Actual source code: almm.c
1: #include <../src/tao/constrained/impls/almm/almm.h>
2: #include <petsctao.h>
3: #include <petsc/private/petscimpl.h>
4: #include <petsc/private/vecimpl.h>
6: static PetscErrorCode TaoALMMCombinePrimal_Private(Tao, Vec, Vec, Vec);
7: static PetscErrorCode TaoALMMCombineDual_Private(Tao, Vec, Vec, Vec);
8: static PetscErrorCode TaoALMMSplitPrimal_Private(Tao, Vec, Vec, Vec);
9: static PetscErrorCode TaoALMMComputeOptimalityNorms_Private(Tao);
10: static PetscErrorCode TaoALMMComputeAugLagAndGradient_Private(Tao);
11: static PetscErrorCode TaoALMMComputePHRLagAndGradient_Private(Tao);
13: static PetscErrorCode TaoSolve_ALMM(Tao tao)
14: {
15: TAO_ALMM *auglag = (TAO_ALMM *)tao->data;
16: TaoConvergedReason reason;
17: PetscReal updated;
19: PetscFunctionBegin;
20: /* reset initial multiplier/slack guess */
21: if (!tao->recycle) {
22: if (tao->ineq_constrained) {
23: PetscCall(VecZeroEntries(auglag->Ps));
24: PetscCall(TaoALMMCombinePrimal_Private(tao, auglag->Px, auglag->Ps, auglag->P));
25: PetscCall(VecSet(auglag->Yi, 0.0));
26: }
27: if (tao->eq_constrained) PetscCall(VecSet(auglag->Ye, 0.0));
28: }
30: /* compute initial nonlinear Lagrangian and its derivatives */
31: PetscCall((*auglag->sub_obj)(tao));
32: PetscCall(TaoALMMComputeOptimalityNorms_Private(tao));
33: /* print initial step and check convergence */
34: PetscCall(PetscInfo(tao, "Solving with %s formulation\n", TaoALMMTypes[auglag->type]));
35: PetscCall(TaoLogConvergenceHistory(tao, auglag->Lval, auglag->gnorm, auglag->cnorm, tao->ksp_its));
36: PetscCall(TaoMonitor(tao, tao->niter, auglag->fval, auglag->gnorm, auglag->cnorm, 0.0));
37: PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
38: /* set initial penalty factor and inner solver tolerance */
39: switch (auglag->type) {
40: case TAO_ALMM_CLASSIC:
41: auglag->mu = auglag->mu0;
42: break;
43: case TAO_ALMM_PHR:
44: auglag->cenorm = 0.0;
45: if (tao->eq_constrained) PetscCall(VecDot(auglag->Ce, auglag->Ce, &auglag->cenorm));
46: auglag->cinorm = 0.0;
47: if (tao->ineq_constrained) {
48: PetscCall(VecCopy(auglag->Ci, auglag->Ciwork));
49: PetscCall(VecScale(auglag->Ciwork, -1.0));
50: PetscCall(VecPointwiseMax(auglag->Ciwork, auglag->Cizero, auglag->Ciwork));
51: PetscCall(VecDot(auglag->Ciwork, auglag->Ciwork, &auglag->cinorm));
52: }
53: /* determine initial penalty factor based on the balance of constraint violation and objective function value */
54: if (PetscAbsReal(auglag->cenorm + auglag->cinorm) == 0.0) auglag->mu = 10.0;
55: else auglag->mu = PetscMax(1.e-6, PetscMin(10.0, 2.0 * PetscAbsReal(auglag->fval) / (auglag->cenorm + auglag->cinorm)));
56: break;
57: default:
58: break;
59: }
60: auglag->gtol = auglag->gtol0;
61: PetscCall(PetscInfo(tao, "Initial penalty: %.2g\n", (double)auglag->mu));
63: /* start aug-lag outer loop */
64: while (tao->reason == TAO_CONTINUE_ITERATING) {
65: ++tao->niter;
66: /* update subsolver tolerance */
67: PetscCall(PetscInfo(tao, "Subsolver tolerance: ||G|| <= %e\n", (double)auglag->gtol));
68: PetscCall(TaoSetTolerances(auglag->subsolver, auglag->gtol, 0.0, 0.0));
69: /* solve the bound-constrained or unconstrained subproblem */
70: PetscCall(VecCopy(auglag->P, auglag->subsolver->solution));
71: PetscCall(TaoSolve(auglag->subsolver));
72: PetscCall(VecCopy(auglag->subsolver->solution, auglag->P));
73: PetscCall(TaoGetConvergedReason(auglag->subsolver, &reason));
74: tao->ksp_its += auglag->subsolver->ksp_its;
75: if (reason != TAO_CONVERGED_GATOL) PetscCall(PetscInfo(tao, "Subsolver failed to converge, reason: %s\n", TaoConvergedReasons[reason]));
76: /* evaluate solution and test convergence */
77: PetscCall((*auglag->sub_obj)(tao));
78: PetscCall(TaoALMMComputeOptimalityNorms_Private(tao));
79: /* decide whether to update multipliers or not */
80: updated = 0.0;
81: if (auglag->cnorm <= auglag->ytol) {
82: PetscCall(PetscInfo(tao, "Multipliers updated: ||C|| <= %e\n", (double)auglag->ytol));
83: /* constraints are good, update multipliers and convergence tolerances */
84: if (tao->eq_constrained) {
85: PetscCall(VecAXPY(auglag->Ye, auglag->mu, auglag->Ce));
86: PetscCall(VecSet(auglag->Cework, auglag->ye_max));
87: PetscCall(VecPointwiseMin(auglag->Ye, auglag->Cework, auglag->Ye));
88: PetscCall(VecSet(auglag->Cework, auglag->ye_min));
89: PetscCall(VecPointwiseMax(auglag->Ye, auglag->Cework, auglag->Ye));
90: }
91: if (tao->ineq_constrained) {
92: PetscCall(VecAXPY(auglag->Yi, auglag->mu, auglag->Ci));
93: PetscCall(VecSet(auglag->Ciwork, auglag->yi_max));
94: PetscCall(VecPointwiseMin(auglag->Yi, auglag->Ciwork, auglag->Yi));
95: PetscCall(VecSet(auglag->Ciwork, auglag->yi_min));
96: PetscCall(VecPointwiseMax(auglag->Yi, auglag->Ciwork, auglag->Yi));
97: }
98: /* tolerances are updated only for non-PHR methods */
99: if (auglag->type != TAO_ALMM_PHR) {
100: auglag->ytol = PetscMax(tao->catol, auglag->ytol / PetscPowReal(auglag->mu, auglag->mu_pow_good));
101: auglag->gtol = PetscMax(tao->gatol, auglag->gtol / auglag->mu);
102: }
103: updated = 1.0;
104: } else {
105: /* constraints are bad, update penalty factor */
106: auglag->mu = PetscMin(auglag->mu_max, auglag->mu_fac * auglag->mu);
107: /* tolerances are reset only for non-PHR methods */
108: if (auglag->type != TAO_ALMM_PHR) {
109: auglag->ytol = PetscMax(tao->catol, 1.0 / PetscPowReal(auglag->mu, auglag->mu_pow_bad));
110: auglag->gtol = PetscMax(tao->gatol, 1.0 / auglag->mu);
111: }
112: PetscCall(PetscInfo(tao, "Penalty increased: mu = %.2g\n", (double)auglag->mu));
113: }
114: PetscCall(TaoLogConvergenceHistory(tao, auglag->fval, auglag->gnorm, auglag->cnorm, tao->ksp_its));
115: PetscCall(TaoMonitor(tao, tao->niter, auglag->fval, auglag->gnorm, auglag->cnorm, updated));
116: PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
117: }
118: PetscFunctionReturn(PETSC_SUCCESS);
119: }
121: static PetscErrorCode TaoView_ALMM(Tao tao, PetscViewer viewer)
122: {
123: TAO_ALMM *auglag = (TAO_ALMM *)tao->data;
124: PetscBool isascii;
126: PetscFunctionBegin;
127: PetscCall(PetscViewerASCIIPushTab(viewer));
128: PetscCall(TaoView(auglag->subsolver, viewer));
129: PetscCall(PetscViewerASCIIPopTab(viewer));
130: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
131: if (isascii) {
132: PetscCall(PetscViewerASCIIPushTab(viewer));
133: PetscCall(PetscViewerASCIIPrintf(viewer, "ALMM Formulation Type: %s\n", TaoALMMTypes[auglag->type]));
134: PetscCall(PetscViewerASCIIPopTab(viewer));
135: }
136: PetscFunctionReturn(PETSC_SUCCESS);
137: }
139: static PetscErrorCode TaoSetUp_ALMM(Tao tao)
140: {
141: TAO_ALMM *auglag = (TAO_ALMM *)tao->data;
142: VecType vec_type;
143: Vec SL, SU;
144: PetscBool is_cg = PETSC_FALSE, is_lmvm = PETSC_FALSE;
146: PetscFunctionBegin;
147: PetscCheck(!tao->ineq_doublesided, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_WRONGSTATE, "TAOALMM does not support double-sided inequality constraint definition. Please restructure your inequality constraint to fit the form c(x) >= 0.");
148: PetscCheck(tao->eq_constrained || tao->ineq_constrained, PetscObjectComm((PetscObject)tao), PETSC_ERR_ORDER, "Equality and/or inequality constraints must be defined before solver setup.");
149: PetscCall(TaoComputeVariableBounds(tao));
150: /* alias base vectors and create extras */
151: PetscCall(VecGetType(tao->solution, &vec_type));
152: auglag->Px = tao->solution;
153: if (!tao->gradient) { /* base gradient */
154: PetscCall(VecDuplicate(tao->solution, &tao->gradient));
155: }
156: auglag->LgradX = tao->gradient;
157: if (!auglag->Xwork) { /* opt var work vector */
158: PetscCall(VecDuplicate(tao->solution, &auglag->Xwork));
159: }
160: if (tao->eq_constrained) {
161: auglag->Ce = tao->constraints_equality;
162: auglag->Ae = tao->jacobian_equality;
163: if (!auglag->Ye) { /* equality multipliers */
164: PetscCall(VecDuplicate(auglag->Ce, &auglag->Ye));
165: }
166: if (!auglag->Cework) PetscCall(VecDuplicate(auglag->Ce, &auglag->Cework));
167: }
168: if (tao->ineq_constrained) {
169: auglag->Ci = tao->constraints_inequality;
170: auglag->Ai = tao->jacobian_inequality;
171: if (!auglag->Yi) { /* inequality multipliers */
172: PetscCall(VecDuplicate(auglag->Ci, &auglag->Yi));
173: }
174: if (!auglag->Ciwork) PetscCall(VecDuplicate(auglag->Ci, &auglag->Ciwork));
175: if (!auglag->Cizero) {
176: PetscCall(VecDuplicate(auglag->Ci, &auglag->Cizero));
177: PetscCall(VecZeroEntries(auglag->Cizero));
178: }
179: if (!auglag->Ps) { /* slack vars */
180: PetscCall(VecDuplicate(auglag->Ci, &auglag->Ps));
181: }
182: if (!auglag->LgradS) { /* slack component of Lagrangian gradient */
183: PetscCall(VecDuplicate(auglag->Ci, &auglag->LgradS));
184: }
185: /* create vector for combined primal space and the associated communication objects */
186: if (!auglag->P) {
187: PetscCall(PetscMalloc1(2, &auglag->Parr));
188: auglag->Parr[0] = auglag->Px;
189: auglag->Parr[1] = auglag->Ps;
190: PetscCall(VecConcatenate(2, auglag->Parr, &auglag->P, &auglag->Pis));
191: PetscCall(PetscMalloc1(2, &auglag->Pscatter));
192: PetscCall(VecScatterCreate(auglag->P, auglag->Pis[0], auglag->Px, NULL, &auglag->Pscatter[0]));
193: PetscCall(VecScatterCreate(auglag->P, auglag->Pis[1], auglag->Ps, NULL, &auglag->Pscatter[1]));
194: }
195: if (tao->eq_constrained) {
196: /* create vector for combined dual space and the associated communication objects */
197: if (!auglag->Y) {
198: PetscCall(PetscMalloc1(2, &auglag->Yarr));
199: auglag->Yarr[0] = auglag->Ye;
200: auglag->Yarr[1] = auglag->Yi;
201: PetscCall(VecConcatenate(2, auglag->Yarr, &auglag->Y, &auglag->Yis));
202: PetscCall(PetscMalloc1(2, &auglag->Yscatter));
203: PetscCall(VecScatterCreate(auglag->Y, auglag->Yis[0], auglag->Ye, NULL, &auglag->Yscatter[0]));
204: PetscCall(VecScatterCreate(auglag->Y, auglag->Yis[1], auglag->Yi, NULL, &auglag->Yscatter[1]));
205: }
206: if (!auglag->C) PetscCall(VecDuplicate(auglag->Y, &auglag->C));
207: } else {
208: if (!auglag->C) auglag->C = auglag->Ci;
209: if (!auglag->Y) auglag->Y = auglag->Yi;
210: }
211: } else {
212: if (!auglag->P) auglag->P = auglag->Px;
213: if (!auglag->G) auglag->G = auglag->LgradX;
214: if (!auglag->C) auglag->C = auglag->Ce;
215: if (!auglag->Y) auglag->Y = auglag->Ye;
216: }
217: /* create tao primal solution and gradient to interface with subsolver */
218: PetscCall(VecDuplicate(auglag->P, &auglag->Psub));
219: PetscCall(VecDuplicate(auglag->P, &auglag->G));
220: /* initialize parameters */
221: if (auglag->type == TAO_ALMM_PHR) {
222: auglag->mu_fac = 10.0;
223: auglag->yi_min = 0.0;
224: auglag->ytol0 = 0.5;
225: auglag->gtol0 = tao->gatol;
226: if (tao->gatol != tao->default_gatol && tao->catol != tao->default_catol) {
227: PetscCall(PetscInfo(tao, "TAOALMM with PHR: different gradient and constraint tolerances are not supported, setting catol = gatol\n"));
228: tao->catol = tao->gatol;
229: }
230: }
231: /* set the Lagrangian formulation type for the subsolver */
232: switch (auglag->type) {
233: case TAO_ALMM_CLASSIC:
234: auglag->sub_obj = TaoALMMComputeAugLagAndGradient_Private;
235: break;
236: case TAO_ALMM_PHR:
237: auglag->sub_obj = TaoALMMComputePHRLagAndGradient_Private;
238: break;
239: default:
240: break;
241: }
242: /* set up the subsolver */
243: PetscCall(TaoSetSolution(auglag->subsolver, auglag->Psub));
244: PetscCall(TaoSetObjective(auglag->subsolver, TaoALMMSubsolverObjective_Private, (void *)auglag));
245: PetscCall(TaoSetObjectiveAndGradient(auglag->subsolver, NULL, TaoALMMSubsolverObjectiveAndGradient_Private, (void *)auglag));
246: if (tao->bounded) {
247: /* make sure that the subsolver is a bound-constrained method */
248: PetscCall(PetscObjectTypeCompare((PetscObject)auglag->subsolver, TAOCG, &is_cg));
249: PetscCall(PetscObjectTypeCompare((PetscObject)auglag->subsolver, TAOLMVM, &is_lmvm));
250: if (is_cg) {
251: PetscCall(TaoSetType(auglag->subsolver, TAOBNCG));
252: PetscCall(PetscInfo(tao, "TAOCG detected for bound-constrained problem, switching to TAOBNCG.\n"));
253: }
254: if (is_lmvm) {
255: PetscCall(TaoSetType(auglag->subsolver, TAOBQNLS));
256: PetscCall(PetscInfo(tao, "TAOLMVM detected for bound-constrained problem, switching to TAOBQNLS.\n"));
257: }
258: /* create lower and upper bound clone vectors for subsolver */
259: if (!auglag->PL) PetscCall(VecDuplicate(auglag->P, &auglag->PL));
260: if (!auglag->PU) PetscCall(VecDuplicate(auglag->P, &auglag->PU));
261: if (tao->ineq_constrained) {
262: /* create lower and upper bounds for slack, set lower to 0 */
263: PetscCall(VecDuplicate(auglag->Ci, &SL));
264: PetscCall(VecSet(SL, 0.0));
265: PetscCall(VecDuplicate(auglag->Ci, &SU));
266: PetscCall(VecSet(SU, PETSC_INFINITY));
267: /* combine opt var bounds with slack bounds */
268: PetscCall(TaoALMMCombinePrimal_Private(tao, tao->XL, SL, auglag->PL));
269: PetscCall(TaoALMMCombinePrimal_Private(tao, tao->XU, SU, auglag->PU));
270: /* destroy work vectors */
271: PetscCall(VecDestroy(&SL));
272: PetscCall(VecDestroy(&SU));
273: } else {
274: /* no inequality constraints, just copy bounds into the subsolver */
275: PetscCall(VecCopy(tao->XL, auglag->PL));
276: PetscCall(VecCopy(tao->XU, auglag->PU));
277: }
278: PetscCall(TaoSetVariableBounds(auglag->subsolver, auglag->PL, auglag->PU));
279: } else {
280: /* CLASSIC's slack variable is bounded, so need to set bounds */
281: //TODO what happens for non-constrained ALMM CLASSIC?
282: if (auglag->type == TAO_ALMM_CLASSIC) {
283: if (tao->ineq_constrained) {
284: /* create lower and upper bound clone vectors for subsolver
285: * They should be NFINITY and INFINITY */
286: if (!auglag->PL) PetscCall(VecDuplicate(auglag->P, &auglag->PL));
287: if (!auglag->PU) PetscCall(VecDuplicate(auglag->P, &auglag->PU));
288: PetscCall(VecSet(auglag->PL, PETSC_NINFINITY));
289: PetscCall(VecSet(auglag->PU, PETSC_INFINITY));
290: /* create lower and upper bounds for slack, set lower to 0 */
291: PetscCall(VecDuplicate(auglag->Ci, &SL));
292: PetscCall(VecSet(SL, 0.0));
293: PetscCall(VecDuplicate(auglag->Ci, &SU));
294: PetscCall(VecSet(SU, PETSC_INFINITY));
295: /* PL, PU is already set. Only copy Slack variable parts */
296: PetscCall(VecScatterBegin(auglag->Pscatter[1], SL, auglag->PL, INSERT_VALUES, SCATTER_REVERSE));
297: PetscCall(VecScatterEnd(auglag->Pscatter[1], SL, auglag->PL, INSERT_VALUES, SCATTER_REVERSE));
298: PetscCall(VecScatterBegin(auglag->Pscatter[1], SU, auglag->PU, INSERT_VALUES, SCATTER_REVERSE));
299: PetscCall(VecScatterEnd(auglag->Pscatter[1], SU, auglag->PU, INSERT_VALUES, SCATTER_REVERSE));
300: /* destroy work vectors */
301: PetscCall(VecDestroy(&SL));
302: PetscCall(VecDestroy(&SU));
303: /* make sure that the subsolver is a bound-constrained method
304: * Unfortunately duplicate code */
305: PetscCall(PetscObjectTypeCompare((PetscObject)auglag->subsolver, TAOCG, &is_cg));
306: PetscCall(PetscObjectTypeCompare((PetscObject)auglag->subsolver, TAOLMVM, &is_lmvm));
307: if (is_cg) {
308: PetscCall(TaoSetType(auglag->subsolver, TAOBNCG));
309: PetscCall(PetscInfo(tao, "TAOCG detected for TAO_ALMM_CLASSIC, switching to TAOBNCG.\n"));
310: }
311: if (is_lmvm) {
312: PetscCall(TaoSetType(auglag->subsolver, TAOBQNLS));
313: PetscCall(PetscInfo(tao, "TAOLMVM detected for TAO_ALMM_CLASSIC, switching to TAOBQNLS.\n"));
314: }
315: PetscCall(TaoSetVariableBounds(auglag->subsolver, auglag->PL, auglag->PU));
316: }
317: }
318: }
319: PetscCall(TaoSetUp(auglag->subsolver));
320: PetscFunctionReturn(PETSC_SUCCESS);
321: }
323: static PetscErrorCode TaoDestroy_ALMM(Tao tao)
324: {
325: TAO_ALMM *auglag = (TAO_ALMM *)tao->data;
327: PetscFunctionBegin;
328: PetscCall(TaoDestroy(&auglag->subsolver));
329: PetscCall(VecDestroy(&auglag->Psub));
330: PetscCall(VecDestroy(&auglag->G));
331: if (tao->setupcalled) {
332: PetscCall(VecDestroy(&auglag->Xwork));
333: if (tao->eq_constrained) {
334: PetscCall(VecDestroy(&auglag->Ye)); /* equality multipliers */
335: PetscCall(VecDestroy(&auglag->Cework)); /* equality work vector */
336: }
337: if (tao->ineq_constrained) {
338: PetscCall(VecDestroy(&auglag->Ps)); /* slack vars */
339: PetscCall(PetscFree(auglag->Parr)); /* array of primal vectors */
340: PetscCall(VecDestroy(&auglag->LgradS)); /* slack grad */
341: PetscCall(VecDestroy(&auglag->Cizero)); /* zero vector for pointwise max */
342: PetscCall(VecDestroy(&auglag->Yi)); /* inequality multipliers */
343: PetscCall(VecDestroy(&auglag->Ciwork)); /* inequality work vector */
344: PetscCall(VecDestroy(&auglag->P)); /* combo primal solution */
345: PetscCall(ISDestroy(&auglag->Pis[0])); /* index set for X inside P */
346: PetscCall(ISDestroy(&auglag->Pis[1])); /* index set for S inside P */
347: PetscCall(PetscFree(auglag->Pis)); /* array of P index sets */
348: PetscCall(VecScatterDestroy(&auglag->Pscatter[0]));
349: PetscCall(VecScatterDestroy(&auglag->Pscatter[1]));
350: PetscCall(PetscFree(auglag->Pscatter));
351: if (tao->eq_constrained) {
352: PetscCall(VecDestroy(&auglag->Y)); /* combo multipliers */
353: PetscCall(PetscFree(auglag->Yarr)); /* array of dual vectors */
354: PetscCall(VecDestroy(&auglag->C)); /* combo constraints */
355: PetscCall(ISDestroy(&auglag->Yis[0])); /* index set for Ye inside Y */
356: PetscCall(ISDestroy(&auglag->Yis[1])); /* index set for Yi inside Y */
357: PetscCall(PetscFree(auglag->Yis));
358: PetscCall(VecScatterDestroy(&auglag->Yscatter[0]));
359: PetscCall(VecScatterDestroy(&auglag->Yscatter[1]));
360: PetscCall(PetscFree(auglag->Yscatter));
361: }
362: }
363: if (tao->bounded) {
364: PetscCall(VecDestroy(&auglag->PL)); /* lower bounds for subsolver */
365: PetscCall(VecDestroy(&auglag->PU)); /* upper bounds for subsolver */
366: } else {
367: if (auglag->type == TAO_ALMM_CLASSIC) {
368: PetscCall(VecDestroy(&auglag->PL)); /* lower bounds for subsolver */
369: PetscCall(VecDestroy(&auglag->PU)); /* upper bounds for subsolver */
370: }
371: }
372: }
373: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetType_C", NULL));
374: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMSetType_C", NULL));
375: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetSubsolver_C", NULL));
376: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMSetSubsolver_C", NULL));
377: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetMultipliers_C", NULL));
378: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMSetMultipliers_C", NULL));
379: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetPrimalIS_C", NULL));
380: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetDualIS_C", NULL));
381: PetscCall(PetscFree(tao->data));
382: PetscFunctionReturn(PETSC_SUCCESS);
383: }
385: static PetscErrorCode TaoSetFromOptions_ALMM(Tao tao, PetscOptionItems PetscOptionsObject)
386: {
387: TAO_ALMM *auglag = (TAO_ALMM *)tao->data;
389: PetscFunctionBegin;
390: PetscOptionsHeadBegin(PetscOptionsObject, "Augmented Lagrangian multiplier method solves problems with general constraints by converting them into a sequence of unconstrained problems.");
391: PetscCall(PetscOptionsReal("-tao_almm_mu_init", "initial penalty parameter", "", auglag->mu0, &auglag->mu0, NULL));
392: PetscCall(PetscOptionsReal("-tao_almm_mu_factor", "increase factor for the penalty parameter", "", auglag->mu_fac, &auglag->mu_fac, NULL));
393: PetscCall(PetscOptionsReal("-tao_almm_mu_power_good", "exponential for penalty parameter when multiplier update is accepted", "", auglag->mu_pow_good, &auglag->mu_pow_good, NULL));
394: PetscCall(PetscOptionsReal("-tao_almm_mu_power_bad", "exponential for penalty parameter when multiplier update is rejected", "", auglag->mu_pow_bad, &auglag->mu_pow_bad, NULL));
395: PetscCall(PetscOptionsReal("-tao_almm_mu_max", "maximum safeguard for penalty parameter updates", "", auglag->mu_max, &auglag->mu_max, NULL));
396: PetscCall(PetscOptionsReal("-tao_almm_ye_min", "minimum safeguard for equality multiplier updates", "", auglag->ye_min, &auglag->ye_min, NULL));
397: PetscCall(PetscOptionsReal("-tao_almm_ye_max", "maximum safeguard for equality multipliers updates", "", auglag->ye_max, &auglag->ye_max, NULL));
398: PetscCall(PetscOptionsReal("-tao_almm_yi_min", "minimum safeguard for inequality multipliers updates", "", auglag->yi_min, &auglag->yi_min, NULL));
399: PetscCall(PetscOptionsReal("-tao_almm_yi_max", "maximum safeguard for inequality multipliers updates", "", auglag->yi_max, &auglag->yi_max, NULL));
400: PetscCall(PetscOptionsEnum("-tao_almm_type", "augmented Lagrangian formulation type for the subproblem", "TaoALMMType", TaoALMMTypes, (PetscEnum)auglag->type, (PetscEnum *)&auglag->type, NULL));
401: PetscOptionsHeadEnd();
402: PetscCall(TaoSetOptionsPrefix(auglag->subsolver, ((PetscObject)tao)->prefix));
403: PetscCall(TaoAppendOptionsPrefix(auglag->subsolver, "tao_almm_subsolver_"));
404: PetscCall(TaoSetFromOptions(auglag->subsolver));
405: PetscFunctionReturn(PETSC_SUCCESS);
406: }
408: /*MC
409: TAOALMM - Augmented Lagrangian multiplier method for solving nonlinear optimization problems with general constraints.
411: Options Database Keys:
412: + -tao_almm_mu_init <real> - initial penalty parameter (default: 10.)
413: . -tao_almm_mu_factor <real> - increase factor for the penalty parameter (default: 100.)
414: . -tao_almm_mu_max <real> - maximum safeguard for penalty parameter updates (default: 1.e20)
415: . -tao_almm_mu_power_good <real> - exponential for penalty parameter when multiplier update is accepted (default: 0.9)
416: . -tao_almm_mu_power_bad <real> - exponential for penalty parameter when multiplier update is rejected (default: 0.1)
417: . -tao_almm_ye_min <real> - minimum safeguard for equality multiplier updates (default: -1.e20)
418: . -tao_almm_ye_max <real> - maximum safeguard for equality multiplier updates (default: 1.e20)
419: . -tao_almm_yi_min <real> - minimum safeguard for inequality multiplier updates (default: -1.e20)
420: . -tao_almm_yi_max <real> - maximum safeguard for inequality multiplier updates (default: 1.e20)
421: - -tao_almm_type <phr,classic> - change formulation of the augmented Lagrangian merit function for the subproblem (default: phr)
423: Level: beginner
425: Notes:
426: This method converts a constrained problem into a sequence of unconstrained problems via the augmented
427: Lagrangian merit function. Bound constraints are pushed down to the subproblem without any modifications.
429: Two formulations are offered for the subproblem: canonical Hestenes-Powell augmented Lagrangian with slack
430: variables for inequality constraints, and a slack-less Powell-Hestenes-Rockafellar (PHR) formulation utilizing a
431: pointwise max() penalty on inequality constraints. The canonical augmented Lagrangian formulation may converge
432: faster for smaller problems but is highly susceptible to poor step lengths in the subproblem due to the positivity
433: constraint on slack variables. PHR avoids this issue by eliminating the slack variables entirely, and is highly
434: desirable for problems with a large number of inequality constraints.
436: The subproblem is solved using a nested first-order TAO solver (default: `TAOBQNLS`). The user can retrieve a
437: pointer to the subsolver via `TaoALMMGetSubsolver()` or pass command line arguments to it using the
438: "-tao_almm_subsolver_" prefix. Currently, `TAOALMM` does not support second-order methods for the subproblem.
440: .vb
441: while unconverged
442: solve argmin_x L(x) s.t. l <= x <= u
443: if ||c|| <= y_tol
444: if ||c|| <= c_tol && ||Lgrad|| <= g_tol:
445: problem converged, return solution
446: else
447: constraints sufficiently improved
448: update multipliers and tighten tolerances
449: endif
450: else
451: constraints did not improve
452: update penalty and loosen tolerances
453: endif
454: endwhile
455: .ve
457: .seealso: `TAOALMM`, `Tao`, `TaoALMMGetType()`, `TaoALMMSetType()`, `TaoALMMSetSubsolver()`, `TaoALMMGetSubsolver()`,
458: `TaoALMMGetMultipliers()`, `TaoALMMSetMultipliers()`, `TaoALMMGetPrimalIS()`, `TaoALMMGetDualIS()`
459: M*/
460: PETSC_EXTERN PetscErrorCode TaoCreate_ALMM(Tao tao)
461: {
462: TAO_ALMM *auglag;
464: PetscFunctionBegin;
465: PetscCall(PetscNew(&auglag));
467: tao->ops->destroy = TaoDestroy_ALMM;
468: tao->ops->setup = TaoSetUp_ALMM;
469: tao->ops->setfromoptions = TaoSetFromOptions_ALMM;
470: tao->ops->view = TaoView_ALMM;
471: tao->ops->solve = TaoSolve_ALMM;
473: PetscCall(TaoParametersInitialize(tao));
474: PetscObjectParameterSetDefault(tao, gatol, 1.e-5);
475: PetscObjectParameterSetDefault(tao, grtol, 0.0);
476: PetscObjectParameterSetDefault(tao, gttol, 0.0);
477: PetscObjectParameterSetDefault(tao, catol, 1.e-5);
478: PetscObjectParameterSetDefault(tao, crtol, 0.0);
480: tao->data = (void *)auglag;
481: auglag->parent = tao;
482: auglag->mu0 = 10.0;
483: auglag->mu = auglag->mu0;
484: auglag->mu_fac = 10.0;
485: auglag->mu_max = PETSC_INFINITY;
486: auglag->mu_pow_good = 0.9;
487: auglag->mu_pow_bad = 0.1;
488: auglag->ye_min = PETSC_NINFINITY;
489: auglag->ye_max = PETSC_INFINITY;
490: auglag->yi_min = PETSC_NINFINITY;
491: auglag->yi_max = PETSC_INFINITY;
492: auglag->ytol0 = 1.0 / PetscPowReal(auglag->mu0, auglag->mu_pow_bad);
493: auglag->ytol = auglag->ytol0;
494: auglag->gtol0 = 1.0 / auglag->mu0;
495: auglag->gtol = auglag->gtol0;
497: auglag->sub_obj = TaoALMMComputeAugLagAndGradient_Private;
498: auglag->type = TAO_ALMM_PHR;
500: PetscCall(TaoCreate(PetscObjectComm((PetscObject)tao), &auglag->subsolver));
501: PetscCall(TaoSetType(auglag->subsolver, TAOBQNLS));
502: PetscCall(TaoSetTolerances(auglag->subsolver, auglag->gtol, 0.0, 0.0));
503: PetscCall(TaoSetMaximumIterations(auglag->subsolver, 1000));
504: PetscCall(TaoSetMaximumFunctionEvaluations(auglag->subsolver, 10000));
505: PetscCall(TaoSetFunctionLowerBound(auglag->subsolver, PETSC_NINFINITY));
506: PetscCall(PetscObjectIncrementTabLevel((PetscObject)auglag->subsolver, (PetscObject)tao, 1));
508: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetType_C", TaoALMMGetType_Private));
509: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMSetType_C", TaoALMMSetType_Private));
510: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetSubsolver_C", TaoALMMGetSubsolver_Private));
511: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMSetSubsolver_C", TaoALMMSetSubsolver_Private));
512: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetMultipliers_C", TaoALMMGetMultipliers_Private));
513: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMSetMultipliers_C", TaoALMMSetMultipliers_Private));
514: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetPrimalIS_C", TaoALMMGetPrimalIS_Private));
515: PetscCall(PetscObjectComposeFunction((PetscObject)tao, "TaoALMMGetDualIS_C", TaoALMMGetDualIS_Private));
516: PetscFunctionReturn(PETSC_SUCCESS);
517: }
519: static PetscErrorCode TaoALMMCombinePrimal_Private(Tao tao, Vec X, Vec S, Vec P)
520: {
521: TAO_ALMM *auglag = (TAO_ALMM *)tao->data;
523: PetscFunctionBegin;
524: if (tao->ineq_constrained) {
525: PetscCall(VecScatterBegin(auglag->Pscatter[0], X, P, INSERT_VALUES, SCATTER_REVERSE));
526: PetscCall(VecScatterEnd(auglag->Pscatter[0], X, P, INSERT_VALUES, SCATTER_REVERSE));
527: PetscCall(VecScatterBegin(auglag->Pscatter[1], S, P, INSERT_VALUES, SCATTER_REVERSE));
528: PetscCall(VecScatterEnd(auglag->Pscatter[1], S, P, INSERT_VALUES, SCATTER_REVERSE));
529: } else {
530: PetscCall(VecCopy(X, P));
531: }
532: PetscFunctionReturn(PETSC_SUCCESS);
533: }
535: static PetscErrorCode TaoALMMCombineDual_Private(Tao tao, Vec EQ, Vec IN, Vec Y)
536: {
537: TAO_ALMM *auglag = (TAO_ALMM *)tao->data;
539: PetscFunctionBegin;
540: if (tao->eq_constrained) {
541: if (tao->ineq_constrained) {
542: PetscCall(VecScatterBegin(auglag->Yscatter[0], EQ, Y, INSERT_VALUES, SCATTER_REVERSE));
543: PetscCall(VecScatterEnd(auglag->Yscatter[0], EQ, Y, INSERT_VALUES, SCATTER_REVERSE));
544: PetscCall(VecScatterBegin(auglag->Yscatter[1], IN, Y, INSERT_VALUES, SCATTER_REVERSE));
545: PetscCall(VecScatterEnd(auglag->Yscatter[1], IN, Y, INSERT_VALUES, SCATTER_REVERSE));
546: } else {
547: PetscCall(VecCopy(EQ, Y));
548: }
549: } else {
550: PetscCall(VecCopy(IN, Y));
551: }
552: PetscFunctionReturn(PETSC_SUCCESS);
553: }
555: static PetscErrorCode TaoALMMSplitPrimal_Private(Tao tao, Vec P, Vec X, Vec S)
556: {
557: TAO_ALMM *auglag = (TAO_ALMM *)tao->data;
559: PetscFunctionBegin;
560: if (tao->ineq_constrained) {
561: PetscCall(VecScatterBegin(auglag->Pscatter[0], P, X, INSERT_VALUES, SCATTER_FORWARD));
562: PetscCall(VecScatterEnd(auglag->Pscatter[0], P, X, INSERT_VALUES, SCATTER_FORWARD));
563: PetscCall(VecScatterBegin(auglag->Pscatter[1], P, S, INSERT_VALUES, SCATTER_FORWARD));
564: PetscCall(VecScatterEnd(auglag->Pscatter[1], P, S, INSERT_VALUES, SCATTER_FORWARD));
565: } else {
566: PetscCall(VecCopy(P, X));
567: }
568: PetscFunctionReturn(PETSC_SUCCESS);
569: }
571: /* this assumes that the latest constraints are stored in Ce and Ci, and also combined in C */
572: static PetscErrorCode TaoALMMComputeOptimalityNorms_Private(Tao tao)
573: {
574: TAO_ALMM *auglag = (TAO_ALMM *)tao->data;
576: PetscFunctionBegin;
577: /* if bounded, project the gradient */
578: if (tao->bounded) PetscCall(VecBoundGradientProjection(auglag->LgradX, auglag->Px, tao->XL, tao->XU, auglag->LgradX));
579: if (auglag->type == TAO_ALMM_PHR) {
580: PetscCall(VecNorm(auglag->LgradX, NORM_INFINITY, &auglag->gnorm));
581: auglag->cenorm = 0.0;
582: if (tao->eq_constrained) PetscCall(VecNorm(auglag->Ce, NORM_INFINITY, &auglag->cenorm));
583: auglag->cinorm = 0.0;
584: if (tao->ineq_constrained) {
585: PetscCall(VecCopy(auglag->Yi, auglag->Ciwork));
586: PetscCall(VecScale(auglag->Ciwork, -1.0 / auglag->mu));
587: PetscCall(VecPointwiseMax(auglag->Ciwork, auglag->Ci, auglag->Ciwork));
588: PetscCall(VecNorm(auglag->Ciwork, NORM_INFINITY, &auglag->cinorm));
589: }
590: auglag->cnorm_old = auglag->cnorm;
591: auglag->cnorm = PetscMax(auglag->cenorm, auglag->cinorm);
592: auglag->ytol = auglag->ytol0 * auglag->cnorm_old;
593: } else {
594: PetscCall(VecNorm(auglag->LgradX, NORM_2, &auglag->gnorm));
595: PetscCall(VecNorm(auglag->C, NORM_2, &auglag->cnorm));
596: }
597: PetscFunctionReturn(PETSC_SUCCESS);
598: }
600: static PetscErrorCode TaoALMMEvaluateIterate_Private(Tao tao)
601: {
602: TAO_ALMM *auglag = (TAO_ALMM *)tao->data;
604: PetscFunctionBegin;
605: /* split solution into primal and slack components */
606: PetscCall(TaoALMMSplitPrimal_Private(tao, auglag->P, auglag->Px, auglag->Ps));
608: /* compute f, df/dx and the constraints */
609: PetscCall(TaoComputeObjectiveAndGradient(tao, auglag->Px, &auglag->fval, auglag->LgradX));
610: if (tao->eq_constrained) {
611: PetscCall(TaoComputeEqualityConstraints(tao, auglag->Px, auglag->Ce));
612: PetscCall(TaoComputeJacobianEquality(tao, auglag->Px, auglag->Ae, auglag->Ae));
613: }
614: if (tao->ineq_constrained) {
615: PetscCall(TaoComputeInequalityConstraints(tao, auglag->Px, auglag->Ci));
616: PetscCall(TaoComputeJacobianInequality(tao, auglag->Px, auglag->Ai, auglag->Ai));
617: switch (auglag->type) {
618: case TAO_ALMM_CLASSIC:
619: /* classic formulation converts inequality to equality constraints via slack variables */
620: PetscCall(VecAXPY(auglag->Ci, -1.0, auglag->Ps));
621: break;
622: case TAO_ALMM_PHR:
623: /* PHR is based on Ci <= 0 while TAO defines Ci >= 0 so we hit it with a negative sign */
624: PetscCall(VecScale(auglag->Ci, -1.0));
625: PetscCall(MatScale(auglag->Ai, -1.0));
626: break;
627: default:
628: break;
629: }
630: }
631: /* combine constraints into one vector */
632: PetscCall(TaoALMMCombineDual_Private(tao, auglag->Ce, auglag->Ci, auglag->C));
633: PetscFunctionReturn(PETSC_SUCCESS);
634: }
636: /*
637: Lphr = f + 0.5*mu*[ (Ce + Ye/mu)^T (Ce + Ye/mu) + pmax(0, Ci + Yi/mu)^T pmax(0, Ci + Yi/mu)]
639: dLphr/dX = dF/dX + mu*[ (Ce + Ye/mu)^T Ae + pmax(0, Ci + Yi/mu)^T Ai]
641: dLphr/dS = 0
642: */
643: static PetscErrorCode TaoALMMComputePHRLagAndGradient_Private(Tao tao)
644: {
645: TAO_ALMM *auglag = (TAO_ALMM *)tao->data;
646: PetscReal eq_norm = 0.0, ineq_norm = 0.0;
648: PetscFunctionBegin;
649: PetscCall(TaoALMMEvaluateIterate_Private(tao));
650: if (tao->eq_constrained) {
651: /* Ce_work = mu*(Ce + Ye/mu) */
652: PetscCall(VecWAXPY(auglag->Cework, 1.0 / auglag->mu, auglag->Ye, auglag->Ce));
653: PetscCall(VecDot(auglag->Cework, auglag->Cework, &eq_norm)); /* contribution to scalar Lagrangian */
654: PetscCall(VecScale(auglag->Cework, auglag->mu));
655: /* dL/dX += mu*(Ce + Ye/mu)^T Ae */
656: PetscCall(MatMultTransposeAdd(auglag->Ae, auglag->Cework, auglag->LgradX, auglag->LgradX));
657: }
658: if (tao->ineq_constrained) {
659: /* Ci_work = mu * pmax(0, Ci + Yi/mu) where pmax() is pointwise max() */
660: PetscCall(VecWAXPY(auglag->Ciwork, 1.0 / auglag->mu, auglag->Yi, auglag->Ci));
661: PetscCall(VecPointwiseMax(auglag->Ciwork, auglag->Cizero, auglag->Ciwork));
662: PetscCall(VecDot(auglag->Ciwork, auglag->Ciwork, &ineq_norm)); /* contribution to scalar Lagrangian */
663: /* dL/dX += mu * pmax(0, Ci + Yi/mu)^T Ai */
664: PetscCall(VecScale(auglag->Ciwork, auglag->mu));
665: PetscCall(MatMultTransposeAdd(auglag->Ai, auglag->Ciwork, auglag->LgradX, auglag->LgradX));
666: /* dL/dS = 0 because there are no slacks in PHR */
667: PetscCall(VecZeroEntries(auglag->LgradS));
668: }
669: /* combine gradient together */
670: PetscCall(TaoALMMCombinePrimal_Private(tao, auglag->LgradX, auglag->LgradS, auglag->G));
671: /* compute L = f + 0.5 * mu * [(Ce + Ye/mu)^T (Ce + Ye/mu) + pmax(0, Ci + Yi/mu)^T pmax(0, Ci + Yi/mu)] */
672: auglag->Lval = auglag->fval + 0.5 * auglag->mu * (eq_norm + ineq_norm);
673: PetscFunctionReturn(PETSC_SUCCESS);
674: }
676: /*
677: Lc = F + Ye^TCe + Yi^T(Ci - S) + 0.5*mu*[Ce^TCe + (Ci - S)^T(Ci - S)]
679: dLc/dX = dF/dX + Ye^TAe + Yi^TAi + mu*[Ce^TAe + (Ci - S)^TAi]
681: dLc/dS = -[Yi + mu*(Ci - S)]
682: */
683: static PetscErrorCode TaoALMMComputeAugLagAndGradient_Private(Tao tao)
684: {
685: TAO_ALMM *auglag = (TAO_ALMM *)tao->data;
686: PetscReal yeTce = 0.0, yiTcims = 0.0, ceTce = 0.0, cimsTcims = 0.0;
688: PetscFunctionBegin;
689: PetscCall(TaoALMMEvaluateIterate_Private(tao));
690: if (tao->eq_constrained) {
691: /* compute scalar contributions */
692: PetscCall(VecDot(auglag->Ye, auglag->Ce, &yeTce));
693: PetscCall(VecDot(auglag->Ce, auglag->Ce, &ceTce));
694: /* dL/dX += ye^T Ae */
695: PetscCall(MatMultTransposeAdd(auglag->Ae, auglag->Ye, auglag->LgradX, auglag->LgradX));
696: /* dL/dX += mu * ce^T Ae */
697: PetscCall(MatMultTranspose(auglag->Ae, auglag->Ce, auglag->Xwork));
698: PetscCall(VecAXPY(auglag->LgradX, auglag->mu, auglag->Xwork));
699: }
700: if (tao->ineq_constrained) {
701: /* compute scalar contributions */
702: PetscCall(VecDot(auglag->Yi, auglag->Ci, &yiTcims));
703: PetscCall(VecDot(auglag->Ci, auglag->Ci, &cimsTcims));
704: /* dL/dX += yi^T Ai */
705: PetscCall(MatMultTransposeAdd(auglag->Ai, auglag->Yi, auglag->LgradX, auglag->LgradX));
706: /* dL/dX += mu * (ci - s)^T Ai */
707: PetscCall(MatMultTranspose(auglag->Ai, auglag->Ci, auglag->Xwork));
708: PetscCall(VecAXPY(auglag->LgradX, auglag->mu, auglag->Xwork));
709: /* dL/dS = -[yi + mu*(ci - s)] */
710: PetscCall(VecWAXPY(auglag->LgradS, auglag->mu, auglag->Ci, auglag->Yi));
711: PetscCall(VecScale(auglag->LgradS, -1.0));
712: }
713: /* combine gradient together */
714: PetscCall(TaoALMMCombinePrimal_Private(tao, auglag->LgradX, auglag->LgradS, auglag->G));
715: /* compute L = f + ye^T ce + yi^T (ci - s) + 0.5*mu*||ce||^2 + 0.5*mu*||ci - s||^2 */
716: auglag->Lval = auglag->fval + yeTce + yiTcims + 0.5 * auglag->mu * (ceTce + cimsTcims);
717: PetscFunctionReturn(PETSC_SUCCESS);
718: }
720: PetscErrorCode TaoALMMSubsolverObjective_Private(Tao tao, Vec P, PetscReal *Lval, PetscCtx ctx)
721: {
722: TAO_ALMM *auglag = (TAO_ALMM *)ctx;
724: PetscFunctionBegin;
725: PetscCall(VecCopy(P, auglag->P));
726: PetscCall((*auglag->sub_obj)(auglag->parent));
727: *Lval = auglag->Lval;
728: PetscFunctionReturn(PETSC_SUCCESS);
729: }
731: PetscErrorCode TaoALMMSubsolverObjectiveAndGradient_Private(Tao tao, Vec P, PetscReal *Lval, Vec G, PetscCtx ctx)
732: {
733: TAO_ALMM *auglag = (TAO_ALMM *)ctx;
735: PetscFunctionBegin;
736: PetscCall(VecCopy(P, auglag->P));
737: PetscCall((*auglag->sub_obj)(auglag->parent));
738: PetscCall(VecCopy(auglag->G, G));
739: *Lval = auglag->Lval;
740: PetscFunctionReturn(PETSC_SUCCESS);
741: }