Actual source code: lcl.c
petsc-3.10.5 2019-03-28
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(PETSC_COMM_WORLD,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: tao->ksp_its=0;
252: /* Compute a descent direction for the linearly constrained subproblem
253: minimize f(u+du, v+dv)
254: s.t. A(u0,v0)du + B(u0,v0)dv = -g(u0,v0) */
256: /* Store the points around the linearization */
257: VecCopy(lclP->U, lclP->U0);
258: VecCopy(lclP->V, lclP->V0);
259: VecCopy(lclP->GU,lclP->GU0);
260: VecCopy(lclP->GV,lclP->GV0);
261: VecCopy(lclP->GAugL_U,lclP->GAugL_U0);
262: VecCopy(lclP->GAugL_V,lclP->GAugL_V0);
263: VecCopy(lclP->GL_U,lclP->GL_U0);
264: VecCopy(lclP->GL_V,lclP->GL_V0);
266: lclP->aug0 = lclP->aug;
267: lclP->lgn0 = lclP->lgn;
269: /* Given the design variables, we need to project the current iterate
270: onto the linearized constraint. We choose to fix the design variables
271: and solve the linear system for the state variables. The resulting
272: point is the Newton direction */
274: /* Solve r = A\con */
275: lclP->solve_type = LCL_FORWARD1;
276: VecSet(lclP->r,0.0); /* Initial guess in CG */
278: if (tao->jacobian_state_inv) {
279: MatMult(tao->jacobian_state_inv, tao->constraints, lclP->r);
280: } else {
281: KSPSetOperators(tao->ksp, tao->jacobian_state, tao->jacobian_state_pre);
282: KSPSolve(tao->ksp, tao->constraints, lclP->r);
283: KSPGetIterationNumber(tao->ksp,&its);
284: tao->ksp_its+=its;
285: tao->ksp_tot_its+=tao->ksp_its;
286: }
288: /* Set design step direction dv to zero */
289: VecSet(lclP->s, 0.0);
291: /*
292: Check sufficient descent for constraint merit function .5*||con||^2
293: con' Ak r >= eps1 ||r||^(2+eps2)
294: */
296: /* Compute WU= Ak' * con */
297: if (symmetric) {
298: MatMult(tao->jacobian_state,tao->constraints,lclP->WU);
299: } else {
300: MatMultTranspose(tao->jacobian_state,tao->constraints,lclP->WU);
301: }
302: /* Compute r * Ak' * con */
303: VecDot(lclP->r,lclP->WU,&rWU);
305: /* compute ||r||^(2+eps2) */
306: VecNorm(lclP->r,NORM_2,&r2);
307: r2 = PetscPowScalar(r2,2.0+lclP->eps2);
308: adec = lclP->eps1 * r2;
310: if (rWU < adec) {
311: PetscInfo(tao,"Newton direction not descent for constraint, feasibility phase required\n");
312: if (lclP->verbose) {
313: PetscPrintf(PETSC_COMM_WORLD,"Newton direction not descent for constraint: %g -- using steepest descent\n",(double)descent);
314: }
316: PetscInfo(tao,"Using steepest descent direction instead.\n");
317: VecSet(lclP->r,0.0);
318: VecAXPY(lclP->r,-1.0,lclP->WU);
319: VecDot(lclP->r,lclP->r,&rWU);
320: VecNorm(lclP->r,NORM_2,&r2);
321: r2 = PetscPowScalar(r2,2.0+lclP->eps2);
322: VecDot(lclP->r,lclP->GAugL_U,&descent);
323: adec = lclP->eps1 * r2;
324: }
327: /*
328: Check descent for aug. lagrangian
329: r' (GUk - Ak'*yk - rho*Ak'*con) <= -eps1 ||r||^(2+eps2)
330: GL_U = GUk - Ak'*yk
331: WU = Ak'*con
332: adec=eps1||r||^(2+eps2)
334: ==>
335: Check r'GL_U - rho*r'WU <= adec
336: */
338: VecDot(lclP->r,lclP->GL_U,&rGL_U);
339: aldescent = rGL_U - lclP->rho*rWU;
340: if (aldescent > -adec) {
341: if (lclP->verbose) {
342: PetscPrintf(PETSC_COMM_WORLD," Newton direction not descent for augmented Lagrangian: %g",(double)aldescent);
343: }
344: PetscInfo1(tao,"Newton direction not descent for augmented Lagrangian: %g\n",(double)aldescent);
345: lclP->rho = (rGL_U - adec)/rWU;
346: if (lclP->rho > lclP->rhomax) {
347: lclP->rho = lclP->rhomax;
348: SETERRQ1(PETSC_COMM_WORLD,0,"rho=%g > rhomax, case not implemented. Increase rhomax (-tao_lcl_rhomax)",(double)lclP->rho);
349: }
350: if (lclP->verbose) {
351: PetscPrintf(PETSC_COMM_WORLD," Increasing penalty parameter to %g\n",(double)lclP->rho);
352: }
353: PetscInfo1(tao," Increasing penalty parameter to %g\n",(double)lclP->rho);
354: }
356: LCLComputeAugmentedLagrangianAndGradient(tao->linesearch,tao->solution,&lclP->aug,lclP->GAugL,tao);
357: LCLScatter(lclP,lclP->GL,lclP->GL_U,lclP->GL_V);
358: LCLScatter(lclP,lclP->GAugL,lclP->GAugL_U,lclP->GAugL_V);
360: /* We now minimize the augmented Lagrangian along the Newton direction */
361: VecScale(lclP->r,-1.0);
362: LCLGather(lclP, lclP->r,lclP->s,tao->stepdirection);
363: VecScale(lclP->r,-1.0);
364: LCLGather(lclP, lclP->GAugL_U0, lclP->GAugL_V0, lclP->GAugL);
365: LCLGather(lclP, lclP->U0,lclP->V0,lclP->X0);
367: lclP->recompute_jacobian_flag = PETSC_TRUE;
369: TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);
370: TaoLineSearchSetType(tao->linesearch, TAOLINESEARCHMT);
371: TaoLineSearchSetFromOptions(tao->linesearch);
372: TaoLineSearchApply(tao->linesearch, tao->solution, &lclP->aug, lclP->GAugL, tao->stepdirection, &step, &ls_reason);
373: if (lclP->verbose) {
374: PetscPrintf(PETSC_COMM_WORLD,"Steplength = %g\n",(double)step);
375: }
377: LCLScatter(lclP,tao->solution,lclP->U,lclP->V);
378: TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);
379: LCLScatter(lclP,tao->gradient,lclP->GU,lclP->GV);
381: LCLScatter(lclP,lclP->GAugL,lclP->GAugL_U,lclP->GAugL_V);
383: /* Check convergence */
384: VecNorm(lclP->GAugL, NORM_2, &mnorm);
385: VecNorm(tao->constraints, NORM_2, &cnorm);
386: TaoLogConvergenceHistory(tao,f,mnorm,cnorm,tao->ksp_its);
387: TaoMonitor(tao,tao->niter,f,mnorm,cnorm,step);
388: (*tao->ops->convergencetest)(tao,tao->cnvP);
389: if (tao->reason != TAO_CONTINUE_ITERATING){
390: break;
391: }
393: /* TODO: use a heuristic to choose how many iterations should be performed within phase 2 */
394: for (phase2_iter=0; phase2_iter<lclP->phase2_niter; phase2_iter++){
395: /* We now minimize the objective function starting from the fraction of
396: the Newton point accepted by applying one step of a reduced-space
397: method. The optimization problem is:
399: minimize f(u+du, v+dv)
400: s. t. A(u0,v0)du + B(u0,v0)du = -alpha g(u0,v0)
402: In particular, we have that
403: du = -inv(A)*(Bdv + alpha g) */
405: TaoComputeJacobianState(tao,lclP->X0,tao->jacobian_state,tao->jacobian_state_pre,tao->jacobian_state_inv);
406: TaoComputeJacobianDesign(tao,lclP->X0,tao->jacobian_design);
408: /* Store V and constraints */
409: VecCopy(lclP->V, lclP->V1);
410: VecCopy(tao->constraints,lclP->con1);
412: /* Compute multipliers */
413: /* p1 */
414: VecSet(lclP->lamda,0.0); /* Initial guess in CG */
415: lclP->solve_type = LCL_ADJOINT1;
416: MatIsSymmetricKnown(tao->jacobian_state,&set,&flag);
417: if (tao->jacobian_state_pre) {
418: MatIsSymmetricKnown(tao->jacobian_state_pre,&pset,&pflag);
419: } else {
420: pset = pflag = PETSC_TRUE;
421: }
422: if (set && pset && flag && pflag) symmetric = PETSC_TRUE;
423: else symmetric = PETSC_FALSE;
425: if (tao->jacobian_state_inv) {
426: if (symmetric) {
427: MatMult(tao->jacobian_state_inv, lclP->GAugL_U, lclP->lamda);
428: } else {
429: MatMultTranspose(tao->jacobian_state_inv, lclP->GAugL_U, lclP->lamda);
430: }
431: } else {
432: if (symmetric) {
433: KSPSolve(tao->ksp, lclP->GAugL_U, lclP->lamda);
434: } else {
435: KSPSolveTranspose(tao->ksp, lclP->GAugL_U, lclP->lamda);
436: }
437: KSPGetIterationNumber(tao->ksp,&its);
438: tao->ksp_its+=its;
439: tao->ksp_tot_its+=its;
440: }
441: MatMultTranspose(tao->jacobian_design,lclP->lamda,lclP->g1);
442: VecAXPY(lclP->g1,-1.0,lclP->GAugL_V);
444: /* Compute the limited-memory quasi-newton direction */
445: if (tao->niter > 0) {
446: MatSolve(lclP->R,lclP->g1,lclP->s);
447: VecDot(lclP->s,lclP->g1,&descent);
448: if (descent <= 0) {
449: if (lclP->verbose) {
450: PetscPrintf(PETSC_COMM_WORLD,"Reduced-space direction not descent: %g\n",(double)descent);
451: }
452: VecCopy(lclP->g1,lclP->s);
453: }
454: } else {
455: VecCopy(lclP->g1,lclP->s);
456: }
457: VecScale(lclP->g1,-1.0);
459: /* Recover the full space direction */
460: MatMult(tao->jacobian_design,lclP->s,lclP->WU);
461: /* VecSet(lclP->r,0.0); */ /* Initial guess in CG */
462: lclP->solve_type = LCL_FORWARD2;
463: if (tao->jacobian_state_inv) {
464: MatMult(tao->jacobian_state_inv,lclP->WU,lclP->r);
465: } else {
466: KSPSolve(tao->ksp, lclP->WU, lclP->r);
467: KSPGetIterationNumber(tao->ksp,&its);
468: tao->ksp_its += its;
469: tao->ksp_tot_its+=its;
470: }
472: /* We now minimize the augmented Lagrangian along the direction -r,s */
473: VecScale(lclP->r, -1.0);
474: LCLGather(lclP,lclP->r,lclP->s,tao->stepdirection);
475: VecScale(lclP->r, -1.0);
476: lclP->recompute_jacobian_flag = PETSC_TRUE;
478: TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);
479: TaoLineSearchSetType(tao->linesearch,TAOLINESEARCHMT);
480: TaoLineSearchSetFromOptions(tao->linesearch);
481: TaoLineSearchApply(tao->linesearch, tao->solution, &lclP->aug, lclP->GAugL, tao->stepdirection,&step,&ls_reason);
482: if (lclP->verbose){
483: PetscPrintf(PETSC_COMM_WORLD,"Reduced-space steplength = %g\n",(double)step);
484: }
486: LCLScatter(lclP,tao->solution,lclP->U,lclP->V);
487: LCLScatter(lclP,lclP->GL,lclP->GL_U,lclP->GL_V);
488: LCLScatter(lclP,lclP->GAugL,lclP->GAugL_U,lclP->GAugL_V);
489: TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);
490: LCLScatter(lclP,tao->gradient,lclP->GU,lclP->GV);
492: /* Compute the reduced gradient at the new point */
494: TaoComputeJacobianState(tao,lclP->X0,tao->jacobian_state,tao->jacobian_state_pre,tao->jacobian_state_inv);
495: TaoComputeJacobianDesign(tao,lclP->X0,tao->jacobian_design);
497: /* p2 */
498: /* Compute multipliers, using lamda-rho*con as an initial guess in PCG */
499: if (phase2_iter==0){
500: VecWAXPY(lclP->lamda,-lclP->rho,lclP->con1,lclP->lamda0);
501: } else {
502: VecAXPY(lclP->lamda,-lclP->rho,tao->constraints);
503: }
505: MatIsSymmetricKnown(tao->jacobian_state,&set,&flag);
506: if (tao->jacobian_state_pre) {
507: MatIsSymmetricKnown(tao->jacobian_state_pre,&pset,&pflag);
508: } else {
509: pset = pflag = PETSC_TRUE;
510: }
511: if (set && pset && flag && pflag) symmetric = PETSC_TRUE;
512: else symmetric = PETSC_FALSE;
514: lclP->solve_type = LCL_ADJOINT2;
515: if (tao->jacobian_state_inv) {
516: if (symmetric) {
517: MatMult(tao->jacobian_state_inv, lclP->GU, lclP->lamda);
518: } else {
519: MatMultTranspose(tao->jacobian_state_inv, lclP->GU, lclP->lamda);
520: }
521: } else {
522: if (symmetric) {
523: KSPSolve(tao->ksp, lclP->GU, lclP->lamda);
524: } else {
525: KSPSolveTranspose(tao->ksp, lclP->GU, lclP->lamda);
526: }
527: KSPGetIterationNumber(tao->ksp,&its);
528: tao->ksp_its += its;
529: tao->ksp_tot_its += its;
530: }
532: MatMultTranspose(tao->jacobian_design,lclP->lamda,lclP->g2);
533: VecAXPY(lclP->g2,-1.0,lclP->GV);
535: VecScale(lclP->g2,-1.0);
537: /* Update the quasi-newton approximation */
538: MatLMVMUpdate(lclP->R,lclP->V,lclP->g2);
539: /* 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 */
541: }
543: VecCopy(lclP->lamda,lclP->lamda0);
545: /* Evaluate Function, Gradient, Constraints, and Jacobian */
546: TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);
547: LCLScatter(lclP,tao->solution,lclP->U,lclP->V);
548: LCLScatter(lclP,tao->gradient,lclP->GU,lclP->GV);
550: TaoComputeJacobianState(tao,tao->solution,tao->jacobian_state,tao->jacobian_state_pre,tao->jacobian_state_inv);
551: TaoComputeJacobianDesign(tao,tao->solution,tao->jacobian_design);
552: TaoComputeConstraints(tao,tao->solution, tao->constraints);
554: LCLComputeAugmentedLagrangianAndGradient(tao->linesearch,tao->solution,&lclP->aug,lclP->GAugL,tao);
556: VecNorm(lclP->GAugL, NORM_2, &mnorm);
558: /* Evaluate constraint norm */
559: VecNorm(tao->constraints, NORM_2, &cnorm);
561: /* Monitor convergence */
562: tao->niter++;
563: TaoLogConvergenceHistory(tao,f,mnorm,cnorm,tao->ksp_its);
564: TaoMonitor(tao,tao->niter,f,mnorm,cnorm,step);
565: (*tao->ops->convergencetest)(tao,tao->cnvP);
566: }
567: return(0);
568: }
570: /*MC
571: TAOLCL - linearly constrained lagrangian method for pde-constrained optimization
573: + -tao_lcl_eps1 - epsilon 1 tolerance
574: . -tao_lcl_eps2","epsilon 2 tolerance","",lclP->eps2,&lclP->eps2,NULL);
575: . -tao_lcl_rho0","init value for rho","",lclP->rho0,&lclP->rho0,NULL);
576: . -tao_lcl_rhomax","max value for rho","",lclP->rhomax,&lclP->rhomax,NULL);
577: . -tao_lcl_phase2_niter - Number of phase 2 iterations in LCL algorithm
578: . -tao_lcl_verbose - Print verbose output if True
579: . -tao_lcl_tola - Tolerance for first forward solve
580: . -tao_lcl_tolb - Tolerance for first adjoint solve
581: . -tao_lcl_tolc - Tolerance for second forward solve
582: - -tao_lcl_told - Tolerance for second adjoint solve
584: Level: beginner
585: M*/
586: PETSC_EXTERN PetscErrorCode TaoCreate_LCL(Tao tao)
587: {
588: TAO_LCL *lclP;
590: const char *morethuente_type = TAOLINESEARCHMT;
593: tao->ops->setup = TaoSetup_LCL;
594: tao->ops->solve = TaoSolve_LCL;
595: tao->ops->view = TaoView_LCL;
596: tao->ops->setfromoptions = TaoSetFromOptions_LCL;
597: tao->ops->destroy = TaoDestroy_LCL;
598: PetscNewLog(tao,&lclP);
599: tao->data = (void*)lclP;
601: /* Override default settings (unless already changed) */
602: if (!tao->max_it_changed) tao->max_it = 200;
603: if (!tao->catol_changed) tao->catol = 1.0e-4;
604: if (!tao->gatol_changed) tao->gttol = 1.0e-4;
605: if (!tao->grtol_changed) tao->gttol = 1.0e-4;
606: if (!tao->gttol_changed) tao->gttol = 1.0e-4;
607: lclP->rho0 = 1.0e-4;
608: lclP->rhomax=1e5;
609: lclP->eps1 = 1.0e-8;
610: lclP->eps2 = 0.0;
611: lclP->solve_type=2;
612: lclP->tau[0] = lclP->tau[1] = lclP->tau[2] = lclP->tau[3] = 1.0e-4;
613: TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch);
614: PetscObjectIncrementTabLevel((PetscObject)tao->linesearch, (PetscObject)tao, 1);
615: TaoLineSearchSetType(tao->linesearch, morethuente_type);
616: TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);
618: TaoLineSearchSetObjectiveAndGradientRoutine(tao->linesearch,LCLComputeAugmentedLagrangianAndGradient, tao);
619: KSPCreate(((PetscObject)tao)->comm,&tao->ksp);
620: PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1);
621: KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix);
622: KSPSetFromOptions(tao->ksp);
623:
624: MatCreate(((PetscObject)tao)->comm, &lclP->R);
625: MatSetType(lclP->R, MATLMVMBFGS);
626: return(0);
627: }
629: static PetscErrorCode LCLComputeLagrangianAndGradient(TaoLineSearch ls, Vec X, PetscReal *f, Vec G, void *ptr)
630: {
631: Tao tao = (Tao)ptr;
632: TAO_LCL *lclP = (TAO_LCL*)tao->data;
633: PetscBool set,pset,flag,pflag,symmetric;
634: PetscReal cdotl;
638: TaoComputeObjectiveAndGradient(tao,X,f,G);
639: LCLScatter(lclP,G,lclP->GU,lclP->GV);
640: if (lclP->recompute_jacobian_flag) {
641: TaoComputeJacobianState(tao,X,tao->jacobian_state,tao->jacobian_state_pre,tao->jacobian_state_inv);
642: TaoComputeJacobianDesign(tao,X,tao->jacobian_design);
643: }
644: TaoComputeConstraints(tao,X, tao->constraints);
645: MatIsSymmetricKnown(tao->jacobian_state,&set,&flag);
646: if (tao->jacobian_state_pre) {
647: MatIsSymmetricKnown(tao->jacobian_state_pre,&pset,&pflag);
648: } else {
649: pset = pflag = PETSC_TRUE;
650: }
651: if (set && pset && flag && pflag) symmetric = PETSC_TRUE;
652: else symmetric = PETSC_FALSE;
654: VecDot(lclP->lamda0, tao->constraints, &cdotl);
655: lclP->lgn = *f - cdotl;
657: /* Gradient of Lagrangian GL = G - J' * lamda */
658: /* WU = A' * WL
659: WV = B' * WL */
660: if (symmetric) {
661: MatMult(tao->jacobian_state,lclP->lamda0,lclP->GL_U);
662: } else {
663: MatMultTranspose(tao->jacobian_state,lclP->lamda0,lclP->GL_U);
664: }
665: MatMultTranspose(tao->jacobian_design,lclP->lamda0,lclP->GL_V);
666: VecScale(lclP->GL_U,-1.0);
667: VecScale(lclP->GL_V,-1.0);
668: VecAXPY(lclP->GL_U,1.0,lclP->GU);
669: VecAXPY(lclP->GL_V,1.0,lclP->GV);
670: LCLGather(lclP,lclP->GL_U,lclP->GL_V,lclP->GL);
672: f[0] = lclP->lgn;
673: VecCopy(lclP->GL,G);
674: return(0);
675: }
677: static PetscErrorCode LCLComputeAugmentedLagrangianAndGradient(TaoLineSearch ls, Vec X, PetscReal *f, Vec G, void *ptr)
678: {
679: Tao tao = (Tao)ptr;
680: TAO_LCL *lclP = (TAO_LCL*)tao->data;
681: PetscReal con2;
682: PetscBool flag,pflag,set,pset,symmetric;
686: LCLComputeLagrangianAndGradient(tao->linesearch,X,f,G,tao);
687: LCLScatter(lclP,G,lclP->GL_U,lclP->GL_V);
688: VecDot(tao->constraints,tao->constraints,&con2);
689: lclP->aug = lclP->lgn + 0.5*lclP->rho*con2;
691: /* Gradient of Aug. Lagrangian GAugL = GL + rho * J' c */
692: /* WU = A' * c
693: WV = B' * c */
694: MatIsSymmetricKnown(tao->jacobian_state,&set,&flag);
695: if (tao->jacobian_state_pre) {
696: MatIsSymmetricKnown(tao->jacobian_state_pre,&pset,&pflag);
697: } else {
698: pset = pflag = PETSC_TRUE;
699: }
700: if (set && pset && flag && pflag) symmetric = PETSC_TRUE;
701: else symmetric = PETSC_FALSE;
703: if (symmetric) {
704: MatMult(tao->jacobian_state,tao->constraints,lclP->GAugL_U);
705: } else {
706: MatMultTranspose(tao->jacobian_state,tao->constraints,lclP->GAugL_U);
707: }
709: MatMultTranspose(tao->jacobian_design,tao->constraints,lclP->GAugL_V);
710: VecAYPX(lclP->GAugL_U,lclP->rho,lclP->GL_U);
711: VecAYPX(lclP->GAugL_V,lclP->rho,lclP->GL_V);
712: LCLGather(lclP,lclP->GAugL_U,lclP->GAugL_V,lclP->GAugL);
714: f[0] = lclP->aug;
715: VecCopy(lclP->GAugL,G);
716: return(0);
717: }
719: PetscErrorCode LCLGather(TAO_LCL *lclP, Vec u, Vec v, Vec x)
720: {
723: VecScatterBegin(lclP->state_scatter, u, x, INSERT_VALUES, SCATTER_REVERSE);
724: VecScatterEnd(lclP->state_scatter, u, x, INSERT_VALUES, SCATTER_REVERSE);
725: VecScatterBegin(lclP->design_scatter, v, x, INSERT_VALUES, SCATTER_REVERSE);
726: VecScatterEnd(lclP->design_scatter, v, x, INSERT_VALUES, SCATTER_REVERSE);
727: return(0);
729: }
730: PetscErrorCode LCLScatter(TAO_LCL *lclP, Vec x, Vec u, Vec v)
731: {
734: VecScatterBegin(lclP->state_scatter, x, u, INSERT_VALUES, SCATTER_FORWARD);
735: VecScatterEnd(lclP->state_scatter, x, u, INSERT_VALUES, SCATTER_FORWARD);
736: VecScatterBegin(lclP->design_scatter, x, v, INSERT_VALUES, SCATTER_FORWARD);
737: VecScatterEnd(lclP->design_scatter, x, v, INSERT_VALUES, SCATTER_FORWARD);
738: return(0);
740: }