Actual source code: lcl.c
1: #include <../src/tao/pde_constrained/impls/lcl/lcl.h>
2: static PetscErrorCode LCLComputeLagrangianAndGradient(TaoLineSearch,Vec,PetscReal*,Vec,void*);
3: static PetscErrorCode LCLComputeAugmentedLagrangianAndGradient(TaoLineSearch,Vec,PetscReal*,Vec,void*);
4: static PetscErrorCode LCLScatter(TAO_LCL*,Vec,Vec,Vec);
5: static PetscErrorCode LCLGather(TAO_LCL*,Vec,Vec,Vec);
7: static PetscErrorCode TaoDestroy_LCL(Tao tao)
8: {
9: TAO_LCL *lclP = (TAO_LCL*)tao->data;
13: if (tao->setupcalled) {
14: MatDestroy(&lclP->R);
15: VecDestroy(&lclP->lamda);
16: VecDestroy(&lclP->lamda0);
17: VecDestroy(&lclP->WL);
18: VecDestroy(&lclP->W);
19: VecDestroy(&lclP->X0);
20: VecDestroy(&lclP->G0);
21: VecDestroy(&lclP->GL);
22: VecDestroy(&lclP->GAugL);
23: VecDestroy(&lclP->dbar);
24: VecDestroy(&lclP->U);
25: VecDestroy(&lclP->U0);
26: VecDestroy(&lclP->V);
27: VecDestroy(&lclP->V0);
28: VecDestroy(&lclP->V1);
29: VecDestroy(&lclP->GU);
30: VecDestroy(&lclP->GV);
31: VecDestroy(&lclP->GU0);
32: VecDestroy(&lclP->GV0);
33: VecDestroy(&lclP->GL_U);
34: VecDestroy(&lclP->GL_V);
35: VecDestroy(&lclP->GAugL_U);
36: VecDestroy(&lclP->GAugL_V);
37: VecDestroy(&lclP->GL_U0);
38: VecDestroy(&lclP->GL_V0);
39: VecDestroy(&lclP->GAugL_U0);
40: VecDestroy(&lclP->GAugL_V0);
41: VecDestroy(&lclP->DU);
42: VecDestroy(&lclP->DV);
43: VecDestroy(&lclP->WU);
44: VecDestroy(&lclP->WV);
45: VecDestroy(&lclP->g1);
46: VecDestroy(&lclP->g2);
47: VecDestroy(&lclP->con1);
49: VecDestroy(&lclP->r);
50: VecDestroy(&lclP->s);
52: ISDestroy(&tao->state_is);
53: ISDestroy(&tao->design_is);
55: VecScatterDestroy(&lclP->state_scatter);
56: VecScatterDestroy(&lclP->design_scatter);
57: }
58: MatDestroy(&lclP->R);
59: PetscFree(tao->data);
60: return(0);
61: }
63: static PetscErrorCode TaoSetFromOptions_LCL(PetscOptionItems *PetscOptionsObject,Tao tao)
64: {
65: TAO_LCL *lclP = (TAO_LCL*)tao->data;
69: PetscOptionsHead(PetscOptionsObject,"Linearly-Constrained Augmented Lagrangian Method for PDE-constrained optimization");
70: PetscOptionsReal("-tao_lcl_eps1","epsilon 1 tolerance","",lclP->eps1,&lclP->eps1,NULL);
71: PetscOptionsReal("-tao_lcl_eps2","epsilon 2 tolerance","",lclP->eps2,&lclP->eps2,NULL);
72: PetscOptionsReal("-tao_lcl_rho0","init value for rho","",lclP->rho0,&lclP->rho0,NULL);
73: PetscOptionsReal("-tao_lcl_rhomax","max value for rho","",lclP->rhomax,&lclP->rhomax,NULL);
74: lclP->phase2_niter = 1;
75: PetscOptionsInt("-tao_lcl_phase2_niter","Number of phase 2 iterations in LCL algorithm","",lclP->phase2_niter,&lclP->phase2_niter,NULL);
76: lclP->verbose = PETSC_FALSE;
77: PetscOptionsBool("-tao_lcl_verbose","Print verbose output","",lclP->verbose,&lclP->verbose,NULL);
78: lclP->tau[0] = lclP->tau[1] = lclP->tau[2] = lclP->tau[3] = 1.0e-4;
79: PetscOptionsReal("-tao_lcl_tola","Tolerance for first forward solve","",lclP->tau[0],&lclP->tau[0],NULL);
80: PetscOptionsReal("-tao_lcl_tolb","Tolerance for first adjoint solve","",lclP->tau[1],&lclP->tau[1],NULL);
81: PetscOptionsReal("-tao_lcl_tolc","Tolerance for second forward solve","",lclP->tau[2],&lclP->tau[2],NULL);
82: PetscOptionsReal("-tao_lcl_told","Tolerance for second adjoint solve","",lclP->tau[3],&lclP->tau[3],NULL);
83: PetscOptionsTail();
84: TaoLineSearchSetFromOptions(tao->linesearch);
85: MatSetFromOptions(lclP->R);
86: return(0);
87: }
89: static PetscErrorCode TaoView_LCL(Tao tao, PetscViewer viewer)
90: {
91: return 0;
92: }
94: static PetscErrorCode TaoSetup_LCL(Tao tao)
95: {
96: TAO_LCL *lclP = (TAO_LCL*)tao->data;
97: PetscInt lo, hi, nlocalstate, nlocaldesign;
99: IS is_state, is_design;
102: if (!tao->state_is) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_ARG_WRONGSTATE,"LCL Solver requires an initial state index set -- use TaoSetStateIS()");
103: VecDuplicate(tao->solution, &tao->gradient);
104: VecDuplicate(tao->solution, &tao->stepdirection);
105: VecDuplicate(tao->solution, &lclP->W);
106: VecDuplicate(tao->solution, &lclP->X0);
107: VecDuplicate(tao->solution, &lclP->G0);
108: VecDuplicate(tao->solution, &lclP->GL);
109: VecDuplicate(tao->solution, &lclP->GAugL);
111: VecDuplicate(tao->constraints, &lclP->lamda);
112: VecDuplicate(tao->constraints, &lclP->WL);
113: VecDuplicate(tao->constraints, &lclP->lamda0);
114: VecDuplicate(tao->constraints, &lclP->con1);
116: VecSet(lclP->lamda,0.0);
118: VecGetSize(tao->solution, &lclP->n);
119: VecGetSize(tao->constraints, &lclP->m);
121: VecCreate(((PetscObject)tao)->comm,&lclP->U);
122: VecCreate(((PetscObject)tao)->comm,&lclP->V);
123: ISGetLocalSize(tao->state_is,&nlocalstate);
124: ISGetLocalSize(tao->design_is,&nlocaldesign);
125: VecSetSizes(lclP->U,nlocalstate,lclP->m);
126: VecSetSizes(lclP->V,nlocaldesign,lclP->n-lclP->m);
127: VecSetType(lclP->U,((PetscObject)(tao->solution))->type_name);
128: VecSetType(lclP->V,((PetscObject)(tao->solution))->type_name);
129: VecSetFromOptions(lclP->U);
130: VecSetFromOptions(lclP->V);
131: VecDuplicate(lclP->U,&lclP->DU);
132: VecDuplicate(lclP->U,&lclP->U0);
133: VecDuplicate(lclP->U,&lclP->GU);
134: VecDuplicate(lclP->U,&lclP->GU0);
135: VecDuplicate(lclP->U,&lclP->GAugL_U);
136: VecDuplicate(lclP->U,&lclP->GL_U);
137: VecDuplicate(lclP->U,&lclP->GAugL_U0);
138: VecDuplicate(lclP->U,&lclP->GL_U0);
139: VecDuplicate(lclP->U,&lclP->WU);
140: VecDuplicate(lclP->U,&lclP->r);
141: VecDuplicate(lclP->V,&lclP->V0);
142: VecDuplicate(lclP->V,&lclP->V1);
143: VecDuplicate(lclP->V,&lclP->DV);
144: VecDuplicate(lclP->V,&lclP->s);
145: VecDuplicate(lclP->V,&lclP->GV);
146: VecDuplicate(lclP->V,&lclP->GV0);
147: VecDuplicate(lclP->V,&lclP->dbar);
148: VecDuplicate(lclP->V,&lclP->GAugL_V);
149: VecDuplicate(lclP->V,&lclP->GL_V);
150: VecDuplicate(lclP->V,&lclP->GAugL_V0);
151: VecDuplicate(lclP->V,&lclP->GL_V0);
152: VecDuplicate(lclP->V,&lclP->WV);
153: VecDuplicate(lclP->V,&lclP->g1);
154: VecDuplicate(lclP->V,&lclP->g2);
156: /* create scatters for state, design subvecs */
157: VecGetOwnershipRange(lclP->U,&lo,&hi);
158: ISCreateStride(((PetscObject)lclP->U)->comm,hi-lo,lo,1,&is_state);
159: VecGetOwnershipRange(lclP->V,&lo,&hi);
160: if (0) {
161: PetscInt sizeU,sizeV;
162: VecGetSize(lclP->U,&sizeU);
163: VecGetSize(lclP->V,&sizeV);
164: PetscPrintf(PETSC_COMM_WORLD,"size(U)=%D, size(V)=%D\n",sizeU,sizeV);
165: }
166: ISCreateStride(((PetscObject)lclP->V)->comm,hi-lo,lo,1,&is_design);
167: VecScatterCreate(tao->solution,tao->state_is,lclP->U,is_state,&lclP->state_scatter);
168: VecScatterCreate(tao->solution,tao->design_is,lclP->V,is_design,&lclP->design_scatter);
169: ISDestroy(&is_state);
170: ISDestroy(&is_design);
171: return(0);
172: }
174: static PetscErrorCode TaoSolve_LCL(Tao tao)
175: {
176: TAO_LCL *lclP = (TAO_LCL*)tao->data;
177: PetscInt phase2_iter,nlocal,its;
178: TaoLineSearchConvergedReason ls_reason = TAOLINESEARCH_CONTINUE_ITERATING;
179: PetscReal step=1.0,f, descent, aldescent;
180: PetscReal cnorm, mnorm;
181: PetscReal adec,r2,rGL_U,rWU;
182: PetscBool set,pset,flag,pflag,symmetric;
183: PetscErrorCode ierr;
186: lclP->rho = lclP->rho0;
187: VecGetLocalSize(lclP->U,&nlocal);
188: VecGetLocalSize(lclP->V,&nlocal);
189: MatSetSizes(lclP->R, nlocal, nlocal, lclP->n-lclP->m, lclP->n-lclP->m);
190: MatLMVMAllocate(lclP->R,lclP->V,lclP->V);
191: lclP->recompute_jacobian_flag = PETSC_TRUE;
193: /* Scatter to U,V */
194: LCLScatter(lclP,tao->solution,lclP->U,lclP->V);
196: /* Evaluate Function, Gradient, Constraints, and Jacobian */
197: TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);
198: TaoComputeJacobianState(tao,tao->solution,tao->jacobian_state,tao->jacobian_state_pre,tao->jacobian_state_inv);
199: TaoComputeJacobianDesign(tao,tao->solution,tao->jacobian_design);
200: TaoComputeConstraints(tao,tao->solution, tao->constraints);
202: /* Scatter gradient to GU,GV */
203: LCLScatter(lclP,tao->gradient,lclP->GU,lclP->GV);
205: /* Evaluate Lagrangian function and gradient */
206: /* p0 */
207: VecSet(lclP->lamda,0.0); /* Initial guess in CG */
208: MatIsSymmetricKnown(tao->jacobian_state,&set,&flag);
209: if (tao->jacobian_state_pre) {
210: MatIsSymmetricKnown(tao->jacobian_state_pre,&pset,&pflag);
211: } else {
212: pset = pflag = PETSC_TRUE;
213: }
214: if (set && pset && flag && pflag) symmetric = PETSC_TRUE;
215: else symmetric = PETSC_FALSE;
217: lclP->solve_type = LCL_ADJOINT2;
218: if (tao->jacobian_state_inv) {
219: if (symmetric) {
220: MatMult(tao->jacobian_state_inv, lclP->GU, lclP->lamda); } else {
221: MatMultTranspose(tao->jacobian_state_inv, lclP->GU, lclP->lamda);
222: }
223: } else {
224: KSPSetOperators(tao->ksp, tao->jacobian_state, tao->jacobian_state_pre);
225: if (symmetric) {
226: KSPSolve(tao->ksp, lclP->GU, lclP->lamda);
227: } else {
228: KSPSolveTranspose(tao->ksp, lclP->GU, lclP->lamda);
229: }
230: KSPGetIterationNumber(tao->ksp,&its);
231: tao->ksp_its+=its;
232: tao->ksp_tot_its+=its;
233: }
234: VecCopy(lclP->lamda,lclP->lamda0);
235: LCLComputeAugmentedLagrangianAndGradient(tao->linesearch,tao->solution,&lclP->aug,lclP->GAugL,tao);
237: LCLScatter(lclP,lclP->GL,lclP->GL_U,lclP->GL_V);
238: LCLScatter(lclP,lclP->GAugL,lclP->GAugL_U,lclP->GAugL_V);
240: /* Evaluate constraint norm */
241: VecNorm(tao->constraints, NORM_2, &cnorm);
242: VecNorm(lclP->GAugL, NORM_2, &mnorm);
244: /* Monitor convergence */
245: tao->reason = TAO_CONTINUE_ITERATING;
246: TaoLogConvergenceHistory(tao,f,mnorm,cnorm,tao->ksp_its);
247: TaoMonitor(tao,tao->niter,f,mnorm,cnorm,step);
248: (*tao->ops->convergencetest)(tao,tao->cnvP);
250: while (tao->reason == TAO_CONTINUE_ITERATING) {
251: /* Call general purpose update function */
252: if (tao->ops->update) {
253: (*tao->ops->update)(tao, tao->niter, tao->user_update);
254: }
255: tao->ksp_its=0;
256: /* Compute a descent direction for the linearly constrained subproblem
257: minimize f(u+du, v+dv)
258: s.t. A(u0,v0)du + B(u0,v0)dv = -g(u0,v0) */
260: /* Store the points around the linearization */
261: VecCopy(lclP->U, lclP->U0);
262: VecCopy(lclP->V, lclP->V0);
263: VecCopy(lclP->GU,lclP->GU0);
264: VecCopy(lclP->GV,lclP->GV0);
265: VecCopy(lclP->GAugL_U,lclP->GAugL_U0);
266: VecCopy(lclP->GAugL_V,lclP->GAugL_V0);
267: VecCopy(lclP->GL_U,lclP->GL_U0);
268: VecCopy(lclP->GL_V,lclP->GL_V0);
270: lclP->aug0 = lclP->aug;
271: lclP->lgn0 = lclP->lgn;
273: /* Given the design variables, we need to project the current iterate
274: onto the linearized constraint. We choose to fix the design variables
275: and solve the linear system for the state variables. The resulting
276: point is the Newton direction */
278: /* Solve r = A\con */
279: lclP->solve_type = LCL_FORWARD1;
280: VecSet(lclP->r,0.0); /* Initial guess in CG */
282: if (tao->jacobian_state_inv) {
283: MatMult(tao->jacobian_state_inv, tao->constraints, lclP->r);
284: } else {
285: KSPSetOperators(tao->ksp, tao->jacobian_state, tao->jacobian_state_pre);
286: KSPSolve(tao->ksp, tao->constraints, lclP->r);
287: KSPGetIterationNumber(tao->ksp,&its);
288: tao->ksp_its+=its;
289: tao->ksp_tot_its+=tao->ksp_its;
290: }
292: /* Set design step direction dv to zero */
293: VecSet(lclP->s, 0.0);
295: /*
296: Check sufficient descent for constraint merit function .5*||con||^2
297: con' Ak r >= eps1 ||r||^(2+eps2)
298: */
300: /* Compute WU= Ak' * con */
301: if (symmetric) {
302: MatMult(tao->jacobian_state,tao->constraints,lclP->WU);
303: } else {
304: MatMultTranspose(tao->jacobian_state,tao->constraints,lclP->WU);
305: }
306: /* Compute r * Ak' * con */
307: VecDot(lclP->r,lclP->WU,&rWU);
309: /* compute ||r||^(2+eps2) */
310: VecNorm(lclP->r,NORM_2,&r2);
311: r2 = PetscPowScalar(r2,2.0+lclP->eps2);
312: adec = lclP->eps1 * r2;
314: if (rWU < adec) {
315: PetscInfo(tao,"Newton direction not descent for constraint, feasibility phase required\n");
316: if (lclP->verbose) {
317: PetscPrintf(PETSC_COMM_WORLD,"Newton direction not descent for constraint: %g -- using steepest descent\n",(double)descent);
318: }
320: PetscInfo(tao,"Using steepest descent direction instead.\n");
321: VecSet(lclP->r,0.0);
322: VecAXPY(lclP->r,-1.0,lclP->WU);
323: VecDot(lclP->r,lclP->r,&rWU);
324: VecNorm(lclP->r,NORM_2,&r2);
325: r2 = PetscPowScalar(r2,2.0+lclP->eps2);
326: VecDot(lclP->r,lclP->GAugL_U,&descent);
327: adec = lclP->eps1 * r2;
328: }
330: /*
331: Check descent for aug. lagrangian
332: r' (GUk - Ak'*yk - rho*Ak'*con) <= -eps1 ||r||^(2+eps2)
333: GL_U = GUk - Ak'*yk
334: WU = Ak'*con
335: adec=eps1||r||^(2+eps2)
337: ==>
338: Check r'GL_U - rho*r'WU <= adec
339: */
341: VecDot(lclP->r,lclP->GL_U,&rGL_U);
342: aldescent = rGL_U - lclP->rho*rWU;
343: if (aldescent > -adec) {
344: if (lclP->verbose) {
345: PetscPrintf(PETSC_COMM_WORLD," Newton direction not descent for augmented Lagrangian: %g",(double)aldescent);
346: }
347: PetscInfo1(tao,"Newton direction not descent for augmented Lagrangian: %g\n",(double)aldescent);
348: lclP->rho = (rGL_U - adec)/rWU;
349: if (lclP->rho > lclP->rhomax) {
350: lclP->rho = lclP->rhomax;
351: SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"rho=%g > rhomax, case not implemented. Increase rhomax (-tao_lcl_rhomax)",(double)lclP->rho);
352: }
353: if (lclP->verbose) {
354: PetscPrintf(PETSC_COMM_WORLD," Increasing penalty parameter to %g\n",(double)lclP->rho);
355: }
356: PetscInfo1(tao," Increasing penalty parameter to %g\n",(double)lclP->rho);
357: }
359: LCLComputeAugmentedLagrangianAndGradient(tao->linesearch,tao->solution,&lclP->aug,lclP->GAugL,tao);
360: LCLScatter(lclP,lclP->GL,lclP->GL_U,lclP->GL_V);
361: LCLScatter(lclP,lclP->GAugL,lclP->GAugL_U,lclP->GAugL_V);
363: /* We now minimize the augmented Lagrangian along the Newton direction */
364: VecScale(lclP->r,-1.0);
365: LCLGather(lclP, lclP->r,lclP->s,tao->stepdirection);
366: VecScale(lclP->r,-1.0);
367: LCLGather(lclP, lclP->GAugL_U0, lclP->GAugL_V0, lclP->GAugL);
368: LCLGather(lclP, lclP->U0,lclP->V0,lclP->X0);
370: lclP->recompute_jacobian_flag = PETSC_TRUE;
372: TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);
373: TaoLineSearchSetType(tao->linesearch, TAOLINESEARCHMT);
374: TaoLineSearchSetFromOptions(tao->linesearch);
375: TaoLineSearchApply(tao->linesearch, tao->solution, &lclP->aug, lclP->GAugL, tao->stepdirection, &step, &ls_reason);
376: if (lclP->verbose) {
377: PetscPrintf(PETSC_COMM_WORLD,"Steplength = %g\n",(double)step);
378: }
380: LCLScatter(lclP,tao->solution,lclP->U,lclP->V);
381: TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);
382: LCLScatter(lclP,tao->gradient,lclP->GU,lclP->GV);
384: LCLScatter(lclP,lclP->GAugL,lclP->GAugL_U,lclP->GAugL_V);
386: /* Check convergence */
387: VecNorm(lclP->GAugL, NORM_2, &mnorm);
388: VecNorm(tao->constraints, NORM_2, &cnorm);
389: TaoLogConvergenceHistory(tao,f,mnorm,cnorm,tao->ksp_its);
390: TaoMonitor(tao,tao->niter,f,mnorm,cnorm,step);
391: (*tao->ops->convergencetest)(tao,tao->cnvP);
392: if (tao->reason != TAO_CONTINUE_ITERATING) {
393: break;
394: }
396: /* TODO: use a heuristic to choose how many iterations should be performed within phase 2 */
397: for (phase2_iter=0; phase2_iter<lclP->phase2_niter; phase2_iter++) {
398: /* We now minimize the objective function starting from the fraction of
399: the Newton point accepted by applying one step of a reduced-space
400: method. The optimization problem is:
402: minimize f(u+du, v+dv)
403: s. t. A(u0,v0)du + B(u0,v0)du = -alpha g(u0,v0)
405: In particular, we have that
406: du = -inv(A)*(Bdv + alpha g) */
408: TaoComputeJacobianState(tao,lclP->X0,tao->jacobian_state,tao->jacobian_state_pre,tao->jacobian_state_inv);
409: TaoComputeJacobianDesign(tao,lclP->X0,tao->jacobian_design);
411: /* Store V and constraints */
412: VecCopy(lclP->V, lclP->V1);
413: VecCopy(tao->constraints,lclP->con1);
415: /* Compute multipliers */
416: /* p1 */
417: VecSet(lclP->lamda,0.0); /* Initial guess in CG */
418: lclP->solve_type = LCL_ADJOINT1;
419: MatIsSymmetricKnown(tao->jacobian_state,&set,&flag);
420: if (tao->jacobian_state_pre) {
421: MatIsSymmetricKnown(tao->jacobian_state_pre,&pset,&pflag);
422: } else {
423: pset = pflag = PETSC_TRUE;
424: }
425: if (set && pset && flag && pflag) symmetric = PETSC_TRUE;
426: else symmetric = PETSC_FALSE;
428: if (tao->jacobian_state_inv) {
429: if (symmetric) {
430: MatMult(tao->jacobian_state_inv, lclP->GAugL_U, lclP->lamda);
431: } else {
432: MatMultTranspose(tao->jacobian_state_inv, lclP->GAugL_U, lclP->lamda);
433: }
434: } else {
435: if (symmetric) {
436: KSPSolve(tao->ksp, lclP->GAugL_U, lclP->lamda);
437: } else {
438: KSPSolveTranspose(tao->ksp, lclP->GAugL_U, lclP->lamda);
439: }
440: KSPGetIterationNumber(tao->ksp,&its);
441: tao->ksp_its+=its;
442: tao->ksp_tot_its+=its;
443: }
444: MatMultTranspose(tao->jacobian_design,lclP->lamda,lclP->g1);
445: VecAXPY(lclP->g1,-1.0,lclP->GAugL_V);
447: /* Compute the limited-memory quasi-newton direction */
448: if (tao->niter > 0) {
449: MatSolve(lclP->R,lclP->g1,lclP->s);
450: VecDot(lclP->s,lclP->g1,&descent);
451: if (descent <= 0) {
452: if (lclP->verbose) {
453: PetscPrintf(PETSC_COMM_WORLD,"Reduced-space direction not descent: %g\n",(double)descent);
454: }
455: VecCopy(lclP->g1,lclP->s);
456: }
457: } else {
458: VecCopy(lclP->g1,lclP->s);
459: }
460: VecScale(lclP->g1,-1.0);
462: /* Recover the full space direction */
463: MatMult(tao->jacobian_design,lclP->s,lclP->WU);
464: /* VecSet(lclP->r,0.0); */ /* Initial guess in CG */
465: lclP->solve_type = LCL_FORWARD2;
466: if (tao->jacobian_state_inv) {
467: MatMult(tao->jacobian_state_inv,lclP->WU,lclP->r);
468: } else {
469: KSPSolve(tao->ksp, lclP->WU, lclP->r);
470: KSPGetIterationNumber(tao->ksp,&its);
471: tao->ksp_its += its;
472: tao->ksp_tot_its+=its;
473: }
475: /* We now minimize the augmented Lagrangian along the direction -r,s */
476: VecScale(lclP->r, -1.0);
477: LCLGather(lclP,lclP->r,lclP->s,tao->stepdirection);
478: VecScale(lclP->r, -1.0);
479: lclP->recompute_jacobian_flag = PETSC_TRUE;
481: TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);
482: TaoLineSearchSetType(tao->linesearch,TAOLINESEARCHMT);
483: TaoLineSearchSetFromOptions(tao->linesearch);
484: TaoLineSearchApply(tao->linesearch, tao->solution, &lclP->aug, lclP->GAugL, tao->stepdirection,&step,&ls_reason);
485: if (lclP->verbose) {
486: PetscPrintf(PETSC_COMM_WORLD,"Reduced-space steplength = %g\n",(double)step);
487: }
489: LCLScatter(lclP,tao->solution,lclP->U,lclP->V);
490: LCLScatter(lclP,lclP->GL,lclP->GL_U,lclP->GL_V);
491: LCLScatter(lclP,lclP->GAugL,lclP->GAugL_U,lclP->GAugL_V);
492: TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);
493: LCLScatter(lclP,tao->gradient,lclP->GU,lclP->GV);
495: /* Compute the reduced gradient at the new point */
497: TaoComputeJacobianState(tao,lclP->X0,tao->jacobian_state,tao->jacobian_state_pre,tao->jacobian_state_inv);
498: TaoComputeJacobianDesign(tao,lclP->X0,tao->jacobian_design);
500: /* p2 */
501: /* Compute multipliers, using lamda-rho*con as an initial guess in PCG */
502: if (phase2_iter==0) {
503: VecWAXPY(lclP->lamda,-lclP->rho,lclP->con1,lclP->lamda0);
504: } else {
505: VecAXPY(lclP->lamda,-lclP->rho,tao->constraints);
506: }
508: MatIsSymmetricKnown(tao->jacobian_state,&set,&flag);
509: if (tao->jacobian_state_pre) {
510: MatIsSymmetricKnown(tao->jacobian_state_pre,&pset,&pflag);
511: } else {
512: pset = pflag = PETSC_TRUE;
513: }
514: if (set && pset && flag && pflag) symmetric = PETSC_TRUE;
515: else symmetric = PETSC_FALSE;
517: lclP->solve_type = LCL_ADJOINT2;
518: if (tao->jacobian_state_inv) {
519: if (symmetric) {
520: MatMult(tao->jacobian_state_inv, lclP->GU, lclP->lamda);
521: } else {
522: MatMultTranspose(tao->jacobian_state_inv, lclP->GU, lclP->lamda);
523: }
524: } else {
525: if (symmetric) {
526: KSPSolve(tao->ksp, lclP->GU, lclP->lamda);
527: } else {
528: KSPSolveTranspose(tao->ksp, lclP->GU, lclP->lamda);
529: }
530: KSPGetIterationNumber(tao->ksp,&its);
531: tao->ksp_its += its;
532: tao->ksp_tot_its += its;
533: }
535: MatMultTranspose(tao->jacobian_design,lclP->lamda,lclP->g2);
536: VecAXPY(lclP->g2,-1.0,lclP->GV);
538: VecScale(lclP->g2,-1.0);
540: /* Update the quasi-newton approximation */
541: MatLMVMUpdate(lclP->R,lclP->V,lclP->g2);
542: /* Use "-tao_ls_type gpcg -tao_ls_ftol 0 -tao_lmm_broyden_phi 0.0 -tao_lmm_scale_type scalar" to obtain agreement with Matlab code */
544: }
546: VecCopy(lclP->lamda,lclP->lamda0);
548: /* Evaluate Function, Gradient, Constraints, and Jacobian */
549: TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);
550: LCLScatter(lclP,tao->solution,lclP->U,lclP->V);
551: LCLScatter(lclP,tao->gradient,lclP->GU,lclP->GV);
553: TaoComputeJacobianState(tao,tao->solution,tao->jacobian_state,tao->jacobian_state_pre,tao->jacobian_state_inv);
554: TaoComputeJacobianDesign(tao,tao->solution,tao->jacobian_design);
555: TaoComputeConstraints(tao,tao->solution, tao->constraints);
557: LCLComputeAugmentedLagrangianAndGradient(tao->linesearch,tao->solution,&lclP->aug,lclP->GAugL,tao);
559: VecNorm(lclP->GAugL, NORM_2, &mnorm);
561: /* Evaluate constraint norm */
562: VecNorm(tao->constraints, NORM_2, &cnorm);
564: /* Monitor convergence */
565: tao->niter++;
566: TaoLogConvergenceHistory(tao,f,mnorm,cnorm,tao->ksp_its);
567: TaoMonitor(tao,tao->niter,f,mnorm,cnorm,step);
568: (*tao->ops->convergencetest)(tao,tao->cnvP);
569: }
570: return(0);
571: }
573: /*MC
574: TAOLCL - linearly constrained lagrangian method for pde-constrained optimization
576: + -tao_lcl_eps1 - epsilon 1 tolerance
577: . -tao_lcl_eps2","epsilon 2 tolerance","",lclP->eps2,&lclP->eps2,NULL);
578: . -tao_lcl_rho0","init value for rho","",lclP->rho0,&lclP->rho0,NULL);
579: . -tao_lcl_rhomax","max value for rho","",lclP->rhomax,&lclP->rhomax,NULL);
580: . -tao_lcl_phase2_niter - Number of phase 2 iterations in LCL algorithm
581: . -tao_lcl_verbose - Print verbose output if True
582: . -tao_lcl_tola - Tolerance for first forward solve
583: . -tao_lcl_tolb - Tolerance for first adjoint solve
584: . -tao_lcl_tolc - Tolerance for second forward solve
585: - -tao_lcl_told - Tolerance for second adjoint solve
587: Level: beginner
588: M*/
589: PETSC_EXTERN PetscErrorCode TaoCreate_LCL(Tao tao)
590: {
591: TAO_LCL *lclP;
593: const char *morethuente_type = TAOLINESEARCHMT;
596: tao->ops->setup = TaoSetup_LCL;
597: tao->ops->solve = TaoSolve_LCL;
598: tao->ops->view = TaoView_LCL;
599: tao->ops->setfromoptions = TaoSetFromOptions_LCL;
600: tao->ops->destroy = TaoDestroy_LCL;
601: PetscNewLog(tao,&lclP);
602: tao->data = (void*)lclP;
604: /* Override default settings (unless already changed) */
605: if (!tao->max_it_changed) tao->max_it = 200;
606: if (!tao->catol_changed) tao->catol = 1.0e-4;
607: if (!tao->gatol_changed) tao->gttol = 1.0e-4;
608: if (!tao->grtol_changed) tao->gttol = 1.0e-4;
609: if (!tao->gttol_changed) tao->gttol = 1.0e-4;
610: lclP->rho0 = 1.0e-4;
611: lclP->rhomax=1e5;
612: lclP->eps1 = 1.0e-8;
613: lclP->eps2 = 0.0;
614: lclP->solve_type=2;
615: lclP->tau[0] = lclP->tau[1] = lclP->tau[2] = lclP->tau[3] = 1.0e-4;
616: TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch);
617: PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);
618: TaoLineSearchSetType(tao->linesearch, morethuente_type);
619: TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);
621: TaoLineSearchSetObjectiveAndGradientRoutine(tao->linesearch,LCLComputeAugmentedLagrangianAndGradient, tao);
622: KSPCreate(((PetscObject)tao)->comm,&tao->ksp);
623: PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1);
624: KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix);
625: KSPSetFromOptions(tao->ksp);
627: MatCreate(((PetscObject)tao)->comm, &lclP->R);
628: MatSetType(lclP->R, MATLMVMBFGS);
629: return(0);
630: }
632: static PetscErrorCode LCLComputeLagrangianAndGradient(TaoLineSearch ls, Vec X, PetscReal *f, Vec G, void *ptr)
633: {
634: Tao tao = (Tao)ptr;
635: TAO_LCL *lclP = (TAO_LCL*)tao->data;
636: PetscBool set,pset,flag,pflag,symmetric;
637: PetscReal cdotl;
641: TaoComputeObjectiveAndGradient(tao,X,f,G);
642: LCLScatter(lclP,G,lclP->GU,lclP->GV);
643: if (lclP->recompute_jacobian_flag) {
644: TaoComputeJacobianState(tao,X,tao->jacobian_state,tao->jacobian_state_pre,tao->jacobian_state_inv);
645: TaoComputeJacobianDesign(tao,X,tao->jacobian_design);
646: }
647: TaoComputeConstraints(tao,X, tao->constraints);
648: MatIsSymmetricKnown(tao->jacobian_state,&set,&flag);
649: if (tao->jacobian_state_pre) {
650: MatIsSymmetricKnown(tao->jacobian_state_pre,&pset,&pflag);
651: } else {
652: pset = pflag = PETSC_TRUE;
653: }
654: if (set && pset && flag && pflag) symmetric = PETSC_TRUE;
655: else symmetric = PETSC_FALSE;
657: VecDot(lclP->lamda0, tao->constraints, &cdotl);
658: lclP->lgn = *f - cdotl;
660: /* Gradient of Lagrangian GL = G - J' * lamda */
661: /* WU = A' * WL
662: WV = B' * WL */
663: if (symmetric) {
664: MatMult(tao->jacobian_state,lclP->lamda0,lclP->GL_U);
665: } else {
666: MatMultTranspose(tao->jacobian_state,lclP->lamda0,lclP->GL_U);
667: }
668: MatMultTranspose(tao->jacobian_design,lclP->lamda0,lclP->GL_V);
669: VecScale(lclP->GL_U,-1.0);
670: VecScale(lclP->GL_V,-1.0);
671: VecAXPY(lclP->GL_U,1.0,lclP->GU);
672: VecAXPY(lclP->GL_V,1.0,lclP->GV);
673: LCLGather(lclP,lclP->GL_U,lclP->GL_V,lclP->GL);
675: f[0] = lclP->lgn;
676: VecCopy(lclP->GL,G);
677: return(0);
678: }
680: static PetscErrorCode LCLComputeAugmentedLagrangianAndGradient(TaoLineSearch ls, Vec X, PetscReal *f, Vec G, void *ptr)
681: {
682: Tao tao = (Tao)ptr;
683: TAO_LCL *lclP = (TAO_LCL*)tao->data;
684: PetscReal con2;
685: PetscBool flag,pflag,set,pset,symmetric;
689: LCLComputeLagrangianAndGradient(tao->linesearch,X,f,G,tao);
690: LCLScatter(lclP,G,lclP->GL_U,lclP->GL_V);
691: VecDot(tao->constraints,tao->constraints,&con2);
692: lclP->aug = lclP->lgn + 0.5*lclP->rho*con2;
694: /* Gradient of Aug. Lagrangian GAugL = GL + rho * J' c */
695: /* WU = A' * c
696: WV = B' * c */
697: MatIsSymmetricKnown(tao->jacobian_state,&set,&flag);
698: if (tao->jacobian_state_pre) {
699: MatIsSymmetricKnown(tao->jacobian_state_pre,&pset,&pflag);
700: } else {
701: pset = pflag = PETSC_TRUE;
702: }
703: if (set && pset && flag && pflag) symmetric = PETSC_TRUE;
704: else symmetric = PETSC_FALSE;
706: if (symmetric) {
707: MatMult(tao->jacobian_state,tao->constraints,lclP->GAugL_U);
708: } else {
709: MatMultTranspose(tao->jacobian_state,tao->constraints,lclP->GAugL_U);
710: }
712: MatMultTranspose(tao->jacobian_design,tao->constraints,lclP->GAugL_V);
713: VecAYPX(lclP->GAugL_U,lclP->rho,lclP->GL_U);
714: VecAYPX(lclP->GAugL_V,lclP->rho,lclP->GL_V);
715: LCLGather(lclP,lclP->GAugL_U,lclP->GAugL_V,lclP->GAugL);
717: f[0] = lclP->aug;
718: VecCopy(lclP->GAugL,G);
719: return(0);
720: }
722: PetscErrorCode LCLGather(TAO_LCL *lclP, Vec u, Vec v, Vec x)
723: {
726: VecScatterBegin(lclP->state_scatter, u, x, INSERT_VALUES, SCATTER_REVERSE);
727: VecScatterEnd(lclP->state_scatter, u, x, INSERT_VALUES, SCATTER_REVERSE);
728: VecScatterBegin(lclP->design_scatter, v, x, INSERT_VALUES, SCATTER_REVERSE);
729: VecScatterEnd(lclP->design_scatter, v, x, INSERT_VALUES, SCATTER_REVERSE);
730: return(0);
732: }
733: PetscErrorCode LCLScatter(TAO_LCL *lclP, Vec x, Vec u, Vec v)
734: {
737: VecScatterBegin(lclP->state_scatter, x, u, INSERT_VALUES, SCATTER_FORWARD);
738: VecScatterEnd(lclP->state_scatter, x, u, INSERT_VALUES, SCATTER_FORWARD);
739: VecScatterBegin(lclP->design_scatter, x, v, INSERT_VALUES, SCATTER_FORWARD);
740: VecScatterEnd(lclP->design_scatter, x, v, INSERT_VALUES, SCATTER_FORWARD);
741: return(0);
743: }