Actual source code: admm.c

  1: #include <../src/tao/constrained/impls/admm/admm.h>
  2: #include <petsctao.h>
  3: #include <petsc/private/petscimpl.h>

  5: /* Updates terminating criteria
  6:  *
  7:  * 1  ||r_k|| = ||Ax+Bz-c|| =< catol_admm* max{||Ax||,||Bz||,||c||}
  8:  *
  9:  * 2. Updates dual residual, d_k
 10:  *
 11:  * 3. ||d_k|| = ||mu*A^T*B(z_k-z_{k-1})|| =< gatol_admm * ||A^Ty||   */

 13: static PetscBool  cited      = PETSC_FALSE;
 14: static const char citation[] = "@misc{xu2017adaptive,\n"
 15:                                "   title={Adaptive Relaxed ADMM: Convergence Theory and Practical Implementation},\n"
 16:                                "   author={Zheng Xu and Mario A. T. Figueiredo and Xiaoming Yuan and Christoph Studer and Tom Goldstein},\n"
 17:                                "   year={2017},\n"
 18:                                "   eprint={1704.02712},\n"
 19:                                "   archivePrefix={arXiv},\n"
 20:                                "   primaryClass={cs.CV}\n"
 21:                                "}  \n";

 23: const char *const TaoADMMRegularizerTypes[] = {"REGULARIZER_USER", "REGULARIZER_SOFT_THRESH", "TaoADMMRegularizerType", "TAO_ADMM_", NULL};
 24: const char *const TaoADMMUpdateTypes[]      = {"UPDATE_BASIC", "UPDATE_ADAPTIVE", "UPDATE_ADAPTIVE_RELAXED", "TaoADMMUpdateType", "TAO_ADMM_", NULL};
 25: const char *const TaoALMMTypes[]            = {"CLASSIC", "PHR", "TaoALMMType", "TAO_ALMM_", NULL};

 27: static PetscErrorCode TaoADMMToleranceUpdate(Tao tao)
 28: {
 29:   TAO_ADMM *am = (TAO_ADMM *)tao->data;
 30:   PetscReal Axnorm, Bznorm, ATynorm, temp;
 31:   Vec       tempJR, tempL;
 32:   Tao       mis;

 34:   PetscFunctionBegin;
 35:   mis    = am->subsolverX;
 36:   tempJR = am->workJacobianRight;
 37:   tempL  = am->workLeft;
 38:   /* ATy */
 39:   PetscCall(TaoComputeJacobianEquality(mis, am->y, mis->jacobian_equality, mis->jacobian_equality_pre));
 40:   PetscCall(MatMultTranspose(mis->jacobian_equality, am->y, tempJR));
 41:   PetscCall(VecNorm(tempJR, NORM_2, &ATynorm));
 42:   /* dualres = mu * ||AT(Bz-Bzold)||_2 */
 43:   PetscCall(VecWAXPY(tempJR, -1., am->Bzold, am->Bz));
 44:   PetscCall(MatMultTranspose(mis->jacobian_equality, tempJR, tempL));
 45:   PetscCall(VecNorm(tempL, NORM_2, &am->dualres));
 46:   am->dualres *= am->mu;

 48:   /* ||Ax||_2, ||Bz||_2 */
 49:   PetscCall(VecNorm(am->Ax, NORM_2, &Axnorm));
 50:   PetscCall(VecNorm(am->Bz, NORM_2, &Bznorm));

 52:   /* Set catol to be catol_admm *  max{||Ax||,||Bz||,||c||} *
 53:    * Set gatol to be gatol_admm *  ||A^Ty|| *
 54:    * while cnorm is ||r_k||_2, and gnorm is ||d_k||_2 */
 55:   temp = am->catol_admm * PetscMax(Axnorm, (!am->const_norm) ? Bznorm : PetscMax(Bznorm, am->const_norm));
 56:   PetscCall(TaoSetConstraintTolerances(tao, temp, PETSC_DEFAULT));
 57:   PetscCall(TaoSetTolerances(tao, am->gatol_admm * ATynorm, PETSC_DEFAULT, PETSC_DEFAULT));
 58:   PetscFunctionReturn(PETSC_SUCCESS);
 59: }

 61: /* Penaly Update for Adaptive ADMM. */
 62: static PetscErrorCode AdaptiveADMMPenaltyUpdate(Tao tao)
 63: {
 64:   TAO_ADMM *am = (TAO_ADMM *)tao->data;
 65:   PetscReal ydiff_norm, yhatdiff_norm, Axdiff_norm, Bzdiff_norm, Axyhat, Bzy, a_sd, a_mg, a_k, b_sd, b_mg, b_k;
 66:   PetscBool hflag, gflag;
 67:   Vec       tempJR, tempJR2;

 69:   PetscFunctionBegin;
 70:   tempJR  = am->workJacobianRight;
 71:   tempJR2 = am->workJacobianRight2;
 72:   hflag   = PETSC_FALSE;
 73:   gflag   = PETSC_FALSE;
 74:   a_k     = -1;
 75:   b_k     = -1;

 77:   PetscCall(VecWAXPY(tempJR, -1., am->Axold, am->Ax));
 78:   PetscCall(VecWAXPY(tempJR2, -1., am->yhatold, am->yhat));
 79:   PetscCall(VecNorm(tempJR, NORM_2, &Axdiff_norm));
 80:   PetscCall(VecNorm(tempJR2, NORM_2, &yhatdiff_norm));
 81:   PetscCall(VecDot(tempJR, tempJR2, &Axyhat));

 83:   PetscCall(VecWAXPY(tempJR, -1., am->Bz0, am->Bz));
 84:   PetscCall(VecWAXPY(tempJR2, -1., am->y, am->y0));
 85:   PetscCall(VecNorm(tempJR, NORM_2, &Bzdiff_norm));
 86:   PetscCall(VecNorm(tempJR2, NORM_2, &ydiff_norm));
 87:   PetscCall(VecDot(tempJR, tempJR2, &Bzy));

 89:   if (Axyhat > am->orthval * Axdiff_norm * yhatdiff_norm + am->mueps) {
 90:     hflag = PETSC_TRUE;
 91:     a_sd  = PetscSqr(yhatdiff_norm) / Axyhat; /* alphaSD */
 92:     a_mg  = Axyhat / PetscSqr(Axdiff_norm);   /* alphaMG */
 93:     a_k   = (a_mg / a_sd) > 0.5 ? a_mg : a_sd - 0.5 * a_mg;
 94:   }
 95:   if (Bzy > am->orthval * Bzdiff_norm * ydiff_norm + am->mueps) {
 96:     gflag = PETSC_TRUE;
 97:     b_sd  = PetscSqr(ydiff_norm) / Bzy;  /* betaSD */
 98:     b_mg  = Bzy / PetscSqr(Bzdiff_norm); /* betaMG */
 99:     b_k   = (b_mg / b_sd) > 0.5 ? b_mg : b_sd - 0.5 * b_mg;
100:   }
101:   am->muold = am->mu;
102:   if (gflag && hflag) {
103:     am->mu = PetscSqrtReal(a_k * b_k);
104:   } else if (hflag) {
105:     am->mu = a_k;
106:   } else if (gflag) {
107:     am->mu = b_k;
108:   }
109:   if (am->mu > am->muold) am->mu = am->muold;
110:   if (am->mu < am->mumin) am->mu = am->mumin;
111:   PetscFunctionReturn(PETSC_SUCCESS);
112: }

114: static PetscErrorCode TaoADMMSetRegularizerType_ADMM(Tao tao, TaoADMMRegularizerType type)
115: {
116:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

118:   PetscFunctionBegin;
119:   am->regswitch = type;
120:   PetscFunctionReturn(PETSC_SUCCESS);
121: }

123: static PetscErrorCode TaoADMMGetRegularizerType_ADMM(Tao tao, TaoADMMRegularizerType *type)
124: {
125:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

127:   PetscFunctionBegin;
128:   *type = am->regswitch;
129:   PetscFunctionReturn(PETSC_SUCCESS);
130: }

132: static PetscErrorCode TaoADMMSetUpdateType_ADMM(Tao tao, TaoADMMUpdateType type)
133: {
134:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

136:   PetscFunctionBegin;
137:   am->update = type;
138:   PetscFunctionReturn(PETSC_SUCCESS);
139: }

141: static PetscErrorCode TaoADMMGetUpdateType_ADMM(Tao tao, TaoADMMUpdateType *type)
142: {
143:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

145:   PetscFunctionBegin;
146:   *type = am->update;
147:   PetscFunctionReturn(PETSC_SUCCESS);
148: }

150: /* This routine updates Jacobians with new x,z vectors,
151:  * and then updates Ax and Bz vectors, then computes updated residual vector*/
152: static PetscErrorCode ADMMUpdateConstraintResidualVector(Tao tao, Vec x, Vec z, Vec Ax, Vec Bz, Vec residual)
153: {
154:   TAO_ADMM *am = (TAO_ADMM *)tao->data;
155:   Tao       mis, reg;

157:   PetscFunctionBegin;
158:   mis = am->subsolverX;
159:   reg = am->subsolverZ;
160:   PetscCall(TaoComputeJacobianEquality(mis, x, mis->jacobian_equality, mis->jacobian_equality_pre));
161:   PetscCall(MatMult(mis->jacobian_equality, x, Ax));
162:   PetscCall(TaoComputeJacobianEquality(reg, z, reg->jacobian_equality, reg->jacobian_equality_pre));
163:   PetscCall(MatMult(reg->jacobian_equality, z, Bz));

165:   PetscCall(VecWAXPY(residual, 1., Bz, Ax));
166:   if (am->constraint != NULL) PetscCall(VecAXPY(residual, -1., am->constraint));
167:   PetscFunctionReturn(PETSC_SUCCESS);
168: }

170: /* Updates Augmented Lagrangians to given routines *
171:  * For subsolverX, routine needs to be ComputeObjectiveAndGraidnet
172:  * Separate Objective and Gradient routines are not supported.  */
173: static PetscErrorCode SubObjGradUpdate(Tao tao, Vec x, PetscReal *f, Vec g, void *ptr)
174: {
175:   Tao       parent = (Tao)ptr;
176:   TAO_ADMM *am     = (TAO_ADMM *)parent->data;
177:   PetscReal temp, temp2;
178:   Vec       tempJR;

180:   PetscFunctionBegin;
181:   tempJR = am->workJacobianRight;
182:   PetscCall(ADMMUpdateConstraintResidualVector(parent, x, am->subsolverZ->solution, am->Ax, am->Bz, am->residual));
183:   PetscCall((*am->ops->misfitobjgrad)(am->subsolverX, x, f, g, am->misfitobjgradP));

185:   am->last_misfit_val = *f;
186:   /* Objective  Add + yT(Ax+Bz-c) + mu/2*||Ax+Bz-c||_2^2 */
187:   PetscCall(VecTDot(am->residual, am->y, &temp));
188:   PetscCall(VecTDot(am->residual, am->residual, &temp2));
189:   *f += temp + (am->mu / 2) * temp2;

191:   /* Gradient. Add + mu*AT(Ax+Bz-c) + yTA*/
192:   PetscCall(MatMultTranspose(tao->jacobian_equality, am->residual, tempJR));
193:   PetscCall(VecAXPY(g, am->mu, tempJR));
194:   PetscCall(MatMultTranspose(tao->jacobian_equality, am->y, tempJR));
195:   PetscCall(VecAXPY(g, 1., tempJR));
196:   PetscFunctionReturn(PETSC_SUCCESS);
197: }

199: /* Updates Augmented Lagrangians to given routines
200:  * For subsolverZ, routine needs to be ComputeObjectiveAndGraidnet
201:  * Separate Objective and Gradient routines are not supported.  */
202: static PetscErrorCode RegObjGradUpdate(Tao tao, Vec z, PetscReal *f, Vec g, void *ptr)
203: {
204:   Tao       parent = (Tao)ptr;
205:   TAO_ADMM *am     = (TAO_ADMM *)parent->data;
206:   PetscReal temp, temp2;
207:   Vec       tempJR;

209:   PetscFunctionBegin;
210:   tempJR = am->workJacobianRight;
211:   PetscCall(ADMMUpdateConstraintResidualVector(parent, am->subsolverX->solution, z, am->Ax, am->Bz, am->residual));
212:   PetscCall((*am->ops->regobjgrad)(am->subsolverZ, z, f, g, am->regobjgradP));
213:   am->last_reg_val = *f;
214:   /* Objective  Add  + yT(Ax+Bz-c) + mu/2*||Ax+Bz-c||_2^2 */
215:   PetscCall(VecTDot(am->residual, am->y, &temp));
216:   PetscCall(VecTDot(am->residual, am->residual, &temp2));
217:   *f += temp + (am->mu / 2) * temp2;

219:   /* Gradient. Add + mu*BT(Ax+Bz-c) + yTB*/
220:   PetscCall(MatMultTranspose(am->subsolverZ->jacobian_equality, am->residual, tempJR));
221:   PetscCall(VecAXPY(g, am->mu, tempJR));
222:   PetscCall(MatMultTranspose(am->subsolverZ->jacobian_equality, am->y, tempJR));
223:   PetscCall(VecAXPY(g, 1., tempJR));
224:   PetscFunctionReturn(PETSC_SUCCESS);
225: }

227: /* Computes epsilon padded L1 norm lambda*sum(sqrt(x^2+eps^2)-eps */
228: static PetscErrorCode ADMML1EpsilonNorm(Tao tao, Vec x, PetscReal eps, PetscReal *norm)
229: {
230:   TAO_ADMM *am = (TAO_ADMM *)tao->data;
231:   PetscInt  N;

233:   PetscFunctionBegin;
234:   PetscCall(VecGetSize(am->workLeft, &N));
235:   PetscCall(VecPointwiseMult(am->workLeft, x, x));
236:   PetscCall(VecShift(am->workLeft, am->l1epsilon * am->l1epsilon));
237:   PetscCall(VecSqrtAbs(am->workLeft));
238:   PetscCall(VecSum(am->workLeft, norm));
239:   *norm += N * am->l1epsilon;
240:   *norm *= am->lambda;
241:   PetscFunctionReturn(PETSC_SUCCESS);
242: }

244: static PetscErrorCode ADMMInternalHessianUpdate(Mat H, Mat Constraint, PetscBool Identity, void *ptr)
245: {
246:   TAO_ADMM *am = (TAO_ADMM *)ptr;

248:   PetscFunctionBegin;
249:   switch (am->update) {
250:   case (TAO_ADMM_UPDATE_BASIC):
251:     break;
252:   case (TAO_ADMM_UPDATE_ADAPTIVE):
253:   case (TAO_ADMM_UPDATE_ADAPTIVE_RELAXED):
254:     if (H && (am->muold != am->mu)) {
255:       if (!Identity) {
256:         PetscCall(MatAXPY(H, am->mu - am->muold, Constraint, DIFFERENT_NONZERO_PATTERN));
257:       } else {
258:         PetscCall(MatShift(H, am->mu - am->muold));
259:       }
260:     }
261:     break;
262:   }
263:   PetscFunctionReturn(PETSC_SUCCESS);
264: }

266: /* Updates Hessian - adds second derivative of augmented Lagrangian
267:  * H \gets H + \rho*ATA
268:   Here, \rho does not change in TAO_ADMM_UPDATE_BASIC - thus no-op
269:   For ADAPTAIVE,ADAPTIVE_RELAXED,
270:   H \gets H + (\rho-\rhoold)*ATA
271:   Here, we assume that A is linear constraint i.e., does not change.
272:   Thus, for both ADAPTIVE, and RELAXED, ATA matrix is pre-set (except for A=I (null case)) see TaoSetUp_ADMM */
273: static PetscErrorCode SubHessianUpdate(Tao tao, Vec x, Mat H, Mat Hpre, void *ptr)
274: {
275:   Tao       parent = (Tao)ptr;
276:   TAO_ADMM *am     = (TAO_ADMM *)parent->data;

278:   PetscFunctionBegin;
279:   if (am->Hxchange) {
280:     /* Case where Hessian gets updated with respect to x vector input. */
281:     PetscCall((*am->ops->misfithess)(am->subsolverX, x, H, Hpre, am->misfithessP));
282:     PetscCall(ADMMInternalHessianUpdate(am->subsolverX->hessian, am->ATA, am->xJI, am));
283:   } else if (am->Hxbool) {
284:     /* Hessian doesn't get updated. H(x) = c */
285:     /* Update Lagrangian only once per TAO call */
286:     PetscCall(ADMMInternalHessianUpdate(am->subsolverX->hessian, am->ATA, am->xJI, am));
287:     am->Hxbool = PETSC_FALSE;
288:   }
289:   PetscFunctionReturn(PETSC_SUCCESS);
290: }

292: /* Same as SubHessianUpdate, except for B matrix instead of A matrix */
293: static PetscErrorCode RegHessianUpdate(Tao tao, Vec z, Mat H, Mat Hpre, void *ptr)
294: {
295:   Tao       parent = (Tao)ptr;
296:   TAO_ADMM *am     = (TAO_ADMM *)parent->data;

298:   PetscFunctionBegin;
299:   if (am->Hzchange) {
300:     /* Case where Hessian gets updated with respect to x vector input. */
301:     PetscCall((*am->ops->reghess)(am->subsolverZ, z, H, Hpre, am->reghessP));
302:     PetscCall(ADMMInternalHessianUpdate(am->subsolverZ->hessian, am->BTB, am->zJI, am));
303:   } else if (am->Hzbool) {
304:     /* Hessian doesn't get updated. H(x) = c */
305:     /* Update Lagrangian only once per TAO call */
306:     PetscCall(ADMMInternalHessianUpdate(am->subsolverZ->hessian, am->BTB, am->zJI, am));
307:     am->Hzbool = PETSC_FALSE;
308:   }
309:   PetscFunctionReturn(PETSC_SUCCESS);
310: }

312: /* Shell Matrix routine for A matrix.
313:  * This gets used when user puts NULL for
314:  * TaoSetJacobianEqualityRoutine(tao, NULL,NULL, ...)
315:  * Essentially sets A=I*/
316: static PetscErrorCode JacobianIdentity(Mat mat, Vec in, Vec out)
317: {
318:   PetscFunctionBegin;
319:   PetscCall(VecCopy(in, out));
320:   PetscFunctionReturn(PETSC_SUCCESS);
321: }

323: /* Shell Matrix routine for B matrix.
324:  * This gets used when user puts NULL for
325:  * TaoADMMSetRegularizerConstraintJacobian(tao, NULL,NULL, ...)
326:  * Sets B=-I */
327: static PetscErrorCode JacobianIdentityB(Mat mat, Vec in, Vec out)
328: {
329:   PetscFunctionBegin;
330:   PetscCall(VecCopy(in, out));
331:   PetscCall(VecScale(out, -1.));
332:   PetscFunctionReturn(PETSC_SUCCESS);
333: }

335: /* Solve f(x) + g(z) s.t. Ax + Bz = c */
336: static PetscErrorCode TaoSolve_ADMM(Tao tao)
337: {
338:   TAO_ADMM *am = (TAO_ADMM *)tao->data;
339:   PetscInt  N;
340:   PetscReal reg_func;
341:   PetscBool is_reg_shell;
342:   Vec       tempL;

344:   PetscFunctionBegin;
345:   if (am->regswitch != TAO_ADMM_REGULARIZER_SOFT_THRESH) {
346:     PetscCheck(am->subsolverX->ops->computejacobianequality, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_WRONGSTATE, "Must call TaoADMMSetMisfitConstraintJacobian() first");
347:     PetscCheck(am->subsolverZ->ops->computejacobianequality, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_WRONGSTATE, "Must call TaoADMMSetRegularizerConstraintJacobian() first");
348:     if (am->constraint != NULL) PetscCall(VecNorm(am->constraint, NORM_2, &am->const_norm));
349:   }
350:   tempL = am->workLeft;
351:   PetscCall(VecGetSize(tempL, &N));

353:   if (am->Hx && am->ops->misfithess) PetscCall(TaoSetHessian(am->subsolverX, am->Hx, am->Hx, SubHessianUpdate, tao));

355:   if (!am->zJI) {
356:     /* Currently, B is assumed to be a linear system, i.e., not getting updated*/
357:     PetscCall(MatTransposeMatMult(am->JB, am->JB, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &am->BTB));
358:   }
359:   if (!am->xJI) {
360:     /* Currently, A is assumed to be a linear system, i.e., not getting updated*/
361:     PetscCall(MatTransposeMatMult(am->subsolverX->jacobian_equality, am->subsolverX->jacobian_equality, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &am->ATA));
362:   }

364:   is_reg_shell = PETSC_FALSE;

366:   PetscCall(PetscObjectTypeCompare((PetscObject)am->subsolverZ, TAOSHELL, &is_reg_shell));

368:   if (!is_reg_shell) {
369:     switch (am->regswitch) {
370:     case (TAO_ADMM_REGULARIZER_USER):
371:       break;
372:     case (TAO_ADMM_REGULARIZER_SOFT_THRESH):
373:       /* Soft Threshold. */
374:       break;
375:     }
376:     if (am->ops->regobjgrad) PetscCall(TaoSetObjectiveAndGradient(am->subsolverZ, NULL, RegObjGradUpdate, tao));
377:     if (am->Hz && am->ops->reghess) PetscCall(TaoSetHessian(am->subsolverZ, am->Hz, am->Hzpre, RegHessianUpdate, tao));
378:   }

380:   switch (am->update) {
381:   case TAO_ADMM_UPDATE_BASIC:
382:     if (am->subsolverX->hessian) {
383:       /* In basic case, Hessian does not get updated w.r.t. to spectral penalty
384:        * Here, when A is set, i.e., am->xJI, add mu*ATA to Hessian*/
385:       if (!am->xJI) {
386:         PetscCall(MatAXPY(am->subsolverX->hessian, am->mu, am->ATA, DIFFERENT_NONZERO_PATTERN));
387:       } else {
388:         PetscCall(MatShift(am->subsolverX->hessian, am->mu));
389:       }
390:     }
391:     if (am->subsolverZ->hessian && am->regswitch == TAO_ADMM_REGULARIZER_USER) {
392:       if (am->regswitch == TAO_ADMM_REGULARIZER_USER && !am->zJI) {
393:         PetscCall(MatAXPY(am->subsolverZ->hessian, am->mu, am->BTB, DIFFERENT_NONZERO_PATTERN));
394:       } else {
395:         PetscCall(MatShift(am->subsolverZ->hessian, am->mu));
396:       }
397:     }
398:     break;
399:   case TAO_ADMM_UPDATE_ADAPTIVE:
400:   case TAO_ADMM_UPDATE_ADAPTIVE_RELAXED:
401:     break;
402:   }

404:   PetscCall(PetscCitationsRegister(citation, &cited));
405:   tao->reason = TAO_CONTINUE_ITERATING;

407:   while (tao->reason == TAO_CONTINUE_ITERATING) {
408:     PetscTryTypeMethod(tao, update, tao->niter, tao->user_update);
409:     PetscCall(VecCopy(am->Bz, am->Bzold));

411:     /* x update */
412:     PetscCall(TaoSolve(am->subsolverX));
413:     PetscCall(TaoComputeJacobianEquality(am->subsolverX, am->subsolverX->solution, am->subsolverX->jacobian_equality, am->subsolverX->jacobian_equality_pre));
414:     PetscCall(MatMult(am->subsolverX->jacobian_equality, am->subsolverX->solution, am->Ax));

416:     am->Hxbool = PETSC_TRUE;

418:     /* z update */
419:     switch (am->regswitch) {
420:     case TAO_ADMM_REGULARIZER_USER:
421:       PetscCall(TaoSolve(am->subsolverZ));
422:       break;
423:     case TAO_ADMM_REGULARIZER_SOFT_THRESH:
424:       /* L1 assumes A,B jacobians are identity nxn matrix */
425:       PetscCall(VecWAXPY(am->workJacobianRight, 1 / am->mu, am->y, am->Ax));
426:       PetscCall(TaoSoftThreshold(am->workJacobianRight, -am->lambda / am->mu, am->lambda / am->mu, am->subsolverZ->solution));
427:       break;
428:     }
429:     am->Hzbool = PETSC_TRUE;
430:     /* Returns Ax + Bz - c with updated Ax,Bz vectors */
431:     PetscCall(ADMMUpdateConstraintResidualVector(tao, am->subsolverX->solution, am->subsolverZ->solution, am->Ax, am->Bz, am->residual));
432:     /* Dual variable, y += y + mu*(Ax+Bz-c) */
433:     PetscCall(VecWAXPY(am->y, am->mu, am->residual, am->yold));

435:     /* stopping tolerance update */
436:     PetscCall(TaoADMMToleranceUpdate(tao));

438:     /* Updating Spectral Penalty */
439:     switch (am->update) {
440:     case TAO_ADMM_UPDATE_BASIC:
441:       am->muold = am->mu;
442:       break;
443:     case TAO_ADMM_UPDATE_ADAPTIVE:
444:     case TAO_ADMM_UPDATE_ADAPTIVE_RELAXED:
445:       if (tao->niter == 0) {
446:         PetscCall(VecCopy(am->y, am->y0));
447:         PetscCall(VecWAXPY(am->residual, 1., am->Ax, am->Bzold));
448:         if (am->constraint) PetscCall(VecAXPY(am->residual, -1., am->constraint));
449:         PetscCall(VecWAXPY(am->yhatold, -am->mu, am->residual, am->yold));
450:         PetscCall(VecCopy(am->Ax, am->Axold));
451:         PetscCall(VecCopy(am->Bz, am->Bz0));
452:         am->muold = am->mu;
453:       } else if (tao->niter % am->T == 1) {
454:         /* we have compute Bzold in a previous iteration, and we computed Ax above */
455:         PetscCall(VecWAXPY(am->residual, 1., am->Ax, am->Bzold));
456:         if (am->constraint) PetscCall(VecAXPY(am->residual, -1., am->constraint));
457:         PetscCall(VecWAXPY(am->yhat, -am->mu, am->residual, am->yold));
458:         PetscCall(AdaptiveADMMPenaltyUpdate(tao));
459:         PetscCall(VecCopy(am->Ax, am->Axold));
460:         PetscCall(VecCopy(am->Bz, am->Bz0));
461:         PetscCall(VecCopy(am->yhat, am->yhatold));
462:         PetscCall(VecCopy(am->y, am->y0));
463:       } else {
464:         am->muold = am->mu;
465:       }
466:       break;
467:     default:
468:       break;
469:     }
470:     tao->niter++;

472:     /* Calculate original function values. misfit part was done in TaoADMMToleranceUpdate*/
473:     switch (am->regswitch) {
474:     case TAO_ADMM_REGULARIZER_USER:
475:       if (is_reg_shell) {
476:         PetscCall(ADMML1EpsilonNorm(tao, am->subsolverZ->solution, am->l1epsilon, &reg_func));
477:       } else {
478:         PetscCall((*am->ops->regobjgrad)(am->subsolverZ, am->subsolverX->solution, &reg_func, tempL, am->regobjgradP));
479:       }
480:       break;
481:     case TAO_ADMM_REGULARIZER_SOFT_THRESH:
482:       PetscCall(ADMML1EpsilonNorm(tao, am->subsolverZ->solution, am->l1epsilon, &reg_func));
483:       break;
484:     }
485:     PetscCall(VecCopy(am->y, am->yold));
486:     PetscCall(ADMMUpdateConstraintResidualVector(tao, am->subsolverX->solution, am->subsolverZ->solution, am->Ax, am->Bz, am->residual));
487:     PetscCall(VecNorm(am->residual, NORM_2, &am->resnorm));
488:     PetscCall(TaoLogConvergenceHistory(tao, am->last_misfit_val + reg_func, am->dualres, am->resnorm, tao->ksp_its));

490:     PetscCall(TaoMonitor(tao, tao->niter, am->last_misfit_val + reg_func, am->dualres, am->resnorm, 1.0));
491:     PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
492:   }
493:   /* Update vectors */
494:   PetscCall(VecCopy(am->subsolverX->solution, tao->solution));
495:   PetscCall(VecCopy(am->subsolverX->gradient, tao->gradient));
496:   PetscCall(PetscObjectCompose((PetscObject)am->subsolverX, "TaoGetADMMParentTao_ADMM", NULL));
497:   PetscCall(PetscObjectCompose((PetscObject)am->subsolverZ, "TaoGetADMMParentTao_ADMM", NULL));
498:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoADMMSetRegularizerType_C", NULL));
499:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoADMMGetRegularizerType_C", NULL));
500:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoADMMSetUpdateType_C", NULL));
501:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoADMMGetUpdateType_C", NULL));
502:   PetscFunctionReturn(PETSC_SUCCESS);
503: }

505: static PetscErrorCode TaoSetFromOptions_ADMM(Tao tao, PetscOptionItems *PetscOptionsObject)
506: {
507:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

509:   PetscFunctionBegin;
510:   PetscOptionsHeadBegin(PetscOptionsObject, "ADMM problem that solves f(x) in a form of f(x) + g(z) subject to x - z = 0. Norm 1 and 2 are supported. Different subsolver routines can be selected. ");
511:   PetscCall(PetscOptionsReal("-tao_admm_regularizer_coefficient", "regularizer constant", "", am->lambda, &am->lambda, NULL));
512:   PetscCall(PetscOptionsReal("-tao_admm_spectral_penalty", "Constant for Augmented Lagrangian term.", "", am->mu, &am->mu, NULL));
513:   PetscCall(PetscOptionsReal("-tao_admm_relaxation_parameter", "x relaxation parameter for Z update.", "", am->gamma, &am->gamma, NULL));
514:   PetscCall(PetscOptionsReal("-tao_admm_tolerance_update_factor", "ADMM dynamic tolerance update factor.", "", am->tol, &am->tol, NULL));
515:   PetscCall(PetscOptionsReal("-tao_admm_spectral_penalty_update_factor", "ADMM spectral penalty update curvature safeguard value.", "", am->orthval, &am->orthval, NULL));
516:   PetscCall(PetscOptionsReal("-tao_admm_minimum_spectral_penalty", "Set ADMM minimum spectral penalty.", "", am->mumin, &am->mumin, NULL));
517:   PetscCall(PetscOptionsEnum("-tao_admm_dual_update", "Lagrangian dual update policy", "TaoADMMUpdateType", TaoADMMUpdateTypes, (PetscEnum)am->update, (PetscEnum *)&am->update, NULL));
518:   PetscCall(PetscOptionsEnum("-tao_admm_regularizer_type", "ADMM regularizer update rule", "TaoADMMRegularizerType", TaoADMMRegularizerTypes, (PetscEnum)am->regswitch, (PetscEnum *)&am->regswitch, NULL));
519:   PetscOptionsHeadEnd();
520:   PetscCall(TaoSetFromOptions(am->subsolverX));
521:   if (am->regswitch != TAO_ADMM_REGULARIZER_SOFT_THRESH) PetscCall(TaoSetFromOptions(am->subsolverZ));
522:   PetscFunctionReturn(PETSC_SUCCESS);
523: }

525: static PetscErrorCode TaoView_ADMM(Tao tao, PetscViewer viewer)
526: {
527:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

529:   PetscFunctionBegin;
530:   PetscCall(PetscViewerASCIIPushTab(viewer));
531:   PetscCall(TaoView(am->subsolverX, viewer));
532:   PetscCall(TaoView(am->subsolverZ, viewer));
533:   PetscCall(PetscViewerASCIIPopTab(viewer));
534:   PetscFunctionReturn(PETSC_SUCCESS);
535: }

537: static PetscErrorCode TaoSetUp_ADMM(Tao tao)
538: {
539:   TAO_ADMM *am = (TAO_ADMM *)tao->data;
540:   PetscInt  n, N, M;

542:   PetscFunctionBegin;
543:   PetscCall(VecGetLocalSize(tao->solution, &n));
544:   PetscCall(VecGetSize(tao->solution, &N));
545:   /* If Jacobian is given as NULL, it means Jacobian is identity matrix with size of solution vector */
546:   if (!am->JB) {
547:     am->zJI = PETSC_TRUE;
548:     PetscCall(MatCreateShell(PetscObjectComm((PetscObject)tao), n, n, PETSC_DETERMINE, PETSC_DETERMINE, NULL, &am->JB));
549:     PetscCall(MatShellSetOperation(am->JB, MATOP_MULT, (void (*)(void))JacobianIdentityB));
550:     PetscCall(MatShellSetOperation(am->JB, MATOP_MULT_TRANSPOSE, (void (*)(void))JacobianIdentityB));
551:     am->JBpre = am->JB;
552:   }
553:   if (!am->JA) {
554:     am->xJI = PETSC_TRUE;
555:     PetscCall(MatCreateShell(PetscObjectComm((PetscObject)tao), n, n, PETSC_DETERMINE, PETSC_DETERMINE, NULL, &am->JA));
556:     PetscCall(MatShellSetOperation(am->JA, MATOP_MULT, (void (*)(void))JacobianIdentity));
557:     PetscCall(MatShellSetOperation(am->JA, MATOP_MULT_TRANSPOSE, (void (*)(void))JacobianIdentity));
558:     am->JApre = am->JA;
559:   }
560:   PetscCall(MatCreateVecs(am->JA, NULL, &am->Ax));
561:   if (!tao->gradient) PetscCall(VecDuplicate(tao->solution, &tao->gradient));
562:   PetscCall(TaoSetSolution(am->subsolverX, tao->solution));
563:   if (!am->z) {
564:     PetscCall(VecDuplicate(tao->solution, &am->z));
565:     PetscCall(VecSet(am->z, 0.0));
566:   }
567:   PetscCall(TaoSetSolution(am->subsolverZ, am->z));
568:   if (!am->workLeft) PetscCall(VecDuplicate(tao->solution, &am->workLeft));
569:   if (!am->Axold) PetscCall(VecDuplicate(am->Ax, &am->Axold));
570:   if (!am->workJacobianRight) PetscCall(VecDuplicate(am->Ax, &am->workJacobianRight));
571:   if (!am->workJacobianRight2) PetscCall(VecDuplicate(am->Ax, &am->workJacobianRight2));
572:   if (!am->Bz) PetscCall(VecDuplicate(am->Ax, &am->Bz));
573:   if (!am->Bzold) PetscCall(VecDuplicate(am->Ax, &am->Bzold));
574:   if (!am->Bz0) PetscCall(VecDuplicate(am->Ax, &am->Bz0));
575:   if (!am->y) {
576:     PetscCall(VecDuplicate(am->Ax, &am->y));
577:     PetscCall(VecSet(am->y, 0.0));
578:   }
579:   if (!am->yold) {
580:     PetscCall(VecDuplicate(am->Ax, &am->yold));
581:     PetscCall(VecSet(am->yold, 0.0));
582:   }
583:   if (!am->y0) {
584:     PetscCall(VecDuplicate(am->Ax, &am->y0));
585:     PetscCall(VecSet(am->y0, 0.0));
586:   }
587:   if (!am->yhat) {
588:     PetscCall(VecDuplicate(am->Ax, &am->yhat));
589:     PetscCall(VecSet(am->yhat, 0.0));
590:   }
591:   if (!am->yhatold) {
592:     PetscCall(VecDuplicate(am->Ax, &am->yhatold));
593:     PetscCall(VecSet(am->yhatold, 0.0));
594:   }
595:   if (!am->residual) {
596:     PetscCall(VecDuplicate(am->Ax, &am->residual));
597:     PetscCall(VecSet(am->residual, 0.0));
598:   }
599:   if (!am->constraint) {
600:     am->constraint = NULL;
601:   } else {
602:     PetscCall(VecGetSize(am->constraint, &M));
603:     PetscCheck(M == N, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_WRONGSTATE, "Solution vector and constraint vector must be of same size!");
604:   }

606:   /* Save changed tao tolerance for adaptive tolerance */
607:   if (tao->gatol_changed) am->gatol_admm = tao->gatol;
608:   if (tao->catol_changed) am->catol_admm = tao->catol;

610:   /*Update spectral and dual elements to X subsolver */
611:   PetscCall(TaoSetObjectiveAndGradient(am->subsolverX, NULL, SubObjGradUpdate, tao));
612:   PetscCall(TaoSetJacobianEqualityRoutine(am->subsolverX, am->JA, am->JApre, am->ops->misfitjac, am->misfitjacobianP));
613:   PetscCall(TaoSetJacobianEqualityRoutine(am->subsolverZ, am->JB, am->JBpre, am->ops->regjac, am->regjacobianP));
614:   PetscFunctionReturn(PETSC_SUCCESS);
615: }

617: static PetscErrorCode TaoDestroy_ADMM(Tao tao)
618: {
619:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

621:   PetscFunctionBegin;
622:   PetscCall(VecDestroy(&am->z));
623:   PetscCall(VecDestroy(&am->Ax));
624:   PetscCall(VecDestroy(&am->Axold));
625:   PetscCall(VecDestroy(&am->Bz));
626:   PetscCall(VecDestroy(&am->Bzold));
627:   PetscCall(VecDestroy(&am->Bz0));
628:   PetscCall(VecDestroy(&am->residual));
629:   PetscCall(VecDestroy(&am->y));
630:   PetscCall(VecDestroy(&am->yold));
631:   PetscCall(VecDestroy(&am->y0));
632:   PetscCall(VecDestroy(&am->yhat));
633:   PetscCall(VecDestroy(&am->yhatold));
634:   PetscCall(VecDestroy(&am->workLeft));
635:   PetscCall(VecDestroy(&am->workJacobianRight));
636:   PetscCall(VecDestroy(&am->workJacobianRight2));

638:   PetscCall(MatDestroy(&am->JA));
639:   PetscCall(MatDestroy(&am->JB));
640:   if (!am->xJI) PetscCall(MatDestroy(&am->JApre));
641:   if (!am->zJI) PetscCall(MatDestroy(&am->JBpre));
642:   if (am->Hx) {
643:     PetscCall(MatDestroy(&am->Hx));
644:     PetscCall(MatDestroy(&am->Hxpre));
645:   }
646:   if (am->Hz) {
647:     PetscCall(MatDestroy(&am->Hz));
648:     PetscCall(MatDestroy(&am->Hzpre));
649:   }
650:   PetscCall(MatDestroy(&am->ATA));
651:   PetscCall(MatDestroy(&am->BTB));
652:   PetscCall(TaoDestroy(&am->subsolverX));
653:   PetscCall(TaoDestroy(&am->subsolverZ));
654:   am->parent = NULL;
655:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoADMMSetRegularizerType_C", NULL));
656:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoADMMGetRegularizerType_C", NULL));
657:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoADMMSetUpdateType_C", NULL));
658:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoADMMGetUpdateType_C", NULL));
659:   PetscCall(PetscFree(tao->data));
660:   PetscFunctionReturn(PETSC_SUCCESS);
661: }

663: /*MC
664:   TAOADMM - Alternating direction method of multipliers method for solving linear problems with
665:             constraints. in a $ \min_x f(x) + g(z)$  s.t. $Ax+Bz=c$.
666:             This algorithm employs two sub Tao solvers, of which type can be specified
667:             by the user. User need to provide ObjectiveAndGradient routine, and/or HessianRoutine for both subsolvers.
668:             Hessians can be given boolean flag determining whether they change with respect to a input vector. This can be set via
669:             `TaoADMMSet{Misfit,Regularizer}HessianChangeStatus()`.
670:             Second subsolver does support `TAOSHELL`. It should be noted that L1-norm is used for objective value for `TAOSHELL` type.
671:             There is option to set regularizer option, and currently soft-threshold is implemented. For spectral penalty update,
672:             currently there are basic option and adaptive option.
673:             Constraint is set at Ax+Bz=c, and A and B can be set with `TaoADMMSet{Misfit,Regularizer}ConstraintJacobian()`.
674:             c can be set with `TaoADMMSetConstraintVectorRHS()`.
675:             The user can also provide regularizer weight for second subsolver. {cite}`xu2017adaptive`

677:   Options Database Keys:
678: + -tao_admm_regularizer_coefficient        - regularizer constant (default 1.e-6)
679: . -tao_admm_spectral_penalty               - Constant for Augmented Lagrangian term (default 1.)
680: . -tao_admm_relaxation_parameter           - relaxation parameter for Z update (default 1.)
681: . -tao_admm_tolerance_update_factor        - ADMM dynamic tolerance update factor (default 1.e-12)
682: . -tao_admm_spectral_penalty_update_factor - ADMM spectral penalty update curvature safeguard value (default 0.2)
683: . -tao_admm_minimum_spectral_penalty       - Set ADMM minimum spectral penalty (default 0)
684: . -tao_admm_dual_update                    - Lagrangian dual update policy ("basic","adaptive","adaptive-relaxed") (default "basic")
685: - -tao_admm_regularizer_type               - ADMM regularizer update rule ("user","soft-threshold") (default "soft-threshold")

687:   Level: beginner

689: .seealso: `TaoADMMSetMisfitHessianChangeStatus()`, `TaoADMMSetRegHessianChangeStatus()`, `TaoADMMGetSpectralPenalty()`,
690:           `TaoADMMGetMisfitSubsolver()`, `TaoADMMGetRegularizationSubsolver()`, `TaoADMMSetConstraintVectorRHS()`,
691:           `TaoADMMSetMinimumSpectralPenalty()`, `TaoADMMSetRegularizerCoefficient()`, `TaoADMMGetRegularizerCoefficient()`,
692:           `TaoADMMSetRegularizerConstraintJacobian()`, `TaoADMMSetMisfitConstraintJacobian()`,
693:           `TaoADMMSetMisfitObjectiveAndGradientRoutine()`, `TaoADMMSetMisfitHessianRoutine()`,
694:           `TaoADMMSetRegularizerObjectiveAndGradientRoutine()`, `TaoADMMSetRegularizerHessianRoutine()`,
695:           `TaoGetADMMParentTao()`, `TaoADMMGetDualVector()`, `TaoADMMSetRegularizerType()`,
696:           `TaoADMMGetRegularizerType()`, `TaoADMMSetUpdateType()`, `TaoADMMGetUpdateType()`
697: M*/

699: PETSC_EXTERN PetscErrorCode TaoCreate_ADMM(Tao tao)
700: {
701:   TAO_ADMM *am;

703:   PetscFunctionBegin;
704:   PetscCall(PetscNew(&am));

706:   tao->ops->destroy        = TaoDestroy_ADMM;
707:   tao->ops->setup          = TaoSetUp_ADMM;
708:   tao->ops->setfromoptions = TaoSetFromOptions_ADMM;
709:   tao->ops->view           = TaoView_ADMM;
710:   tao->ops->solve          = TaoSolve_ADMM;

712:   tao->data           = (void *)am;
713:   am->l1epsilon       = 1e-6;
714:   am->lambda          = 1e-4;
715:   am->mu              = 1.;
716:   am->muold           = 0.;
717:   am->mueps           = PETSC_MACHINE_EPSILON;
718:   am->mumin           = 0.;
719:   am->orthval         = 0.2;
720:   am->T               = 2;
721:   am->parent          = tao;
722:   am->update          = TAO_ADMM_UPDATE_BASIC;
723:   am->regswitch       = TAO_ADMM_REGULARIZER_SOFT_THRESH;
724:   am->tol             = PETSC_SMALL;
725:   am->const_norm      = 0;
726:   am->resnorm         = 0;
727:   am->dualres         = 0;
728:   am->ops->regobjgrad = NULL;
729:   am->ops->reghess    = NULL;
730:   am->gamma           = 1;
731:   am->regobjgradP     = NULL;
732:   am->reghessP        = NULL;
733:   am->gatol_admm      = 1e-8;
734:   am->catol_admm      = 0;
735:   am->Hxchange        = PETSC_TRUE;
736:   am->Hzchange        = PETSC_TRUE;
737:   am->Hzbool          = PETSC_TRUE;
738:   am->Hxbool          = PETSC_TRUE;

740:   PetscCall(TaoCreate(PetscObjectComm((PetscObject)tao), &am->subsolverX));
741:   PetscCall(TaoSetOptionsPrefix(am->subsolverX, "misfit_"));
742:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)am->subsolverX, (PetscObject)tao, 1));
743:   PetscCall(TaoCreate(PetscObjectComm((PetscObject)tao), &am->subsolverZ));
744:   PetscCall(TaoSetOptionsPrefix(am->subsolverZ, "reg_"));
745:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)am->subsolverZ, (PetscObject)tao, 1));

747:   PetscCall(TaoSetType(am->subsolverX, TAONLS));
748:   PetscCall(TaoSetType(am->subsolverZ, TAONLS));
749:   PetscCall(PetscObjectCompose((PetscObject)am->subsolverX, "TaoGetADMMParentTao_ADMM", (PetscObject)tao));
750:   PetscCall(PetscObjectCompose((PetscObject)am->subsolverZ, "TaoGetADMMParentTao_ADMM", (PetscObject)tao));
751:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoADMMSetRegularizerType_C", TaoADMMSetRegularizerType_ADMM));
752:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoADMMGetRegularizerType_C", TaoADMMGetRegularizerType_ADMM));
753:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoADMMSetUpdateType_C", TaoADMMSetUpdateType_ADMM));
754:   PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoADMMGetUpdateType_C", TaoADMMGetUpdateType_ADMM));
755:   PetscFunctionReturn(PETSC_SUCCESS);
756: }

758: /*@
759:   TaoADMMSetMisfitHessianChangeStatus - Set boolean that determines  whether Hessian matrix of misfit subsolver changes with respect to input vector.

761:   Collective

763:   Input Parameters:
764: + tao - the Tao solver context.
765: - b   - the Hessian matrix change status boolean, `PETSC_FALSE`  when the Hessian matrix does not change, `PETSC_TRUE` otherwise.

767:   Level: advanced

769: .seealso: `TAOADMM`
770: @*/
771: PetscErrorCode TaoADMMSetMisfitHessianChangeStatus(Tao tao, PetscBool b)
772: {
773:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

775:   PetscFunctionBegin;
776:   am->Hxchange = b;
777:   PetscFunctionReturn(PETSC_SUCCESS);
778: }

780: /*@
781:   TaoADMMSetRegHessianChangeStatus - Set boolean that determines whether Hessian matrix of regularization subsolver changes with respect to input vector.

783:   Collective

785:   Input Parameters:
786: + tao - the `Tao` solver context
787: - b   - the Hessian matrix change status boolean, `PETSC_FALSE` when the Hessian matrix does not change, `PETSC_TRUE` otherwise.

789:   Level: advanced

791: .seealso: `TAOADMM`
792: @*/
793: PetscErrorCode TaoADMMSetRegHessianChangeStatus(Tao tao, PetscBool b)
794: {
795:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

797:   PetscFunctionBegin;
798:   am->Hzchange = b;
799:   PetscFunctionReturn(PETSC_SUCCESS);
800: }

802: /*@
803:   TaoADMMSetSpectralPenalty - Set the spectral penalty (mu) value

805:   Collective

807:   Input Parameters:
808: + tao - the `Tao` solver context
809: - mu  - spectral penalty

811:   Level: advanced

813: .seealso: `TaoADMMSetMinimumSpectralPenalty()`, `TAOADMM`
814: @*/
815: PetscErrorCode TaoADMMSetSpectralPenalty(Tao tao, PetscReal mu)
816: {
817:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

819:   PetscFunctionBegin;
820:   am->mu = mu;
821:   PetscFunctionReturn(PETSC_SUCCESS);
822: }

824: /*@
825:   TaoADMMGetSpectralPenalty - Get the spectral penalty (mu) value

827:   Collective

829:   Input Parameter:
830: . tao - the `Tao` solver context

832:   Output Parameter:
833: . mu - spectral penalty

835:   Level: advanced

837: .seealso: `TaoADMMSetMinimumSpectralPenalty()`, `TaoADMMSetSpectralPenalty()`, `TAOADMM`
838: @*/
839: PetscErrorCode TaoADMMGetSpectralPenalty(Tao tao, PetscReal *mu)
840: {
841:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

843:   PetscFunctionBegin;
845:   PetscAssertPointer(mu, 2);
846:   *mu = am->mu;
847:   PetscFunctionReturn(PETSC_SUCCESS);
848: }

850: /*@
851:   TaoADMMGetMisfitSubsolver - Get the pointer to the misfit subsolver inside `TAOADMM`

853:   Collective

855:   Input Parameter:
856: . tao - the `Tao` solver context

858:   Output Parameter:
859: . misfit - the `Tao` subsolver context

861:   Level: advanced

863: .seealso: `TAOADMM`, `Tao`
864: @*/
865: PetscErrorCode TaoADMMGetMisfitSubsolver(Tao tao, Tao *misfit)
866: {
867:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

869:   PetscFunctionBegin;
870:   *misfit = am->subsolverX;
871:   PetscFunctionReturn(PETSC_SUCCESS);
872: }

874: /*@
875:   TaoADMMGetRegularizationSubsolver - Get the pointer to the regularization subsolver inside `TAOADMM`

877:   Collective

879:   Input Parameter:
880: . tao - the `Tao` solver context

882:   Output Parameter:
883: . reg - the `Tao` subsolver context

885:   Level: advanced

887: .seealso: `TAOADMM`, `Tao`
888: @*/
889: PetscErrorCode TaoADMMGetRegularizationSubsolver(Tao tao, Tao *reg)
890: {
891:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

893:   PetscFunctionBegin;
894:   *reg = am->subsolverZ;
895:   PetscFunctionReturn(PETSC_SUCCESS);
896: }

898: /*@
899:   TaoADMMSetConstraintVectorRHS - Set the RHS constraint vector for `TAOADMM`

901:   Collective

903:   Input Parameters:
904: + tao - the `Tao` solver context
905: - c   - RHS vector

907:   Level: advanced

909: .seealso: `TAOADMM`
910: @*/
911: PetscErrorCode TaoADMMSetConstraintVectorRHS(Tao tao, Vec c)
912: {
913:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

915:   PetscFunctionBegin;
916:   am->constraint = c;
917:   PetscFunctionReturn(PETSC_SUCCESS);
918: }

920: /*@
921:   TaoADMMSetMinimumSpectralPenalty - Set the minimum value for the spectral penalty

923:   Collective

925:   Input Parameters:
926: + tao - the `Tao` solver context
927: - mu  - minimum spectral penalty value

929:   Level: advanced

931: .seealso: `TaoADMMGetSpectralPenalty()`, `TAOADMM`
932: @*/
933: PetscErrorCode TaoADMMSetMinimumSpectralPenalty(Tao tao, PetscReal mu)
934: {
935:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

937:   PetscFunctionBegin;
938:   am->mumin = mu;
939:   PetscFunctionReturn(PETSC_SUCCESS);
940: }

942: /*@
943:   TaoADMMSetRegularizerCoefficient - Set the regularization coefficient lambda for L1 norm regularization case

945:   Collective

947:   Input Parameters:
948: + tao    - the `Tao` solver context
949: - lambda - L1-norm regularizer coefficient

951:   Level: advanced

953: .seealso: `TaoADMMSetMisfitConstraintJacobian()`, `TaoADMMSetRegularizerConstraintJacobian()`, `TAOADMM`
954: @*/
955: PetscErrorCode TaoADMMSetRegularizerCoefficient(Tao tao, PetscReal lambda)
956: {
957:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

959:   PetscFunctionBegin;
960:   am->lambda = lambda;
961:   PetscFunctionReturn(PETSC_SUCCESS);
962: }

964: /*@
965:   TaoADMMGetRegularizerCoefficient - Get the regularization coefficient lambda for L1 norm regularization case

967:   Collective

969:   Input Parameter:
970: . tao - the `Tao` solver context

972:   Output Parameter:
973: . lambda - L1-norm regularizer coefficient

975:   Level: advanced

977: .seealso: `TaoADMMSetMisfitConstraintJacobian()`, `TaoADMMSetRegularizerConstraintJacobian()`, `TAOADMM`
978: @*/
979: PetscErrorCode TaoADMMGetRegularizerCoefficient(Tao tao, PetscReal *lambda)
980: {
981:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

983:   PetscFunctionBegin;
984:   *lambda = am->lambda;
985:   PetscFunctionReturn(PETSC_SUCCESS);
986: }

988: /*@C
989:   TaoADMMSetMisfitConstraintJacobian - Set the constraint matrix B for the `TAOADMM` algorithm. Matrix B constrains the z variable.

991:   Collective

993:   Input Parameters:
994: + tao  - the Tao solver context
995: . J    - user-created regularizer constraint Jacobian matrix
996: . Jpre - user-created regularizer Jacobian constraint matrix for constructing the preconditioner, often this is `J`
997: . func - function pointer for the regularizer constraint Jacobian update function
998: - ctx  - user context for the regularizer Hessian

1000:   Level: advanced

1002: .seealso: `TaoADMMSetRegularizerCoefficient()`, `TaoADMMSetRegularizerConstraintJacobian()`, `TAOADMM`
1003: @*/
1004: PetscErrorCode TaoADMMSetMisfitConstraintJacobian(Tao tao, Mat J, Mat Jpre, PetscErrorCode (*func)(Tao, Vec, Mat, Mat, void *), void *ctx)
1005: {
1006:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

1008:   PetscFunctionBegin;
1010:   if (J) {
1012:     PetscCheckSameComm(tao, 1, J, 2);
1013:   }
1014:   if (Jpre) {
1016:     PetscCheckSameComm(tao, 1, Jpre, 3);
1017:   }
1018:   if (ctx) am->misfitjacobianP = ctx;
1019:   if (func) am->ops->misfitjac = func;

1021:   if (J) {
1022:     PetscCall(PetscObjectReference((PetscObject)J));
1023:     PetscCall(MatDestroy(&am->JA));
1024:     am->JA = J;
1025:   }
1026:   if (Jpre) {
1027:     PetscCall(PetscObjectReference((PetscObject)Jpre));
1028:     PetscCall(MatDestroy(&am->JApre));
1029:     am->JApre = Jpre;
1030:   }
1031:   PetscFunctionReturn(PETSC_SUCCESS);
1032: }

1034: /*@C
1035:   TaoADMMSetRegularizerConstraintJacobian - Set the constraint matrix B for `TAOADMM` algorithm. Matrix B constraints z variable.

1037:   Collective

1039:   Input Parameters:
1040: + tao  - the `Tao` solver context
1041: . J    - user-created regularizer constraint Jacobian matrix
1042: . Jpre - user-created regularizer Jacobian constraint matrix for constructing the preconditioner, often this is `J`
1043: . func - function pointer for the regularizer constraint Jacobian update function
1044: - ctx  - user context for the regularizer Hessian

1046:   Level: advanced

1048: .seealso: `TaoADMMSetRegularizerCoefficient()`, `TaoADMMSetMisfitConstraintJacobian()`, `TAOADMM`
1049: @*/
1050: PetscErrorCode TaoADMMSetRegularizerConstraintJacobian(Tao tao, Mat J, Mat Jpre, PetscErrorCode (*func)(Tao, Vec, Mat, Mat, void *), void *ctx)
1051: {
1052:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

1054:   PetscFunctionBegin;
1056:   if (J) {
1058:     PetscCheckSameComm(tao, 1, J, 2);
1059:   }
1060:   if (Jpre) {
1062:     PetscCheckSameComm(tao, 1, Jpre, 3);
1063:   }
1064:   if (ctx) am->regjacobianP = ctx;
1065:   if (func) am->ops->regjac = func;

1067:   if (J) {
1068:     PetscCall(PetscObjectReference((PetscObject)J));
1069:     PetscCall(MatDestroy(&am->JB));
1070:     am->JB = J;
1071:   }
1072:   if (Jpre) {
1073:     PetscCall(PetscObjectReference((PetscObject)Jpre));
1074:     PetscCall(MatDestroy(&am->JBpre));
1075:     am->JBpre = Jpre;
1076:   }
1077:   PetscFunctionReturn(PETSC_SUCCESS);
1078: }

1080: /*@C
1081:   TaoADMMSetMisfitObjectiveAndGradientRoutine - Sets the user-defined misfit call-back function

1083:   Collective

1085:   Input Parameters:
1086: + tao  - the `Tao` context
1087: . func - function pointer for the misfit value and gradient evaluation
1088: - ctx  - user context for the misfit

1090:   Level: advanced

1092: .seealso: `TAOADMM`
1093: @*/
1094: PetscErrorCode TaoADMMSetMisfitObjectiveAndGradientRoutine(Tao tao, PetscErrorCode (*func)(Tao, Vec, PetscReal *, Vec, void *), void *ctx)
1095: {
1096:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

1098:   PetscFunctionBegin;
1100:   am->misfitobjgradP     = ctx;
1101:   am->ops->misfitobjgrad = func;
1102:   PetscFunctionReturn(PETSC_SUCCESS);
1103: }

1105: /*@C
1106:   TaoADMMSetMisfitHessianRoutine - Sets the user-defined misfit Hessian call-back
1107:   function into the algorithm, to be used for subsolverX.

1109:   Collective

1111:   Input Parameters:
1112: + tao  - the `Tao` context
1113: . H    - user-created matrix for the Hessian of the misfit term
1114: . Hpre - user-created matrix for the preconditioner of Hessian of the misfit term
1115: . func - function pointer for the misfit Hessian evaluation
1116: - ctx  - user context for the misfit Hessian

1118:   Level: advanced

1120: .seealso: `TAOADMM`
1121: @*/
1122: PetscErrorCode TaoADMMSetMisfitHessianRoutine(Tao tao, Mat H, Mat Hpre, PetscErrorCode (*func)(Tao, Vec, Mat, Mat, void *), void *ctx)
1123: {
1124:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

1126:   PetscFunctionBegin;
1128:   if (H) {
1130:     PetscCheckSameComm(tao, 1, H, 2);
1131:   }
1132:   if (Hpre) {
1134:     PetscCheckSameComm(tao, 1, Hpre, 3);
1135:   }
1136:   if (ctx) am->misfithessP = ctx;
1137:   if (func) am->ops->misfithess = func;
1138:   if (H) {
1139:     PetscCall(PetscObjectReference((PetscObject)H));
1140:     PetscCall(MatDestroy(&am->Hx));
1141:     am->Hx = H;
1142:   }
1143:   if (Hpre) {
1144:     PetscCall(PetscObjectReference((PetscObject)Hpre));
1145:     PetscCall(MatDestroy(&am->Hxpre));
1146:     am->Hxpre = Hpre;
1147:   }
1148:   PetscFunctionReturn(PETSC_SUCCESS);
1149: }

1151: /*@C
1152:   TaoADMMSetRegularizerObjectiveAndGradientRoutine - Sets the user-defined regularizer call-back function

1154:   Collective

1156:   Input Parameters:
1157: + tao  - the Tao context
1158: . func - function pointer for the regularizer value and gradient evaluation
1159: - ctx  - user context for the regularizer

1161:   Level: advanced

1163: .seealso: `TAOADMM`
1164: @*/
1165: PetscErrorCode TaoADMMSetRegularizerObjectiveAndGradientRoutine(Tao tao, PetscErrorCode (*func)(Tao, Vec, PetscReal *, Vec, void *), void *ctx)
1166: {
1167:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

1169:   PetscFunctionBegin;
1171:   am->regobjgradP     = ctx;
1172:   am->ops->regobjgrad = func;
1173:   PetscFunctionReturn(PETSC_SUCCESS);
1174: }

1176: /*@C
1177:   TaoADMMSetRegularizerHessianRoutine - Sets the user-defined regularizer Hessian call-back
1178:   function, to be used for subsolverZ.

1180:   Collective

1182:   Input Parameters:
1183: + tao  - the `Tao` context
1184: . H    - user-created matrix for the Hessian of the regularization term
1185: . Hpre - user-created matrix for the preconditioner of Hessian of the regularization term
1186: . func - function pointer for the regularizer Hessian evaluation
1187: - ctx  - user context for the regularizer Hessian

1189:   Level: advanced

1191: .seealso: `TAOADMM`
1192: @*/
1193: PetscErrorCode TaoADMMSetRegularizerHessianRoutine(Tao tao, Mat H, Mat Hpre, PetscErrorCode (*func)(Tao, Vec, Mat, Mat, void *), void *ctx)
1194: {
1195:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

1197:   PetscFunctionBegin;
1199:   if (H) {
1201:     PetscCheckSameComm(tao, 1, H, 2);
1202:   }
1203:   if (Hpre) {
1205:     PetscCheckSameComm(tao, 1, Hpre, 3);
1206:   }
1207:   if (ctx) am->reghessP = ctx;
1208:   if (func) am->ops->reghess = func;
1209:   if (H) {
1210:     PetscCall(PetscObjectReference((PetscObject)H));
1211:     PetscCall(MatDestroy(&am->Hz));
1212:     am->Hz = H;
1213:   }
1214:   if (Hpre) {
1215:     PetscCall(PetscObjectReference((PetscObject)Hpre));
1216:     PetscCall(MatDestroy(&am->Hzpre));
1217:     am->Hzpre = Hpre;
1218:   }
1219:   PetscFunctionReturn(PETSC_SUCCESS);
1220: }

1222: /*@
1223:   TaoGetADMMParentTao - Gets pointer to parent `TAOADMM`, used by inner subsolver.

1225:   Collective

1227:   Input Parameter:
1228: . tao - the `Tao` context

1230:   Output Parameter:
1231: . admm_tao - the parent `Tao` context

1233:   Level: advanced

1235: .seealso: `TAOADMM`
1236: @*/
1237: PetscErrorCode TaoGetADMMParentTao(Tao tao, Tao *admm_tao)
1238: {
1239:   PetscFunctionBegin;
1241:   PetscCall(PetscObjectQuery((PetscObject)tao, "TaoGetADMMParentTao_ADMM", (PetscObject *)admm_tao));
1242:   PetscFunctionReturn(PETSC_SUCCESS);
1243: }

1245: /*@
1246:   TaoADMMGetDualVector - Returns the dual vector associated with the current `TAOADMM` state

1248:   Not Collective

1250:   Input Parameter:
1251: . tao - the `Tao` context

1253:   Output Parameter:
1254: . Y - the current solution

1256:   Level: intermediate

1258: .seealso: `TAOADMM`
1259: @*/
1260: PetscErrorCode TaoADMMGetDualVector(Tao tao, Vec *Y)
1261: {
1262:   TAO_ADMM *am = (TAO_ADMM *)tao->data;

1264:   PetscFunctionBegin;
1266:   *Y = am->y;
1267:   PetscFunctionReturn(PETSC_SUCCESS);
1268: }

1270: /*@
1271:   TaoADMMSetRegularizerType - Set regularizer type for `TAOADMM` routine

1273:   Not Collective

1275:   Input Parameters:
1276: + tao  - the `Tao` context
1277: - type - regularizer type

1279:   Options Database Key:
1280: . -tao_admm_regularizer_type <admm_regularizer_user,admm_regularizer_soft_thresh> - select the regularizer

1282:   Level: intermediate

1284: .seealso: `TaoADMMGetRegularizerType()`, `TaoADMMRegularizerType`, `TAOADMM`
1285: @*/
1286: PetscErrorCode TaoADMMSetRegularizerType(Tao tao, TaoADMMRegularizerType type)
1287: {
1288:   PetscFunctionBegin;
1291:   PetscTryMethod(tao, "TaoADMMSetRegularizerType_C", (Tao, TaoADMMRegularizerType), (tao, type));
1292:   PetscFunctionReturn(PETSC_SUCCESS);
1293: }

1295: /*@
1296:   TaoADMMGetRegularizerType - Gets the type of regularizer routine for `TAOADMM`

1298:   Not Collective

1300:   Input Parameter:
1301: . tao - the `Tao` context

1303:   Output Parameter:
1304: . type - the type of regularizer

1306:   Level: intermediate

1308: .seealso: `TaoADMMSetRegularizerType()`, `TaoADMMRegularizerType`, `TAOADMM`
1309: @*/
1310: PetscErrorCode TaoADMMGetRegularizerType(Tao tao, TaoADMMRegularizerType *type)
1311: {
1312:   PetscFunctionBegin;
1314:   PetscUseMethod(tao, "TaoADMMGetRegularizerType_C", (Tao, TaoADMMRegularizerType *), (tao, type));
1315:   PetscFunctionReturn(PETSC_SUCCESS);
1316: }

1318: /*@
1319:   TaoADMMSetUpdateType - Set update routine for `TAOADMM` routine

1321:   Not Collective

1323:   Input Parameters:
1324: + tao  - the `Tao` context
1325: - type - spectral parameter update type

1327:   Level: intermediate

1329: .seealso: `TaoADMMGetUpdateType()`, `TaoADMMUpdateType`, `TAOADMM`
1330: @*/
1331: PetscErrorCode TaoADMMSetUpdateType(Tao tao, TaoADMMUpdateType type)
1332: {
1333:   PetscFunctionBegin;
1336:   PetscTryMethod(tao, "TaoADMMSetUpdateType_C", (Tao, TaoADMMUpdateType), (tao, type));
1337:   PetscFunctionReturn(PETSC_SUCCESS);
1338: }

1340: /*@
1341:   TaoADMMGetUpdateType - Gets the type of spectral penalty update routine for `TAOADMM`

1343:   Not Collective

1345:   Input Parameter:
1346: . tao - the `Tao` context

1348:   Output Parameter:
1349: . type - the type of spectral penalty update routine

1351:   Level: intermediate

1353: .seealso: `TaoADMMSetUpdateType()`, `TaoADMMUpdateType`, `TAOADMM`
1354: @*/
1355: PetscErrorCode TaoADMMGetUpdateType(Tao tao, TaoADMMUpdateType *type)
1356: {
1357:   PetscFunctionBegin;
1359:   PetscUseMethod(tao, "TaoADMMGetUpdateType_C", (Tao, TaoADMMUpdateType *), (tao, type));
1360:   PetscFunctionReturn(PETSC_SUCCESS);
1361: }