, llast;
646: PetscReal fr, fbest, fv, fc, fv0;
648: c = BMRM_INFTY;
650: DELTAsv = EPS_SV;
651: if (tol <= 1.0e-5 || dim <= 20) ProdDELTAsv = 0.0F;
652: else ProdDELTAsv = EPS_SV;
654: for (i = 0; i < dim; i++) tempv[i] = -x[i];
656: lam_ext = 0.0;
658: /* Project the initial solution */
659: projcount += project(dim, a, b, tempv, l, u, x, &lam_ext, df);
661: /* Compute gradient
662: g = Q*x + f; */
664: it = 0;
665: for (i = 0; i < dim; i++) {
666: if (fabs(x[i]) > ProdDELTAsv) ipt[it++] = i;
667: }
669: PetscMemzero(t, dim*sizeof(PetscReal));
670: for (i = 0; i < it; i++){
671: tempQ = Q[ipt[i]];
672: for (j = 0; j < dim; j++) t[j] += (tempQ[j]*x[ipt[i]]);
673: }
674: for (i = 0; i < dim; i++){
675: g[i] = t[i] + f[i];
676: }
679: /* y = -(x_{k} - g_{k}) */
680: for (i = 0; i < dim; i++){
681: y[i] = g[i] - x[i];
682: }
684: /* Project x_{k} - g_{k} */
685: projcount += project(dim, a, b, y, l, u, tempv, &lam_ext, df);
687: /* y = P(x_{k} - g_{k}) - x_{k} */
688: max = ALPHA_MIN;
689: for (i = 0; i < dim; i++){
690: y[i] = tempv[i] - x[i];
691: if (fabs(y[i]) > max) max = fabs(y[i]);
692: }
694: if (max < tol*1e-3){
695: return 0;
696: }
698: alpha = 1.0 / max;
700: /* fv0 = f(x_{0}). Recall t = Q x_{k} */
701: fv0 = 0.0;
702: for (i = 0; i < dim; i++) fv0 += x[i] * (0.5*t[i] + f[i]);
704: /*** adaptive nonmonotone linesearch ***/
705: L = 2;
706: fr = ALPHA_MAX;
707: fbest = fv0;
708: fc = fv0;
709: llast = 0;
710: akold = bkold = 0.0;
712: /*** Iterator begins ***/
713: for (innerIter = 1; innerIter <= df->maxPGMIter; innerIter++) {
715: /* tempv = -(x_{k} - alpha*g_{k}) */
716: for (i = 0; i < dim; i++) tempv[i] = alpha*g[i] - x[i];
718: /* Project x_{k} - alpha*g_{k} */
719: projcount += project(dim, a, b, tempv, l, u, y, &lam_ext, df);
722: /* gd = \inner{d_{k}}{g_{k}}
723: d = P(x_{k} - alpha*g_{k}) - x_{k}
724: */
725: gd = 0.0;
726: for (i = 0; i < dim; i++){
727: d[i] = y[i] - x[i];
728: gd += d[i] * g[i];
729: }
731: /* Gradient computation */
733: /* compute Qd = Q*d or Qd = Q*y - t depending on their sparsity */
735: it = it2 = 0;
736: for (i = 0; i < dim; i++){
737: if (fabs(d[i]) > (ProdDELTAsv*1.0e-2)) ipt[it++] = i;
738: }
739: for (i = 0; i < dim; i++) {
740: if (fabs(y[i]) > ProdDELTAsv) ipt2[it2++] = i;
741: }
743: PetscMemzero(Qd, dim*sizeof(PetscReal));
744: /* compute Qd = Q*d */
745: if (it < it2){
746: for (i = 0; i < it; i++){
747: tempQ = Q[ipt[i]];
748: for (j = 0; j < dim; j++) Qd[j] += (tempQ[j] * d[ipt[i]]);
749: }
750: } else { /* compute Qd = Q*y-t */
751: for (i = 0; i < it2; i++){
752: tempQ = Q[ipt2[i]];
753: for (j = 0; j < dim; j++) Qd[j] += (tempQ[j] * y[ipt2[i]]);
754: }
755: for (j = 0; j < dim; j++) Qd[j] -= t[j];
756: }
758: /* ak = inner{d_{k}}{d_{k}} */
759: ak = 0.0;
760: for (i = 0; i < dim; i++) ak += d[i] * d[i];
762: bk = 0.0;
763: for (i = 0; i < dim; i++) bk += d[i]*Qd[i];
765: if (bk > EPS*ak && gd < 0.0) lamnew = -gd/bk;
766: else lamnew = 1.0;
768: /* fv is computing f(x_{k} + d_{k}) */
769: fv = 0.0;
770: for (i = 0; i < dim; i++){
771: xplus[i] = x[i] + d[i];
772: tplus[i] = t[i] + Qd[i];
773: fv += xplus[i] * (0.5*tplus[i] + f[i]);
774: }
776: /* fr is fref */
777: if ((innerIter == 1 && fv >= fv0) || (innerIter > 1 && fv >= fr)){
778: lscount++;
779: fv = 0.0;
780: for (i = 0; i < dim; i++){
781: xplus[i] = x[i] + lamnew*d[i];
782: tplus[i] = t[i] + lamnew*Qd[i];
783: fv += xplus[i] * (0.5*tplus[i] + f[i]);
784: }
785: }
787: for (i = 0; i < dim; i++){
788: sk[i] = xplus[i] - x[i];
789: yk[i] = tplus[i] - t[i];
790: x[i] = xplus[i];
791: t[i] = tplus[i];
792: g[i] = t[i] + f[i];
793: }
795: /* update the line search control parameters */
796: if (fv < fbest){
797: fbest = fv;
798: fc = fv;
799: llast = 0;
800: } else {
801: fc = (fc > fv ? fc : fv);
802: llast++;
803: if (llast == L){
804: fr = fc;
805: fc = fv;
806: llast = 0;
807: }
808: }
810: ak = bk = 0.0;
811: for (i = 0; i < dim; i++){
812: ak += sk[i] * sk[i];
813: bk += sk[i] * yk[i];
814: }
816: if (bk <= EPS*ak) alpha = ALPHA_MAX;
817: else {
818: if (bkold < EPS*akold) alpha = ak/bk;
819: else alpha = (akold+ak)/(bkold+bk);
821: if (alpha > ALPHA_MAX) alpha = ALPHA_MAX;
822: else if (alpha < ALPHA_MIN) alpha = ALPHA_MIN;
823: }
825: akold = ak;
826: bkold = bk;
828: /*** stopping criterion based on KKT conditions ***/
829: /* at optimal, gradient of lagrangian w.r.t. x is zero */
831: bk = 0.0;
832: for (i = 0; i < dim; i++) bk += x[i] * x[i];
834: if (PetscSqrtReal(ak) < tol*10 * PetscSqrtReal(bk)){
835: it = 0;
836: luv = 0;
837: kktlam = 0.0;
838: for (i = 0; i < dim; i++){
839: /* x[i] is active hence lagrange multipliers for box constraints
840: are zero. The lagrange multiplier for ineq. const. is then
841: defined as below
842: */
843: if ((x[i] > DELTAsv) && (x[i] < c-DELTAsv)){
844: ipt[it++] = i;
845: kktlam = kktlam - a[i]*g[i];
846: } else uv[luv++] = i;
847: }
849: if (it == 0 && PetscSqrtReal(ak) < tol*0.5 * PetscSqrtReal(bk)) return 0;
850: else {
851: kktlam = kktlam/it;
852: info = 1;
853: for (i = 0; i < it; i++) {
854: if (fabs(a[ipt[i]] * g[ipt[i]] + kktlam) > tol) {
855: info = 0;
856: break;
857: }
858: }
859: if (info == 1) {
860: for (i = 0; i < luv; i++) {
861: if (x[uv[i]] <= DELTAsv){
862: /* x[i] == lower bound, hence, lagrange multiplier (say, beta) for lower bound may
863: not be zero. So, the gradient without beta is > 0
864: */
865: if (g[uv[i]] + kktlam*a[uv[i]] < -tol){
866: info = 0;
867: break;
868: }
869: } else {
870: /* x[i] == upper bound, hence, lagrange multiplier (say, eta) for upper bound may
871: not be zero. So, the gradient without eta is < 0
872: */
873: if (g[uv[i]] + kktlam*a[uv[i]] > tol) {
874: info = 0;
875: break;
876: }
877: }
878: }
879: }
881: if (info == 1) return 0;
882: }
883: }
884: }
885: return 0;
886: }