Actual source code: pdipm.c
1: #include <../src/tao/constrained/impls/ipm/pdipm.h>
3: /*
4: TaoPDIPMEvaluateFunctionsAndJacobians - Evaluate the objective function f, gradient fx, constraints, and all the Jacobians at current vector
6: Collective
8: Input Parameter:
9: + tao - solver context
10: - x - vector at which all objects to be evaluated
12: Level: beginner
14: .seealso: `TAOPDIPM`, `TaoPDIPMUpdateConstraints()`, `TaoPDIPMSetUpBounds()`
15: */
16: static PetscErrorCode TaoPDIPMEvaluateFunctionsAndJacobians(Tao tao, Vec x)
17: {
18: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
20: PetscFunctionBegin;
21: /* Compute user objective function and gradient */
22: PetscCall(TaoComputeObjectiveAndGradient(tao, x, &pdipm->obj, tao->gradient));
24: /* Equality constraints and Jacobian */
25: if (pdipm->Ng) {
26: PetscCall(TaoComputeEqualityConstraints(tao, x, tao->constraints_equality));
27: PetscCall(TaoComputeJacobianEquality(tao, x, tao->jacobian_equality, tao->jacobian_equality_pre));
28: }
30: /* Inequality constraints and Jacobian */
31: if (pdipm->Nh) {
32: PetscCall(TaoComputeInequalityConstraints(tao, x, tao->constraints_inequality));
33: PetscCall(TaoComputeJacobianInequality(tao, x, tao->jacobian_inequality, tao->jacobian_inequality_pre));
34: }
35: PetscFunctionReturn(PETSC_SUCCESS);
36: }
38: /*
39: TaoPDIPMUpdateConstraints - Update the vectors ce and ci at x
41: Collective
43: Input Parameter:
44: + tao - Tao context
45: - x - vector at which constraints to be evaluated
47: Level: beginner
49: .seealso: `TAOPDIPM`, `TaoPDIPMEvaluateFunctionsAndJacobians()`
50: */
51: static PetscErrorCode TaoPDIPMUpdateConstraints(Tao tao, Vec x)
52: {
53: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
54: PetscInt i, offset, offset1, k, xstart;
55: PetscScalar *carr;
56: const PetscInt *ubptr, *lbptr, *bxptr, *fxptr;
57: const PetscScalar *xarr, *xuarr, *xlarr, *garr, *harr;
59: PetscFunctionBegin;
60: PetscCall(VecGetOwnershipRange(x, &xstart, NULL));
61: PetscCall(VecGetArrayRead(x, &xarr));
62: PetscCall(VecGetArrayRead(tao->XU, &xuarr));
63: PetscCall(VecGetArrayRead(tao->XL, &xlarr));
65: /* (1) Update ce vector */
66: PetscCall(VecGetArrayWrite(pdipm->ce, &carr));
68: if (pdipm->Ng) {
69: /* (1.a) Inserting updated g(x) */
70: PetscCall(VecGetArrayRead(tao->constraints_equality, &garr));
71: PetscCall(PetscArraycpy(carr, garr, pdipm->ng));
72: PetscCall(VecRestoreArrayRead(tao->constraints_equality, &garr));
73: }
75: /* (1.b) Update xfixed */
76: if (pdipm->Nxfixed) {
77: offset = pdipm->ng;
78: PetscCall(ISGetIndices(pdipm->isxfixed, &fxptr)); /* global indices in x */
79: for (k = 0; k < pdipm->nxfixed; k++) {
80: i = fxptr[k] - xstart;
81: carr[offset + k] = xarr[i] - xuarr[i];
82: }
83: }
84: PetscCall(VecRestoreArrayWrite(pdipm->ce, &carr));
86: /* (2) Update ci vector */
87: PetscCall(VecGetArrayWrite(pdipm->ci, &carr));
89: if (pdipm->Nh) {
90: /* (2.a) Inserting updated h(x) */
91: PetscCall(VecGetArrayRead(tao->constraints_inequality, &harr));
92: PetscCall(PetscArraycpy(carr, harr, pdipm->nh));
93: PetscCall(VecRestoreArrayRead(tao->constraints_inequality, &harr));
94: }
96: /* (2.b) Update xub */
97: offset = pdipm->nh;
98: if (pdipm->Nxub) {
99: PetscCall(ISGetIndices(pdipm->isxub, &ubptr));
100: for (k = 0; k < pdipm->nxub; k++) {
101: i = ubptr[k] - xstart;
102: carr[offset + k] = xuarr[i] - xarr[i];
103: }
104: }
106: if (pdipm->Nxlb) {
107: /* (2.c) Update xlb */
108: offset += pdipm->nxub;
109: PetscCall(ISGetIndices(pdipm->isxlb, &lbptr)); /* global indices in x */
110: for (k = 0; k < pdipm->nxlb; k++) {
111: i = lbptr[k] - xstart;
112: carr[offset + k] = xarr[i] - xlarr[i];
113: }
114: }
116: if (pdipm->Nxbox) {
117: /* (2.d) Update xbox */
118: offset += pdipm->nxlb;
119: offset1 = offset + pdipm->nxbox;
120: PetscCall(ISGetIndices(pdipm->isxbox, &bxptr)); /* global indices in x */
121: for (k = 0; k < pdipm->nxbox; k++) {
122: i = bxptr[k] - xstart; /* local indices in x */
123: carr[offset + k] = xuarr[i] - xarr[i];
124: carr[offset1 + k] = xarr[i] - xlarr[i];
125: }
126: }
127: PetscCall(VecRestoreArrayWrite(pdipm->ci, &carr));
129: /* Restoring Vectors */
130: PetscCall(VecRestoreArrayRead(x, &xarr));
131: PetscCall(VecRestoreArrayRead(tao->XU, &xuarr));
132: PetscCall(VecRestoreArrayRead(tao->XL, &xlarr));
133: PetscFunctionReturn(PETSC_SUCCESS);
134: }
136: /*
137: TaoPDIPMSetUpBounds - Create upper and lower bound vectors of x
139: Collective
141: Input Parameter:
142: . tao - holds pdipm and XL & XU
144: Level: beginner
146: .seealso: `TAOPDIPM`, `TaoPDIPMUpdateConstraints`
147: */
148: static PetscErrorCode TaoPDIPMSetUpBounds(Tao tao)
149: {
150: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
151: const PetscScalar *xl, *xu;
152: PetscInt n, *ixlb, *ixub, *ixfixed, *ixfree, *ixbox, i, low, high, idx;
153: MPI_Comm comm;
154: PetscInt recvbuf[5];
156: PetscFunctionBegin;
157: /* Creates upper and lower bounds vectors on x, if not created already */
158: PetscCheck((tao->XL && tao->XU) || tao->ops->computebounds, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_WRONGSTATE, "TAOPDIPM requires lower and upper variable bounds; set them with TaoSetVariableBounds() or TaoSetVariableBoundsRoutine()");
159: PetscCall(TaoComputeVariableBounds(tao));
161: PetscCall(VecGetLocalSize(tao->XL, &n));
162: PetscCall(PetscMalloc5(n, &ixlb, n, &ixub, n, &ixfree, n, &ixfixed, n, &ixbox));
164: PetscCall(VecGetOwnershipRange(tao->XL, &low, &high));
165: PetscCall(VecGetArrayRead(tao->XL, &xl));
166: PetscCall(VecGetArrayRead(tao->XU, &xu));
167: for (i = 0; i < n; i++) {
168: idx = low + i;
169: if ((PetscRealPart(xl[i]) > PETSC_NINFINITY) && (PetscRealPart(xu[i]) < PETSC_INFINITY)) {
170: if (PetscRealPart(xl[i]) == PetscRealPart(xu[i])) {
171: ixfixed[pdipm->nxfixed++] = idx;
172: } else ixbox[pdipm->nxbox++] = idx;
173: } else {
174: if ((PetscRealPart(xl[i]) > PETSC_NINFINITY) && (PetscRealPart(xu[i]) >= PETSC_INFINITY)) {
175: ixlb[pdipm->nxlb++] = idx;
176: } else if ((PetscRealPart(xl[i]) <= PETSC_NINFINITY) && (PetscRealPart(xu[i]) < PETSC_INFINITY)) {
177: ixub[pdipm->nxlb++] = idx;
178: } else ixfree[pdipm->nxfree++] = idx;
179: }
180: }
181: PetscCall(VecRestoreArrayRead(tao->XL, &xl));
182: PetscCall(VecRestoreArrayRead(tao->XU, &xu));
184: PetscCall(PetscObjectGetComm((PetscObject)tao, &comm));
185: recvbuf[0] = pdipm->nxlb;
186: recvbuf[1] = pdipm->nxub;
187: recvbuf[2] = pdipm->nxfixed;
188: recvbuf[3] = pdipm->nxbox;
189: recvbuf[4] = pdipm->nxfree;
191: PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, recvbuf, 5, MPIU_INT, MPI_SUM, comm));
192: pdipm->Nxlb = recvbuf[0];
193: pdipm->Nxub = recvbuf[1];
194: pdipm->Nxfixed = recvbuf[2];
195: pdipm->Nxbox = recvbuf[3];
196: pdipm->Nxfree = recvbuf[4];
198: if (pdipm->Nxlb) PetscCall(ISCreateGeneral(comm, pdipm->nxlb, ixlb, PETSC_COPY_VALUES, &pdipm->isxlb));
199: if (pdipm->Nxub) PetscCall(ISCreateGeneral(comm, pdipm->nxub, ixub, PETSC_COPY_VALUES, &pdipm->isxub));
200: if (pdipm->Nxfixed) PetscCall(ISCreateGeneral(comm, pdipm->nxfixed, ixfixed, PETSC_COPY_VALUES, &pdipm->isxfixed));
201: if (pdipm->Nxbox) PetscCall(ISCreateGeneral(comm, pdipm->nxbox, ixbox, PETSC_COPY_VALUES, &pdipm->isxbox));
202: if (pdipm->Nxfree) PetscCall(ISCreateGeneral(comm, pdipm->nxfree, ixfree, PETSC_COPY_VALUES, &pdipm->isxfree));
203: PetscCall(PetscFree5(ixlb, ixub, ixfixed, ixbox, ixfree));
204: PetscFunctionReturn(PETSC_SUCCESS);
205: }
207: /*
208: TaoPDIPMInitializeSolution - Initialize `TAOPDIPM` solution X = [x; lambdae; lambdai; z].
209: X consists of four subvectors in the order [x; lambdae; lambdai; z]. These
210: four subvectors need to be initialized and its values copied over to X. Instead
211: of copying, we use `VecPlaceArray()`/`VecResetArray()` functions to share the memory locations for
212: X and the subvectors
214: Collective
216: Input Parameter:
217: . tao - Tao context
219: Level: beginner
220: */
221: static PetscErrorCode TaoPDIPMInitializeSolution(Tao tao)
222: {
223: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
224: PetscScalar *Xarr, *z, *lambdai;
225: PetscInt i;
226: const PetscScalar *xarr, *h;
228: PetscFunctionBegin;
229: PetscCall(VecGetArrayWrite(pdipm->X, &Xarr));
231: /* Set Initialize X.x = tao->solution */
232: PetscCall(VecGetArrayRead(tao->solution, &xarr));
233: PetscCall(PetscArraycpy(Xarr, xarr, pdipm->nx));
234: PetscCall(VecRestoreArrayRead(tao->solution, &xarr));
236: /* Initialize X.lambdae = 0.0 */
237: if (pdipm->lambdae) PetscCall(VecSet(pdipm->lambdae, 0.0));
239: /* Initialize X.lambdai = push_init_lambdai, X.z = push_init_slack */
240: if (pdipm->Nci) {
241: PetscCall(VecSet(pdipm->lambdai, pdipm->push_init_lambdai));
242: PetscCall(VecSet(pdipm->z, pdipm->push_init_slack));
244: /* Additional modification for X.lambdai and X.z */
245: PetscCall(VecGetArrayWrite(pdipm->lambdai, &lambdai));
246: PetscCall(VecGetArrayWrite(pdipm->z, &z));
247: if (pdipm->Nh) {
248: PetscCall(VecGetArrayRead(tao->constraints_inequality, &h));
249: for (i = 0; i < pdipm->nh; i++) {
250: if (h[i] < -pdipm->push_init_slack) z[i] = -h[i];
251: if (pdipm->mu / z[i] > pdipm->push_init_lambdai) lambdai[i] = pdipm->mu / z[i];
252: }
253: PetscCall(VecRestoreArrayRead(tao->constraints_inequality, &h));
254: }
255: PetscCall(VecRestoreArrayWrite(pdipm->lambdai, &lambdai));
256: PetscCall(VecRestoreArrayWrite(pdipm->z, &z));
257: }
259: PetscCall(VecRestoreArrayWrite(pdipm->X, &Xarr));
260: PetscFunctionReturn(PETSC_SUCCESS);
261: }
263: /*
264: TaoSNESJacobian_PDIPM - Evaluate the Hessian matrix at X
266: Input Parameter:
267: snes - SNES context
268: X - KKT Vector
269: *ctx - pdipm context
271: Output Parameter:
272: J - Hessian matrix
273: Jpre - matrix to build the preconditioner from
274: */
275: static PetscErrorCode TaoSNESJacobian_PDIPM(SNES snes, Vec X, Mat J, Mat Jpre, PetscCtx ctx)
276: {
277: Tao tao = (Tao)ctx;
278: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
279: PetscInt i, row, cols[2], Jrstart, rjstart, nc, j;
280: const PetscInt *aj, *ranges, *Jranges, *rranges, *cranges;
281: const PetscScalar *Xarr, *aa;
282: PetscScalar vals[2];
283: PetscInt proc, nx_all, *nce_all = pdipm->nce_all;
285: PetscFunctionBegin;
286: PetscCall(MatGetOwnershipRanges(Jpre, &Jranges));
287: PetscCall(MatGetOwnershipRange(Jpre, &Jrstart, NULL));
288: PetscCall(MatGetOwnershipRangesColumn(tao->hessian, &rranges));
289: PetscCall(MatGetOwnershipRangesColumn(tao->hessian, &cranges));
291: PetscCall(VecGetArrayRead(X, &Xarr));
293: /* (1) insert Z and Ci to the 4th block of Jpre -- overwrite existing values */
294: if (pdipm->solve_symmetric_kkt) { /* 1 for eq 17 revised pdipm doc 0 for eq 18 (symmetric KKT) */
295: vals[0] = 1.0;
296: for (i = 0; i < pdipm->nci; i++) {
297: row = Jrstart + pdipm->off_z + i;
298: cols[0] = Jrstart + pdipm->off_lambdai + i;
299: cols[1] = row;
300: vals[1] = Xarr[pdipm->off_lambdai + i] / Xarr[pdipm->off_z + i];
301: PetscCall(MatSetValues(Jpre, 1, &row, 2, cols, vals, INSERT_VALUES));
302: }
303: } else {
304: for (i = 0; i < pdipm->nci; i++) {
305: row = Jrstart + pdipm->off_z + i;
306: cols[0] = Jrstart + pdipm->off_lambdai + i;
307: cols[1] = row;
308: vals[0] = Xarr[pdipm->off_z + i];
309: vals[1] = Xarr[pdipm->off_lambdai + i];
310: PetscCall(MatSetValues(Jpre, 1, &row, 2, cols, vals, INSERT_VALUES));
311: }
312: }
314: /* (2) insert 2nd row block of Jpre: [ grad g, 0, 0, 0] */
315: if (pdipm->Ng) {
316: PetscCall(MatGetOwnershipRange(tao->jacobian_equality, &rjstart, NULL));
317: for (i = 0; i < pdipm->ng; i++) {
318: row = Jrstart + pdipm->off_lambdae + i;
320: PetscCall(MatGetRow(tao->jacobian_equality, i + rjstart, &nc, &aj, &aa));
321: proc = 0;
322: for (j = 0; j < nc; j++) {
323: while (aj[j] >= cranges[proc + 1]) proc++;
324: cols[0] = aj[j] - cranges[proc] + Jranges[proc];
325: PetscCall(MatSetValue(Jpre, row, cols[0], aa[j], INSERT_VALUES));
326: }
327: PetscCall(MatRestoreRow(tao->jacobian_equality, i + rjstart, &nc, &aj, &aa));
328: if (pdipm->kkt_pd) {
329: /* add shift \delta_c */
330: PetscCall(MatSetValue(Jpre, row, row, -pdipm->deltac, INSERT_VALUES));
331: }
332: }
333: }
335: /* (3) insert 3rd row block of Jpre: [ -grad h, 0, deltac, I] */
336: if (pdipm->Nh) {
337: PetscCall(MatGetOwnershipRange(tao->jacobian_inequality, &rjstart, NULL));
338: for (i = 0; i < pdipm->nh; i++) {
339: row = Jrstart + pdipm->off_lambdai + i;
340: PetscCall(MatGetRow(tao->jacobian_inequality, i + rjstart, &nc, &aj, &aa));
341: proc = 0;
342: for (j = 0; j < nc; j++) {
343: while (aj[j] >= cranges[proc + 1]) proc++;
344: cols[0] = aj[j] - cranges[proc] + Jranges[proc];
345: PetscCall(MatSetValue(Jpre, row, cols[0], -aa[j], INSERT_VALUES));
346: }
347: PetscCall(MatRestoreRow(tao->jacobian_inequality, i + rjstart, &nc, &aj, &aa));
348: if (pdipm->kkt_pd) {
349: /* add shift \delta_c */
350: PetscCall(MatSetValue(Jpre, row, row, -pdipm->deltac, INSERT_VALUES));
351: }
352: }
353: }
355: /* (4) insert 1st row block of Jpre: [Wxx, grad g', -grad h', 0] */
356: if (pdipm->Ng) { /* grad g' */
357: PetscCall(MatTranspose(tao->jacobian_equality, MAT_REUSE_MATRIX, &pdipm->jac_equality_trans));
358: }
359: if (pdipm->Nh) { /* grad h' */
360: PetscCall(MatTranspose(tao->jacobian_inequality, MAT_REUSE_MATRIX, &pdipm->jac_inequality_trans));
361: }
363: PetscCall(VecPlaceArray(pdipm->x, Xarr));
364: PetscCall(TaoComputeHessian(tao, pdipm->x, tao->hessian, tao->hessian_pre));
365: PetscCall(VecResetArray(pdipm->x));
367: PetscCall(MatGetOwnershipRange(tao->hessian, &rjstart, NULL));
368: for (i = 0; i < pdipm->nx; i++) {
369: row = Jrstart + i;
371: /* insert Wxx = fxx + ... -- provided by user */
372: PetscCall(MatGetRow(tao->hessian, i + rjstart, &nc, &aj, &aa));
373: proc = 0;
374: for (j = 0; j < nc; j++) {
375: while (aj[j] >= cranges[proc + 1]) proc++;
376: cols[0] = aj[j] - cranges[proc] + Jranges[proc];
377: if (row == cols[0] && pdipm->kkt_pd) {
378: /* add shift deltaw to Wxx component */
379: PetscCall(MatSetValue(Jpre, row, cols[0], aa[j] + pdipm->deltaw, INSERT_VALUES));
380: } else {
381: PetscCall(MatSetValue(Jpre, row, cols[0], aa[j], INSERT_VALUES));
382: }
383: }
384: PetscCall(MatRestoreRow(tao->hessian, i + rjstart, &nc, &aj, &aa));
386: /* insert grad g' */
387: if (pdipm->ng) {
388: PetscCall(MatGetRow(pdipm->jac_equality_trans, i + rjstart, &nc, &aj, &aa));
389: PetscCall(MatGetOwnershipRanges(tao->jacobian_equality, &ranges));
390: proc = 0;
391: for (j = 0; j < nc; j++) {
392: /* find row ownership of */
393: while (aj[j] >= ranges[proc + 1]) proc++;
394: nx_all = rranges[proc + 1] - rranges[proc];
395: cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
396: PetscCall(MatSetValue(Jpre, row, cols[0], aa[j], INSERT_VALUES));
397: }
398: PetscCall(MatRestoreRow(pdipm->jac_equality_trans, i + rjstart, &nc, &aj, &aa));
399: }
401: /* insert -grad h' */
402: if (pdipm->nh) {
403: PetscCall(MatGetRow(pdipm->jac_inequality_trans, i + rjstart, &nc, &aj, &aa));
404: PetscCall(MatGetOwnershipRanges(tao->jacobian_inequality, &ranges));
405: proc = 0;
406: for (j = 0; j < nc; j++) {
407: /* find row ownership of */
408: while (aj[j] >= ranges[proc + 1]) proc++;
409: nx_all = rranges[proc + 1] - rranges[proc];
410: cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
411: PetscCall(MatSetValue(Jpre, row, cols[0], -aa[j], INSERT_VALUES));
412: }
413: PetscCall(MatRestoreRow(pdipm->jac_inequality_trans, i + rjstart, &nc, &aj, &aa));
414: }
415: }
416: PetscCall(VecRestoreArrayRead(X, &Xarr));
418: /* (6) assemble Jpre and J */
419: PetscCall(MatAssemblyBegin(Jpre, MAT_FINAL_ASSEMBLY));
420: PetscCall(MatAssemblyEnd(Jpre, MAT_FINAL_ASSEMBLY));
422: if (J != Jpre) {
423: PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
424: PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
425: }
426: PetscFunctionReturn(PETSC_SUCCESS);
427: }
429: /*
430: TaoSnesFunction_PDIPM - Evaluate KKT function at X
432: Input Parameter:
433: snes - SNES context
434: X - KKT Vector
435: *ctx - pdipm
437: Output Parameter:
438: F - Updated Lagrangian vector
439: */
440: static PetscErrorCode TaoSNESFunction_PDIPM(SNES snes, Vec X, Vec F, PetscCtx ctx)
441: {
442: Tao tao = (Tao)ctx;
443: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
444: PetscScalar *Farr;
445: Vec x, L1;
446: PetscInt i;
447: const PetscScalar *Xarr, *carr, *zarr, *larr;
449: PetscFunctionBegin;
450: PetscCall(VecSet(F, 0.0));
452: PetscCall(VecGetArrayRead(X, &Xarr));
453: PetscCall(VecGetArrayWrite(F, &Farr));
455: /* (0) Evaluate f, fx, gradG, gradH at X.x Note: pdipm->x is not changed below */
456: x = pdipm->x;
457: PetscCall(VecPlaceArray(x, Xarr));
458: PetscCall(TaoPDIPMEvaluateFunctionsAndJacobians(tao, x));
460: /* Update ce, ci, and Jci at X.x */
461: PetscCall(TaoPDIPMUpdateConstraints(tao, x));
462: PetscCall(VecResetArray(x));
464: /* (1) L1 = fx + (gradG'*DE + Jce_xfixed'*lambdae_xfixed) - (gradH'*DI + Jci_xb'*lambdai_xb) */
465: L1 = pdipm->x;
466: PetscCall(VecPlaceArray(L1, Farr)); /* L1 = 0.0 */
467: if (pdipm->Nci) {
468: if (pdipm->Nh) {
469: /* L1 += gradH'*DI. Note: tao->DI is not changed below */
470: PetscCall(VecPlaceArray(tao->DI, Xarr + pdipm->off_lambdai));
471: PetscCall(MatMultTransposeAdd(tao->jacobian_inequality, tao->DI, L1, L1));
472: PetscCall(VecResetArray(tao->DI));
473: }
475: /* L1 += Jci_xb'*lambdai_xb */
476: PetscCall(VecPlaceArray(pdipm->lambdai_xb, Xarr + pdipm->off_lambdai + pdipm->nh));
477: PetscCall(MatMultTransposeAdd(pdipm->Jci_xb, pdipm->lambdai_xb, L1, L1));
478: PetscCall(VecResetArray(pdipm->lambdai_xb));
480: /* L1 = - (gradH'*DI + Jci_xb'*lambdai_xb) */
481: PetscCall(VecScale(L1, -1.0));
482: }
484: /* L1 += fx */
485: PetscCall(VecAXPY(L1, 1.0, tao->gradient));
487: if (pdipm->Nce) {
488: if (pdipm->Ng) {
489: /* L1 += gradG'*DE. Note: tao->DE is not changed below */
490: PetscCall(VecPlaceArray(tao->DE, Xarr + pdipm->off_lambdae));
491: PetscCall(MatMultTransposeAdd(tao->jacobian_equality, tao->DE, L1, L1));
492: PetscCall(VecResetArray(tao->DE));
493: }
494: if (pdipm->Nxfixed) {
495: /* L1 += Jce_xfixed'*lambdae_xfixed */
496: PetscCall(VecPlaceArray(pdipm->lambdae_xfixed, Xarr + pdipm->off_lambdae + pdipm->ng));
497: PetscCall(MatMultTransposeAdd(pdipm->Jce_xfixed, pdipm->lambdae_xfixed, L1, L1));
498: PetscCall(VecResetArray(pdipm->lambdae_xfixed));
499: }
500: }
501: PetscCall(VecResetArray(L1));
503: /* (2) L2 = ce(x) */
504: if (pdipm->Nce) {
505: PetscCall(VecGetArrayRead(pdipm->ce, &carr));
506: for (i = 0; i < pdipm->nce; i++) Farr[pdipm->off_lambdae + i] = carr[i];
507: PetscCall(VecRestoreArrayRead(pdipm->ce, &carr));
508: }
510: if (pdipm->Nci) {
511: if (pdipm->solve_symmetric_kkt) {
512: /* (3) L3 = z - ci(x);
513: (4) L4 = Lambdai * e - mu/z *e */
514: PetscCall(VecGetArrayRead(pdipm->ci, &carr));
515: larr = Xarr + pdipm->off_lambdai;
516: zarr = Xarr + pdipm->off_z;
517: for (i = 0; i < pdipm->nci; i++) {
518: Farr[pdipm->off_lambdai + i] = zarr[i] - carr[i];
519: Farr[pdipm->off_z + i] = larr[i] - pdipm->mu / zarr[i];
520: }
521: PetscCall(VecRestoreArrayRead(pdipm->ci, &carr));
522: } else {
523: /* (3) L3 = z - ci(x);
524: (4) L4 = Z * Lambdai * e - mu * e */
525: PetscCall(VecGetArrayRead(pdipm->ci, &carr));
526: larr = Xarr + pdipm->off_lambdai;
527: zarr = Xarr + pdipm->off_z;
528: for (i = 0; i < pdipm->nci; i++) {
529: Farr[pdipm->off_lambdai + i] = zarr[i] - carr[i];
530: Farr[pdipm->off_z + i] = zarr[i] * larr[i] - pdipm->mu;
531: }
532: PetscCall(VecRestoreArrayRead(pdipm->ci, &carr));
533: }
534: }
536: PetscCall(VecRestoreArrayRead(X, &Xarr));
537: PetscCall(VecRestoreArrayWrite(F, &Farr));
538: PetscFunctionReturn(PETSC_SUCCESS);
539: }
541: /*
542: Evaluate F(X); then update tao->gnorm0, tao->step = mu,
543: tao->residual = norm2(F_x,F_z) and tao->cnorm = norm2(F_ce,F_ci).
544: */
545: static PetscErrorCode TaoSNESFunction_PDIPM_residual(SNES snes, Vec X, Vec F, PetscCtx ctx)
546: {
547: Tao tao = (Tao)ctx;
548: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
549: PetscScalar *Farr, *tmparr;
550: Vec L1;
551: PetscInt i;
552: PetscReal res[2], cnorm[2];
553: const PetscScalar *Xarr = NULL;
555: PetscFunctionBegin;
556: PetscCall(TaoSNESFunction_PDIPM(snes, X, F, (void *)tao));
557: PetscCall(VecGetArrayWrite(F, &Farr));
558: PetscCall(VecGetArrayRead(X, &Xarr));
560: /* compute res[0] = norm2(F_x) */
561: L1 = pdipm->x;
562: PetscCall(VecPlaceArray(L1, Farr));
563: PetscCall(VecNorm(L1, NORM_2, &res[0]));
564: PetscCall(VecResetArray(L1));
566: /* compute res[1] = norm2(F_z), cnorm[1] = norm2(F_ci) */
567: if (pdipm->z) {
568: if (pdipm->solve_symmetric_kkt) {
569: PetscCall(VecPlaceArray(pdipm->z, Farr + pdipm->off_z));
570: if (pdipm->Nci) {
571: PetscCall(VecGetArrayWrite(pdipm->z, &tmparr));
572: for (i = 0; i < pdipm->nci; i++) tmparr[i] *= Xarr[pdipm->off_z + i];
573: PetscCall(VecRestoreArrayWrite(pdipm->z, &tmparr));
574: }
576: PetscCall(VecNorm(pdipm->z, NORM_2, &res[1]));
578: if (pdipm->Nci) {
579: PetscCall(VecGetArrayWrite(pdipm->z, &tmparr));
580: for (i = 0; i < pdipm->nci; i++) tmparr[i] /= Xarr[pdipm->off_z + i];
581: PetscCall(VecRestoreArrayWrite(pdipm->z, &tmparr));
582: }
583: PetscCall(VecResetArray(pdipm->z));
584: } else { /* !solve_symmetric_kkt */
585: PetscCall(VecPlaceArray(pdipm->z, Farr + pdipm->off_z));
586: PetscCall(VecNorm(pdipm->z, NORM_2, &res[1]));
587: PetscCall(VecResetArray(pdipm->z));
588: }
590: PetscCall(VecPlaceArray(pdipm->ci, Farr + pdipm->off_lambdai));
591: PetscCall(VecNorm(pdipm->ci, NORM_2, &cnorm[1]));
592: PetscCall(VecResetArray(pdipm->ci));
593: } else {
594: res[1] = 0.0;
595: cnorm[1] = 0.0;
596: }
598: /* compute cnorm[0] = norm2(F_ce) */
599: if (pdipm->Nce) {
600: PetscCall(VecPlaceArray(pdipm->ce, Farr + pdipm->off_lambdae));
601: PetscCall(VecNorm(pdipm->ce, NORM_2, &cnorm[0]));
602: PetscCall(VecResetArray(pdipm->ce));
603: } else cnorm[0] = 0.0;
605: PetscCall(VecRestoreArrayWrite(F, &Farr));
606: PetscCall(VecRestoreArrayRead(X, &Xarr));
608: tao->gnorm0 = tao->residual;
609: tao->residual = PetscSqrtReal(res[0] * res[0] + res[1] * res[1]);
610: tao->cnorm = PetscSqrtReal(cnorm[0] * cnorm[0] + cnorm[1] * cnorm[1]);
611: tao->step = pdipm->mu;
612: PetscFunctionReturn(PETSC_SUCCESS);
613: }
615: /*
616: PCPostSetup_PDIPM -- called when the KKT matrix is Cholesky factored for the preconditioner. Checks the inertia of Cholesky factor of the KKT matrix.
617: If it does not match the numbers of prime and dual variables, add shifts to the KKT matrix.
618: */
619: static PetscErrorCode PCPostSetUp_PDIPM(PC pc)
620: {
621: Tao tao;
622: TAO_PDIPM *pdipm;
623: Vec X;
624: SNES snes;
625: KSP ksp;
626: Mat Factor;
627: PetscBool isCHOL;
628: PetscInt nneg, nzero, npos;
630: PetscFunctionBegin;
631: PetscCall(PCGetApplicationContext(pc, &tao));
632: pdipm = (TAO_PDIPM *)tao->data;
633: X = pdipm->X;
634: snes = pdipm->snes;
636: /* Get the inertia of Cholesky factor */
637: PetscCall(SNESGetKSP(snes, &ksp));
638: PetscCall(KSPGetPC(ksp, &pc));
639: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCCHOLESKY, &isCHOL));
640: if (!isCHOL) PetscFunctionReturn(PETSC_SUCCESS);
642: PetscCall(PCFactorGetMatrix(pc, &Factor));
643: PetscCall(MatGetInertia(Factor, &nneg, &nzero, &npos));
645: if (npos < pdipm->Nx + pdipm->Nci) {
646: pdipm->deltaw = PetscMax(pdipm->lastdeltaw / 3, 1.e-4 * PETSC_MACHINE_EPSILON);
647: PetscCall(PetscInfo(tao, "Test reduced deltaw=%g; previous MatInertia: nneg %" PetscInt_FMT ", nzero %" PetscInt_FMT ", npos %" PetscInt_FMT "(<%" PetscInt_FMT ")\n", (double)pdipm->deltaw, nneg, nzero, npos, pdipm->Nx + pdipm->Nci));
648: PetscCall(TaoSNESJacobian_PDIPM(snes, X, pdipm->K, pdipm->K, tao));
649: PetscCall(PCSetPostSetUp(pc, NULL));
650: PetscCall(PCSetUp(pc));
651: PetscCall(MatGetInertia(Factor, &nneg, &nzero, &npos));
653: if (npos < pdipm->Nx + pdipm->Nci) {
654: pdipm->deltaw = pdipm->lastdeltaw; /* in case reduction update does not help, this prevents that step from impacting increasing update */
655: while (npos < pdipm->Nx + pdipm->Nci && pdipm->deltaw <= 1. / PETSC_SMALL) { /* increase deltaw */
656: PetscCall(PetscInfo(tao, " deltaw=%g fails, MatInertia: nneg %" PetscInt_FMT ", nzero %" PetscInt_FMT ", npos %" PetscInt_FMT "(<%" PetscInt_FMT ")\n", (double)pdipm->deltaw, nneg, nzero, npos, pdipm->Nx + pdipm->Nci));
657: pdipm->deltaw = PetscMin(8 * pdipm->deltaw, PetscPowReal(10, 20));
658: PetscCall(TaoSNESJacobian_PDIPM(snes, X, pdipm->K, pdipm->K, tao));
659: PetscCall(PCSetUp(pc));
660: PetscCall(MatGetInertia(Factor, &nneg, &nzero, &npos));
661: }
663: PetscCheck(pdipm->deltaw < 1. / PETSC_SMALL, PetscObjectComm((PetscObject)tao), PETSC_ERR_CONV_FAILED, "Reached maximum delta w will not converge, try different initial x0");
665: PetscCall(PetscInfo(tao, "Updated deltaw %g\n", (double)pdipm->deltaw));
666: pdipm->lastdeltaw = pdipm->deltaw;
667: pdipm->deltaw = 0.0;
668: }
669: }
671: if (nzero) { /* Jacobian is singular */
672: if (pdipm->deltac == 0.0) {
673: pdipm->deltac = PETSC_SQRT_MACHINE_EPSILON;
674: } else {
675: pdipm->deltac = pdipm->deltac * PetscPowReal(pdipm->mu, .25);
676: }
677: PetscCall(PetscInfo(tao, "Updated deltac=%g, MatInertia: nneg %" PetscInt_FMT ", nzero %" PetscInt_FMT "(!=0), npos %" PetscInt_FMT "\n", (double)pdipm->deltac, nneg, nzero, npos));
678: PetscCall(TaoSNESJacobian_PDIPM(snes, X, pdipm->K, pdipm->K, tao));
679: PetscCall(PCSetPostSetUp(pc, NULL));
680: PetscCall(PCSetUp(pc));
681: PetscCall(MatGetInertia(Factor, &nneg, &nzero, &npos));
682: }
683: PetscCall(PCSetPostSetUp(pc, PCPostSetUp_PDIPM));
684: PetscFunctionReturn(PETSC_SUCCESS);
685: }
687: /*
688: SNESLineSearch_PDIPM - Custom line search used with PDIPM.
690: Collective
692: Notes:
693: This routine employs a simple backtracking line-search to keep
694: the slack variables (z) and inequality constraints Lagrange multipliers
695: (lambdai) positive, i.e., z,lambdai >=0. It does this by calculating scalars
696: alpha_p and alpha_d to keep z,lambdai non-negative. The decision (x), and the
697: slack variables are updated as X = X - alpha_d*dx. The constraint multipliers
698: are updated as Lambdai = Lambdai + alpha_p*dLambdai. The barrier parameter mu
699: is also updated as mu = mu + z'lambdai/Nci
700: */
701: static PetscErrorCode SNESLineSearch_PDIPM(SNESLineSearch linesearch, PetscCtx ctx)
702: {
703: Tao tao = (Tao)ctx;
704: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
705: SNES snes;
706: Vec X, F, Y;
707: PetscInt i, iter;
708: PetscReal alpha_p = 1.0, alpha_d = 1.0, alpha[2];
709: PetscScalar *Xarr, *z, *lambdai, dot, *taosolarr;
710: const PetscScalar *dXarr, *dz, *dlambdai;
712: PetscFunctionBegin;
713: PetscCall(SNESLineSearchGetSNES(linesearch, &snes));
714: PetscCall(SNESGetIterationNumber(snes, &iter));
716: PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_SUCCEEDED));
717: PetscCall(SNESLineSearchGetVecs(linesearch, &X, &F, &Y, NULL, NULL));
719: PetscCall(VecGetArrayWrite(X, &Xarr));
720: PetscCall(VecGetArrayRead(Y, &dXarr));
721: z = Xarr + pdipm->off_z;
722: dz = dXarr + pdipm->off_z;
723: for (i = 0; i < pdipm->nci; i++) {
724: if (z[i] - dz[i] < 0.0) alpha_p = PetscMin(alpha_p, 0.9999 * z[i] / dz[i]);
725: }
727: lambdai = Xarr + pdipm->off_lambdai;
728: dlambdai = dXarr + pdipm->off_lambdai;
730: for (i = 0; i < pdipm->nci; i++) {
731: if (lambdai[i] - dlambdai[i] < 0.0) alpha_d = PetscMin(0.9999 * lambdai[i] / dlambdai[i], alpha_d);
732: }
734: alpha[0] = alpha_p;
735: alpha[1] = alpha_d;
736: PetscCall(VecRestoreArrayRead(Y, &dXarr));
737: PetscCall(VecRestoreArrayWrite(X, &Xarr));
739: /* alpha = min(alpha) over all processes */
740: PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, alpha, 2, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)tao)));
742: alpha_p = alpha[0];
743: alpha_d = alpha[1];
745: /* X = X - alpha * Y */
746: PetscCall(VecGetArrayWrite(X, &Xarr));
747: PetscCall(VecGetArrayRead(Y, &dXarr));
748: for (i = 0; i < pdipm->nx; i++) Xarr[i] -= alpha_p * dXarr[i];
749: for (i = 0; i < pdipm->nce; i++) Xarr[i + pdipm->off_lambdae] -= alpha_d * dXarr[i + pdipm->off_lambdae];
751: for (i = 0; i < pdipm->nci; i++) {
752: Xarr[i + pdipm->off_lambdai] -= alpha_d * dXarr[i + pdipm->off_lambdai];
753: Xarr[i + pdipm->off_z] -= alpha_p * dXarr[i + pdipm->off_z];
754: }
755: PetscCall(VecGetArrayWrite(tao->solution, &taosolarr));
756: PetscCall(PetscArraycpy(taosolarr, Xarr, pdipm->nx));
757: PetscCall(VecRestoreArrayWrite(tao->solution, &taosolarr));
759: PetscCall(VecRestoreArrayWrite(X, &Xarr));
760: PetscCall(VecRestoreArrayRead(Y, &dXarr));
762: /* Update mu = mu_update_factor * dot(z,lambdai)/pdipm->nci at updated X */
763: if (pdipm->z) PetscCall(VecDot(pdipm->z, pdipm->lambdai, &dot));
764: else dot = 0.0;
766: /* if (PetscAbsReal(pdipm->gradL) < 0.9*pdipm->mu) */
767: pdipm->mu = pdipm->Nci ? pdipm->mu_update_factor * dot / pdipm->Nci : 0.;
769: /* Update F; get tao->residual and tao->cnorm */
770: PetscCall(TaoSNESFunction_PDIPM_residual(snes, X, F, (void *)tao));
772: tao->niter++;
773: PetscCall(TaoLogConvergenceHistory(tao, pdipm->obj, tao->residual, tao->cnorm, tao->niter));
774: PetscCall(TaoMonitor(tao, tao->niter, pdipm->obj, tao->residual, tao->cnorm, pdipm->mu));
776: PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
777: if (tao->reason) PetscCall(SNESSetConvergedReason(snes, SNES_CONVERGED_FNORM_ABS));
778: PetscFunctionReturn(PETSC_SUCCESS);
779: }
781: static PetscErrorCode TaoSolve_PDIPM(Tao tao)
782: {
783: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
784: SNESLineSearch linesearch; /* SNESLineSearch context */
785: Vec dummy;
787: PetscFunctionBegin;
788: PetscCheck(tao->constraints_equality || tao->constraints_inequality, PetscObjectComm((PetscObject)tao), PETSC_ERR_ARG_NULL, "Equality and inequality constraints are not set. Either set them or switch to a different algorithm");
790: /* Initialize all variables */
791: PetscCall(TaoPDIPMInitializeSolution(tao));
793: /* Set linesearch */
794: PetscCall(SNESGetLineSearch(pdipm->snes, &linesearch));
795: PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHSHELL));
796: PetscCall(SNESLineSearchShellSetApply(linesearch, SNESLineSearch_PDIPM, tao));
797: PetscCall(SNESLineSearchSetFromOptions(linesearch));
799: tao->reason = TAO_CONTINUE_ITERATING;
801: /* -tao_monitor for iteration 0 and check convergence */
802: PetscCall(VecDuplicate(pdipm->X, &dummy));
803: PetscCall(TaoSNESFunction_PDIPM_residual(pdipm->snes, pdipm->X, dummy, (void *)tao));
805: PetscCall(TaoLogConvergenceHistory(tao, pdipm->obj, tao->residual, tao->cnorm, tao->niter));
806: PetscCall(TaoMonitor(tao, tao->niter, pdipm->obj, tao->residual, tao->cnorm, pdipm->mu));
807: PetscCall(VecDestroy(&dummy));
808: PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
809: if (tao->reason) PetscCall(SNESSetConvergedReason(pdipm->snes, SNES_CONVERGED_FNORM_ABS));
811: while (tao->reason == TAO_CONTINUE_ITERATING) {
812: SNESConvergedReason reason;
813: PetscCall(SNESSolve(pdipm->snes, NULL, pdipm->X));
815: /* Check SNES convergence */
816: PetscCall(SNESGetConvergedReason(pdipm->snes, &reason));
817: if (reason < 0) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)pdipm->snes), "SNES solve did not converged due to reason %s\n", SNESConvergedReasons[reason]));
819: /* Check TAO convergence */
820: PetscCheck(!PetscIsInfOrNanReal(pdipm->obj), PETSC_COMM_SELF, PETSC_ERR_SUP, "User-provided compute function generated infinity or NaN");
821: }
822: PetscFunctionReturn(PETSC_SUCCESS);
823: }
825: static PetscErrorCode TaoView_PDIPM(Tao tao, PetscViewer viewer)
826: {
827: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
829: PetscFunctionBegin;
830: tao->constrained = PETSC_TRUE;
831: PetscCall(PetscViewerASCIIPushTab(viewer));
832: PetscCall(PetscViewerASCIIPrintf(viewer, "Number of prime=%" PetscInt_FMT ", Number of dual=%" PetscInt_FMT "\n", pdipm->Nx + pdipm->Nci, pdipm->Nce + pdipm->Nci));
833: if (pdipm->kkt_pd) PetscCall(PetscViewerASCIIPrintf(viewer, "KKT shifts deltaw=%g, deltac=%g\n", (double)pdipm->deltaw, (double)pdipm->deltac));
834: PetscCall(PetscViewerASCIIPopTab(viewer));
835: PetscFunctionReturn(PETSC_SUCCESS);
836: }
838: static PetscErrorCode TaoSetup_PDIPM(Tao tao)
839: {
840: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
841: MPI_Comm comm;
842: PetscMPIInt size;
843: PetscInt row, col, Jcrstart, Jcrend, k, tmp, nc, proc, *nh_all, *ng_all;
844: PetscInt offset, *xa, *xb, i, j, rstart, rend;
845: PetscScalar one = 1.0, neg_one = -1.0;
846: const PetscInt *cols, *rranges, *cranges, *aj, *ranges;
847: const PetscScalar *aa, *Xarr;
848: Mat J;
849: Mat Jce_xfixed_trans, Jci_xb_trans;
850: PetscInt *dnz, *onz, rjstart, nx_all, *nce_all, *Jranges, cols1[2];
852: PetscFunctionBegin;
853: PetscCall(PetscObjectGetComm((PetscObject)tao, &comm));
854: PetscCallMPI(MPI_Comm_size(comm, &size));
856: /* (1) Setup Bounds and create Tao vectors */
857: PetscCall(TaoPDIPMSetUpBounds(tao));
859: if (!tao->gradient) {
860: PetscCall(VecDuplicate(tao->solution, &tao->gradient));
861: PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));
862: }
864: /* (2) Get sizes */
865: /* Size of vector x - This is set by TaoSetSolution */
866: PetscCall(VecGetSize(tao->solution, &pdipm->Nx));
867: PetscCall(VecGetLocalSize(tao->solution, &pdipm->nx));
869: /* Size of equality constraints and vectors */
870: if (tao->constraints_equality) {
871: PetscCall(VecGetSize(tao->constraints_equality, &pdipm->Ng));
872: PetscCall(VecGetLocalSize(tao->constraints_equality, &pdipm->ng));
873: } else {
874: pdipm->ng = pdipm->Ng = 0;
875: }
877: pdipm->nce = pdipm->ng + pdipm->nxfixed;
878: pdipm->Nce = pdipm->Ng + pdipm->Nxfixed;
880: /* Size of inequality constraints and vectors */
881: if (tao->constraints_inequality) {
882: PetscCall(VecGetSize(tao->constraints_inequality, &pdipm->Nh));
883: PetscCall(VecGetLocalSize(tao->constraints_inequality, &pdipm->nh));
884: } else {
885: pdipm->nh = pdipm->Nh = 0;
886: }
888: pdipm->nci = pdipm->nh + pdipm->nxlb + pdipm->nxub + 2 * pdipm->nxbox;
889: pdipm->Nci = pdipm->Nh + pdipm->Nxlb + pdipm->Nxub + 2 * pdipm->Nxbox;
891: /* Full size of the KKT system to be solved */
892: pdipm->n = pdipm->nx + pdipm->nce + 2 * pdipm->nci;
893: pdipm->N = pdipm->Nx + pdipm->Nce + 2 * pdipm->Nci;
895: /* (3) Offsets for subvectors */
896: pdipm->off_lambdae = pdipm->nx;
897: pdipm->off_lambdai = pdipm->off_lambdae + pdipm->nce;
898: pdipm->off_z = pdipm->off_lambdai + pdipm->nci;
900: /* (4) Create vectors and subvectors */
901: /* Ce and Ci vectors */
902: PetscCall(VecCreate(comm, &pdipm->ce));
903: PetscCall(VecSetSizes(pdipm->ce, pdipm->nce, pdipm->Nce));
904: PetscCall(VecSetFromOptions(pdipm->ce));
906: PetscCall(VecCreate(comm, &pdipm->ci));
907: PetscCall(VecSetSizes(pdipm->ci, pdipm->nci, pdipm->Nci));
908: PetscCall(VecSetFromOptions(pdipm->ci));
910: /* X=[x; lambdae; lambdai; z] for the big KKT system */
911: PetscCall(VecCreate(comm, &pdipm->X));
912: PetscCall(VecSetSizes(pdipm->X, pdipm->n, pdipm->N));
913: PetscCall(VecSetFromOptions(pdipm->X));
915: /* Subvectors; they share local arrays with X */
916: PetscCall(VecGetArrayRead(pdipm->X, &Xarr));
917: /* x shares local array with X.x */
918: if (pdipm->Nx) PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nx, pdipm->Nx, Xarr, &pdipm->x));
920: /* lambdae shares local array with X.lambdae */
921: if (pdipm->Nce) PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nce, pdipm->Nce, Xarr + pdipm->off_lambdae, &pdipm->lambdae));
923: /* tao->DE shares local array with X.lambdae_g */
924: if (pdipm->Ng) {
925: PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->ng, pdipm->Ng, Xarr + pdipm->off_lambdae, &tao->DE));
927: PetscCall(VecCreate(comm, &pdipm->lambdae_xfixed));
928: PetscCall(VecSetSizes(pdipm->lambdae_xfixed, pdipm->nxfixed, PETSC_DECIDE));
929: PetscCall(VecSetFromOptions(pdipm->lambdae_xfixed));
930: }
932: if (pdipm->Nci) {
933: /* lambdai shares local array with X.lambdai */
934: PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nci, pdipm->Nci, Xarr + pdipm->off_lambdai, &pdipm->lambdai));
936: /* z for slack variables; it shares local array with X.z */
937: PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nci, pdipm->Nci, Xarr + pdipm->off_z, &pdipm->z));
938: }
940: /* tao->DI which shares local array with X.lambdai_h */
941: if (pdipm->Nh) PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nh, pdipm->Nh, Xarr + pdipm->off_lambdai, &tao->DI));
942: PetscCall(VecCreate(comm, &pdipm->lambdai_xb));
943: PetscCall(VecSetSizes(pdipm->lambdai_xb, pdipm->nci - pdipm->nh, PETSC_DECIDE));
944: PetscCall(VecSetFromOptions(pdipm->lambdai_xb));
946: PetscCall(VecRestoreArrayRead(pdipm->X, &Xarr));
948: /* (5) Create Jacobians Jce_xfixed and Jci */
949: /* (5.1) PDIPM Jacobian of equality bounds cebound(x) = J_nxfixed */
950: if (pdipm->Nxfixed) {
951: /* Create Jce_xfixed */
952: PetscCall(MatCreate(comm, &pdipm->Jce_xfixed));
953: PetscCall(MatSetSizes(pdipm->Jce_xfixed, pdipm->nxfixed, pdipm->nx, PETSC_DECIDE, pdipm->Nx));
954: PetscCall(MatSetFromOptions(pdipm->Jce_xfixed));
955: PetscCall(MatSeqAIJSetPreallocation(pdipm->Jce_xfixed, 1, NULL));
956: PetscCall(MatMPIAIJSetPreallocation(pdipm->Jce_xfixed, 1, NULL, 1, NULL));
958: PetscCall(MatGetOwnershipRange(pdipm->Jce_xfixed, &Jcrstart, &Jcrend));
959: PetscCall(ISGetIndices(pdipm->isxfixed, &cols));
960: k = 0;
961: for (row = Jcrstart; row < Jcrend; row++) {
962: PetscCall(MatSetValues(pdipm->Jce_xfixed, 1, &row, 1, cols + k, &one, INSERT_VALUES));
963: k++;
964: }
965: PetscCall(ISRestoreIndices(pdipm->isxfixed, &cols));
966: PetscCall(MatAssemblyBegin(pdipm->Jce_xfixed, MAT_FINAL_ASSEMBLY));
967: PetscCall(MatAssemblyEnd(pdipm->Jce_xfixed, MAT_FINAL_ASSEMBLY));
968: }
970: /* (5.2) PDIPM inequality Jacobian Jci = [tao->jacobian_inequality; ...] */
971: PetscCall(MatCreate(comm, &pdipm->Jci_xb));
972: PetscCall(MatSetSizes(pdipm->Jci_xb, pdipm->nci - pdipm->nh, pdipm->nx, PETSC_DECIDE, pdipm->Nx));
973: PetscCall(MatSetFromOptions(pdipm->Jci_xb));
974: PetscCall(MatSeqAIJSetPreallocation(pdipm->Jci_xb, 1, NULL));
975: PetscCall(MatMPIAIJSetPreallocation(pdipm->Jci_xb, 1, NULL, 1, NULL));
977: PetscCall(MatGetOwnershipRange(pdipm->Jci_xb, &Jcrstart, &Jcrend));
978: offset = Jcrstart;
979: if (pdipm->Nxub) {
980: /* Add xub to Jci_xb */
981: PetscCall(ISGetIndices(pdipm->isxub, &cols));
982: k = 0;
983: for (row = offset; row < offset + pdipm->nxub; row++) {
984: PetscCall(MatSetValues(pdipm->Jci_xb, 1, &row, 1, cols + k, &neg_one, INSERT_VALUES));
985: k++;
986: }
987: PetscCall(ISRestoreIndices(pdipm->isxub, &cols));
988: }
990: if (pdipm->Nxlb) {
991: /* Add xlb to Jci_xb */
992: PetscCall(ISGetIndices(pdipm->isxlb, &cols));
993: k = 0;
994: offset += pdipm->nxub;
995: for (row = offset; row < offset + pdipm->nxlb; row++) {
996: PetscCall(MatSetValues(pdipm->Jci_xb, 1, &row, 1, cols + k, &one, INSERT_VALUES));
997: k++;
998: }
999: PetscCall(ISRestoreIndices(pdipm->isxlb, &cols));
1000: }
1002: /* Add xbox to Jci_xb */
1003: if (pdipm->Nxbox) {
1004: PetscCall(ISGetIndices(pdipm->isxbox, &cols));
1005: k = 0;
1006: offset += pdipm->nxlb;
1007: for (row = offset; row < offset + pdipm->nxbox; row++) {
1008: PetscCall(MatSetValues(pdipm->Jci_xb, 1, &row, 1, cols + k, &neg_one, INSERT_VALUES));
1009: tmp = row + pdipm->nxbox;
1010: PetscCall(MatSetValues(pdipm->Jci_xb, 1, &tmp, 1, cols + k, &one, INSERT_VALUES));
1011: k++;
1012: }
1013: PetscCall(ISRestoreIndices(pdipm->isxbox, &cols));
1014: }
1016: PetscCall(MatAssemblyBegin(pdipm->Jci_xb, MAT_FINAL_ASSEMBLY));
1017: PetscCall(MatAssemblyEnd(pdipm->Jci_xb, MAT_FINAL_ASSEMBLY));
1018: /* PetscCall(MatView(pdipm->Jci_xb,PETSC_VIEWER_STDOUT_WORLD)); */
1020: /* (6) Set up ISs for PC Fieldsplit */
1021: if (pdipm->solve_reduced_kkt) {
1022: PetscCall(PetscMalloc2(pdipm->nx + pdipm->nce, &xa, 2 * pdipm->nci, &xb));
1023: for (i = 0; i < pdipm->nx + pdipm->nce; i++) xa[i] = i;
1024: for (i = 0; i < 2 * pdipm->nci; i++) xb[i] = pdipm->off_lambdai + i;
1026: PetscCall(ISCreateGeneral(comm, pdipm->nx + pdipm->nce, xa, PETSC_OWN_POINTER, &pdipm->is1));
1027: PetscCall(ISCreateGeneral(comm, 2 * pdipm->nci, xb, PETSC_OWN_POINTER, &pdipm->is2));
1028: }
1030: /* (7) Gather offsets from all processes */
1031: PetscCall(PetscMalloc1(size, &pdipm->nce_all));
1033: /* Get rstart of KKT matrix */
1034: PetscCallMPI(MPI_Scan(&pdipm->n, &rstart, 1, MPIU_INT, MPI_SUM, comm));
1035: rstart -= pdipm->n;
1037: PetscCallMPI(MPI_Allgather(&pdipm->nce, 1, MPIU_INT, pdipm->nce_all, 1, MPIU_INT, comm));
1039: PetscCall(PetscMalloc3(size, &ng_all, size, &nh_all, size, &Jranges));
1040: PetscCallMPI(MPI_Allgather(&rstart, 1, MPIU_INT, Jranges, 1, MPIU_INT, comm));
1041: PetscCallMPI(MPI_Allgather(&pdipm->nh, 1, MPIU_INT, nh_all, 1, MPIU_INT, comm));
1042: PetscCallMPI(MPI_Allgather(&pdipm->ng, 1, MPIU_INT, ng_all, 1, MPIU_INT, comm));
1044: PetscCall(MatGetOwnershipRanges(tao->hessian, &rranges));
1045: PetscCall(MatGetOwnershipRangesColumn(tao->hessian, &cranges));
1047: if (pdipm->Ng) {
1048: PetscCall(TaoComputeJacobianEquality(tao, tao->solution, tao->jacobian_equality, tao->jacobian_equality_pre));
1049: PetscCall(MatTranspose(tao->jacobian_equality, MAT_INITIAL_MATRIX, &pdipm->jac_equality_trans));
1050: }
1051: if (pdipm->Nh) {
1052: PetscCall(TaoComputeJacobianInequality(tao, tao->solution, tao->jacobian_inequality, tao->jacobian_inequality_pre));
1053: PetscCall(MatTranspose(tao->jacobian_inequality, MAT_INITIAL_MATRIX, &pdipm->jac_inequality_trans));
1054: }
1056: /* Count dnz,onz for preallocation of KKT matrix */
1057: nce_all = pdipm->nce_all;
1059: if (pdipm->Nxfixed) PetscCall(MatTranspose(pdipm->Jce_xfixed, MAT_INITIAL_MATRIX, &Jce_xfixed_trans));
1060: PetscCall(MatTranspose(pdipm->Jci_xb, MAT_INITIAL_MATRIX, &Jci_xb_trans));
1062: MatPreallocateBegin(comm, pdipm->n, pdipm->n, dnz, onz);
1064: /* 1st row block of KKT matrix: [Wxx; gradCe'; -gradCi'; 0] */
1065: PetscCall(TaoPDIPMEvaluateFunctionsAndJacobians(tao, pdipm->x));
1066: PetscCall(TaoComputeHessian(tao, tao->solution, tao->hessian, tao->hessian_pre));
1068: /* Insert tao->hessian */
1069: PetscCall(MatGetOwnershipRange(tao->hessian, &rjstart, NULL));
1070: for (i = 0; i < pdipm->nx; i++) {
1071: row = rstart + i;
1073: PetscCall(MatGetRow(tao->hessian, i + rjstart, &nc, &aj, NULL));
1074: proc = 0;
1075: for (j = 0; j < nc; j++) {
1076: while (aj[j] >= cranges[proc + 1]) proc++;
1077: col = aj[j] - cranges[proc] + Jranges[proc];
1078: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1079: }
1080: PetscCall(MatRestoreRow(tao->hessian, i + rjstart, &nc, &aj, NULL));
1082: if (pdipm->ng) {
1083: /* Insert grad g' */
1084: PetscCall(MatGetRow(pdipm->jac_equality_trans, i + rjstart, &nc, &aj, NULL));
1085: PetscCall(MatGetOwnershipRanges(tao->jacobian_equality, &ranges));
1086: proc = 0;
1087: for (j = 0; j < nc; j++) {
1088: /* find row ownership of */
1089: while (aj[j] >= ranges[proc + 1]) proc++;
1090: nx_all = rranges[proc + 1] - rranges[proc];
1091: col = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
1092: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1093: }
1094: PetscCall(MatRestoreRow(pdipm->jac_equality_trans, i + rjstart, &nc, &aj, NULL));
1095: }
1097: /* Insert Jce_xfixed^T' */
1098: if (pdipm->nxfixed) {
1099: PetscCall(MatGetRow(Jce_xfixed_trans, i + rjstart, &nc, &aj, NULL));
1100: PetscCall(MatGetOwnershipRanges(pdipm->Jce_xfixed, &ranges));
1101: proc = 0;
1102: for (j = 0; j < nc; j++) {
1103: /* find row ownership of */
1104: while (aj[j] >= ranges[proc + 1]) proc++;
1105: nx_all = rranges[proc + 1] - rranges[proc];
1106: col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + ng_all[proc];
1107: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1108: }
1109: PetscCall(MatRestoreRow(Jce_xfixed_trans, i + rjstart, &nc, &aj, NULL));
1110: }
1112: if (pdipm->nh) {
1113: /* Insert -grad h' */
1114: PetscCall(MatGetRow(pdipm->jac_inequality_trans, i + rjstart, &nc, &aj, NULL));
1115: PetscCall(MatGetOwnershipRanges(tao->jacobian_inequality, &ranges));
1116: proc = 0;
1117: for (j = 0; j < nc; j++) {
1118: /* find row ownership of */
1119: while (aj[j] >= ranges[proc + 1]) proc++;
1120: nx_all = rranges[proc + 1] - rranges[proc];
1121: col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
1122: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1123: }
1124: PetscCall(MatRestoreRow(pdipm->jac_inequality_trans, i + rjstart, &nc, &aj, NULL));
1125: }
1127: /* Insert Jci_xb^T' */
1128: PetscCall(MatGetRow(Jci_xb_trans, i + rjstart, &nc, &aj, NULL));
1129: PetscCall(MatGetOwnershipRanges(pdipm->Jci_xb, &ranges));
1130: proc = 0;
1131: for (j = 0; j < nc; j++) {
1132: /* find row ownership of */
1133: while (aj[j] >= ranges[proc + 1]) proc++;
1134: nx_all = rranges[proc + 1] - rranges[proc];
1135: col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc] + nh_all[proc];
1136: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1137: }
1138: PetscCall(MatRestoreRow(Jci_xb_trans, i + rjstart, &nc, &aj, NULL));
1139: }
1141: /* 2nd Row block of KKT matrix: [grad Ce, deltac*I, 0, 0] */
1142: if (pdipm->Ng) {
1143: PetscCall(MatGetOwnershipRange(tao->jacobian_equality, &rjstart, NULL));
1144: for (i = 0; i < pdipm->ng; i++) {
1145: row = rstart + pdipm->off_lambdae + i;
1147: PetscCall(MatGetRow(tao->jacobian_equality, i + rjstart, &nc, &aj, NULL));
1148: proc = 0;
1149: for (j = 0; j < nc; j++) {
1150: while (aj[j] >= cranges[proc + 1]) proc++;
1151: col = aj[j] - cranges[proc] + Jranges[proc];
1152: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz)); /* grad g */
1153: }
1154: PetscCall(MatRestoreRow(tao->jacobian_equality, i + rjstart, &nc, &aj, NULL));
1155: }
1156: }
1157: /* Jce_xfixed */
1158: if (pdipm->Nxfixed) {
1159: PetscCall(MatGetOwnershipRange(pdipm->Jce_xfixed, &Jcrstart, NULL));
1160: for (i = 0; i < (pdipm->nce - pdipm->ng); i++) {
1161: row = rstart + pdipm->off_lambdae + pdipm->ng + i;
1163: PetscCall(MatGetRow(pdipm->Jce_xfixed, i + Jcrstart, &nc, &cols, NULL));
1164: PetscCheck(nc == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "nc != 1");
1166: proc = 0;
1167: j = 0;
1168: while (cols[j] >= cranges[proc + 1]) proc++;
1169: col = cols[j] - cranges[proc] + Jranges[proc];
1170: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1171: PetscCall(MatRestoreRow(pdipm->Jce_xfixed, i + Jcrstart, &nc, &cols, NULL));
1172: }
1173: }
1175: /* 3rd Row block of KKT matrix: [ gradCi, 0, deltac*I, -I] */
1176: if (pdipm->Nh) {
1177: PetscCall(MatGetOwnershipRange(tao->jacobian_inequality, &rjstart, NULL));
1178: for (i = 0; i < pdipm->nh; i++) {
1179: row = rstart + pdipm->off_lambdai + i;
1181: PetscCall(MatGetRow(tao->jacobian_inequality, i + rjstart, &nc, &aj, NULL));
1182: proc = 0;
1183: for (j = 0; j < nc; j++) {
1184: while (aj[j] >= cranges[proc + 1]) proc++;
1185: col = aj[j] - cranges[proc] + Jranges[proc];
1186: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz)); /* grad h */
1187: }
1188: PetscCall(MatRestoreRow(tao->jacobian_inequality, i + rjstart, &nc, &aj, NULL));
1189: }
1190: /* I */
1191: for (i = 0; i < pdipm->nh; i++) {
1192: row = rstart + pdipm->off_lambdai + i;
1193: col = rstart + pdipm->off_z + i;
1194: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1195: }
1196: }
1198: /* Jci_xb */
1199: PetscCall(MatGetOwnershipRange(pdipm->Jci_xb, &Jcrstart, NULL));
1200: for (i = 0; i < (pdipm->nci - pdipm->nh); i++) {
1201: row = rstart + pdipm->off_lambdai + pdipm->nh + i;
1203: PetscCall(MatGetRow(pdipm->Jci_xb, i + Jcrstart, &nc, &cols, NULL));
1204: PetscCheck(nc == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "nc != 1");
1205: proc = 0;
1206: for (j = 0; j < nc; j++) {
1207: while (cols[j] >= cranges[proc + 1]) proc++;
1208: col = cols[j] - cranges[proc] + Jranges[proc];
1209: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1210: }
1211: PetscCall(MatRestoreRow(pdipm->Jci_xb, i + Jcrstart, &nc, &cols, NULL));
1212: /* I */
1213: col = rstart + pdipm->off_z + pdipm->nh + i;
1214: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1215: }
1217: /* 4-th Row block of KKT matrix: Z and Ci */
1218: for (i = 0; i < pdipm->nci; i++) {
1219: row = rstart + pdipm->off_z + i;
1220: cols1[0] = rstart + pdipm->off_lambdai + i;
1221: cols1[1] = row;
1222: PetscCall(MatPreallocateSet(row, 2, cols1, dnz, onz));
1223: }
1225: /* diagonal entry */
1226: for (i = 0; i < pdipm->n; i++) dnz[i]++; /* diagonal entry */
1228: /* Create KKT matrix */
1229: PetscCall(MatCreate(comm, &J));
1230: PetscCall(MatSetSizes(J, pdipm->n, pdipm->n, PETSC_DECIDE, PETSC_DECIDE));
1231: PetscCall(MatSetFromOptions(J));
1232: PetscCall(MatSeqAIJSetPreallocation(J, 0, dnz));
1233: PetscCall(MatMPIAIJSetPreallocation(J, 0, dnz, 0, onz));
1234: MatPreallocateEnd(dnz, onz);
1235: pdipm->K = J;
1237: /* (8) Insert constant entries to K */
1238: /* Set 0.0 to diagonal of K, so that the solver does not complain *about missing diagonal value */
1239: PetscCall(MatGetOwnershipRange(J, &rstart, &rend));
1240: for (i = rstart; i < rend; i++) PetscCall(MatSetValue(J, i, i, 0.0, INSERT_VALUES));
1241: /* In case Wxx has no diagonal entries preset set diagonal to deltaw given */
1242: if (pdipm->kkt_pd) {
1243: for (i = 0; i < pdipm->nh; i++) {
1244: row = rstart + i;
1245: PetscCall(MatSetValue(J, row, row, pdipm->deltaw, INSERT_VALUES));
1246: }
1247: }
1249: /* Row block of K: [ grad Ce, 0, 0, 0] */
1250: if (pdipm->Nxfixed) {
1251: PetscCall(MatGetOwnershipRange(pdipm->Jce_xfixed, &Jcrstart, NULL));
1252: for (i = 0; i < (pdipm->nce - pdipm->ng); i++) {
1253: row = rstart + pdipm->off_lambdae + pdipm->ng + i;
1255: PetscCall(MatGetRow(pdipm->Jce_xfixed, i + Jcrstart, &nc, &cols, &aa));
1256: proc = 0;
1257: for (j = 0; j < nc; j++) {
1258: while (cols[j] >= cranges[proc + 1]) proc++;
1259: col = cols[j] - cranges[proc] + Jranges[proc];
1260: PetscCall(MatSetValue(J, row, col, aa[j], INSERT_VALUES)); /* grad Ce */
1261: PetscCall(MatSetValue(J, col, row, aa[j], INSERT_VALUES)); /* grad Ce' */
1262: }
1263: PetscCall(MatRestoreRow(pdipm->Jce_xfixed, i + Jcrstart, &nc, &cols, &aa));
1264: }
1265: }
1267: /* Row block of K: [ -grad Ci, 0, 0, I] */
1268: PetscCall(MatGetOwnershipRange(pdipm->Jci_xb, &Jcrstart, NULL));
1269: for (i = 0; i < pdipm->nci - pdipm->nh; i++) {
1270: row = rstart + pdipm->off_lambdai + pdipm->nh + i;
1272: PetscCall(MatGetRow(pdipm->Jci_xb, i + Jcrstart, &nc, &cols, &aa));
1273: proc = 0;
1274: for (j = 0; j < nc; j++) {
1275: while (cols[j] >= cranges[proc + 1]) proc++;
1276: col = cols[j] - cranges[proc] + Jranges[proc];
1277: PetscCall(MatSetValue(J, col, row, -aa[j], INSERT_VALUES));
1278: PetscCall(MatSetValue(J, row, col, -aa[j], INSERT_VALUES));
1279: }
1280: PetscCall(MatRestoreRow(pdipm->Jci_xb, i + Jcrstart, &nc, &cols, &aa));
1282: col = rstart + pdipm->off_z + pdipm->nh + i;
1283: PetscCall(MatSetValue(J, row, col, 1, INSERT_VALUES));
1284: }
1286: for (i = 0; i < pdipm->nh; i++) {
1287: row = rstart + pdipm->off_lambdai + i;
1288: col = rstart + pdipm->off_z + i;
1289: PetscCall(MatSetValue(J, row, col, 1, INSERT_VALUES));
1290: }
1292: /* Row block of K: [ 0, 0, I, ...] */
1293: for (i = 0; i < pdipm->nci; i++) {
1294: row = rstart + pdipm->off_z + i;
1295: col = rstart + pdipm->off_lambdai + i;
1296: PetscCall(MatSetValue(J, row, col, 1, INSERT_VALUES));
1297: }
1299: if (pdipm->Nxfixed) PetscCall(MatDestroy(&Jce_xfixed_trans));
1300: PetscCall(MatDestroy(&Jci_xb_trans));
1301: PetscCall(PetscFree3(ng_all, nh_all, Jranges));
1303: /* (9) Set up nonlinear solver SNES */
1304: PetscCall(SNESSetFunction(pdipm->snes, NULL, TaoSNESFunction_PDIPM, (void *)tao));
1305: PetscCall(SNESSetJacobian(pdipm->snes, J, J, TaoSNESJacobian_PDIPM, (void *)tao));
1307: if (pdipm->solve_reduced_kkt) {
1308: PC pc;
1309: PetscCall(KSPGetPC(tao->ksp, &pc));
1310: PetscCall(PCSetType(pc, PCFIELDSPLIT));
1311: PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
1312: PetscCall(PCFieldSplitSetIS(pc, "2", pdipm->is2));
1313: PetscCall(PCFieldSplitSetIS(pc, "1", pdipm->is1));
1314: }
1315: PetscCall(SNESSetFromOptions(pdipm->snes));
1317: /* (10) Setup PCPostSetUp() for pdipm->solve_symmetric_kkt */
1318: if (pdipm->solve_symmetric_kkt) {
1319: KSP ksp;
1320: PC pc;
1321: PetscBool isCHOL;
1323: PetscCall(SNESGetKSP(pdipm->snes, &ksp));
1324: PetscCall(KSPGetPC(ksp, &pc));
1325: PetscCall(PCSetPostSetUp(pc, PCPostSetUp_PDIPM));
1327: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCCHOLESKY, &isCHOL));
1328: if (isCHOL) {
1329: Mat Factor;
1331: PetscCheck(PetscDefined(HAVE_MUMPS), PetscObjectComm((PetscObject)tao), PETSC_ERR_SUP, "Requires external package MUMPS");
1332: PetscCall(PCFactorGetMatrix(pc, &Factor));
1333: PetscCall(MatMumpsSetIcntl(Factor, 24, 1)); /* detection of null pivot rows */
1334: if (size > 1) PetscCall(MatMumpsSetIcntl(Factor, 13, 1)); /* parallelism of the root node (enable ScaLAPACK) and its splitting */
1335: }
1336: }
1337: PetscFunctionReturn(PETSC_SUCCESS);
1338: }
1340: static PetscErrorCode TaoDestroy_PDIPM(Tao tao)
1341: {
1342: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
1344: PetscFunctionBegin;
1345: /* Freeing Vectors assocaiated with KKT (X) */
1346: PetscCall(VecDestroy(&pdipm->x)); /* Solution x */
1347: PetscCall(VecDestroy(&pdipm->lambdae)); /* Equality constraints lagrangian multiplier*/
1348: PetscCall(VecDestroy(&pdipm->lambdai)); /* Inequality constraints lagrangian multiplier*/
1349: PetscCall(VecDestroy(&pdipm->z)); /* Slack variables */
1350: PetscCall(VecDestroy(&pdipm->X)); /* Big KKT system vector [x; lambdae; lambdai; z] */
1352: /* work vectors */
1353: PetscCall(VecDestroy(&pdipm->lambdae_xfixed));
1354: PetscCall(VecDestroy(&pdipm->lambdai_xb));
1356: /* Legrangian equality and inequality Vec */
1357: PetscCall(VecDestroy(&pdipm->ce)); /* Vec of equality constraints */
1358: PetscCall(VecDestroy(&pdipm->ci)); /* Vec of inequality constraints */
1360: /* Matrices */
1361: PetscCall(MatDestroy(&pdipm->Jce_xfixed));
1362: PetscCall(MatDestroy(&pdipm->Jci_xb)); /* Jacobian of inequality constraints Jci = [tao->jacobian_inequality ; J(nxub); J(nxlb); J(nxbx)] */
1363: PetscCall(MatDestroy(&pdipm->K));
1365: /* Index Sets */
1366: if (pdipm->Nxub) PetscCall(ISDestroy(&pdipm->isxub)); /* Finite upper bound only -inf < x < ub */
1368: if (pdipm->Nxlb) PetscCall(ISDestroy(&pdipm->isxlb)); /* Finite lower bound only lb <= x < inf */
1370: if (pdipm->Nxfixed) PetscCall(ISDestroy(&pdipm->isxfixed)); /* Fixed variables lb = x = ub */
1372: if (pdipm->Nxbox) PetscCall(ISDestroy(&pdipm->isxbox)); /* Boxed variables lb <= x <= ub */
1374: if (pdipm->Nxfree) PetscCall(ISDestroy(&pdipm->isxfree)); /* Free variables -inf <= x <= inf */
1376: if (pdipm->solve_reduced_kkt) {
1377: PetscCall(ISDestroy(&pdipm->is1));
1378: PetscCall(ISDestroy(&pdipm->is2));
1379: }
1381: /* SNES */
1382: PetscCall(SNESDestroy(&pdipm->snes)); /* Nonlinear solver */
1383: PetscCall(PetscFree(pdipm->nce_all));
1384: PetscCall(MatDestroy(&pdipm->jac_equality_trans));
1385: PetscCall(MatDestroy(&pdipm->jac_inequality_trans));
1387: /* Destroy pdipm */
1388: PetscCall(PetscFree(tao->data)); /* Holding locations of pdipm */
1390: /* Destroy Dual */
1391: PetscCall(VecDestroy(&tao->DE)); /* equality dual */
1392: PetscCall(VecDestroy(&tao->DI)); /* dinequality dual */
1393: PetscFunctionReturn(PETSC_SUCCESS);
1394: }
1396: static PetscErrorCode TaoSetFromOptions_PDIPM(Tao tao, PetscOptionItems PetscOptionsObject)
1397: {
1398: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
1400: PetscFunctionBegin;
1401: PetscOptionsHeadBegin(PetscOptionsObject, "PDIPM method for constrained optimization");
1402: PetscCall(PetscOptionsReal("-tao_pdipm_push_init_slack", "parameter to push initial slack variables away from bounds", NULL, pdipm->push_init_slack, &pdipm->push_init_slack, NULL));
1403: PetscCall(PetscOptionsReal("-tao_pdipm_push_init_lambdai", "parameter to push initial (inequality) dual variables away from bounds", NULL, pdipm->push_init_lambdai, &pdipm->push_init_lambdai, NULL));
1404: PetscCall(PetscOptionsBool("-tao_pdipm_solve_reduced_kkt", "Solve reduced KKT system using Schur-complement", NULL, pdipm->solve_reduced_kkt, &pdipm->solve_reduced_kkt, NULL));
1405: PetscCall(PetscOptionsReal("-tao_pdipm_mu_update_factor", "Update scalar for barrier parameter (mu) update", NULL, pdipm->mu_update_factor, &pdipm->mu_update_factor, NULL));
1406: PetscCall(PetscOptionsBool("-tao_pdipm_symmetric_kkt", "Solve non reduced symmetric KKT system", NULL, pdipm->solve_symmetric_kkt, &pdipm->solve_symmetric_kkt, NULL));
1407: PetscCall(PetscOptionsBool("-tao_pdipm_kkt_shift_pd", "Add shifts to make KKT matrix positive definite", NULL, pdipm->kkt_pd, &pdipm->kkt_pd, NULL));
1408: PetscOptionsHeadEnd();
1409: PetscFunctionReturn(PETSC_SUCCESS);
1410: }
1412: /*MC
1413: TAOPDIPM - Barrier-based primal-dual interior point algorithm for generally constrained optimization.
1415: Options Database Keys:
1416: + -tao_pdipm_push_init_lambdai - parameter to push initial dual variables away from bounds (> 0)
1417: . -tao_pdipm_push_init_slack - parameter to push initial slack variables away from bounds (> 0)
1418: . -tao_pdipm_mu_update_factor - update scalar for barrier parameter (mu) update (> 0)
1419: . -tao_pdipm_symmetric_kkt - Solve non-reduced symmetric KKT system
1420: - -tao_pdipm_kkt_shift_pd - Add shifts to make KKT matrix positive definite
1422: Level: beginner
1424: Note:
1425: Variable bounds are required; set them with `TaoSetVariableBounds()` or `TaoSetVariableBoundsRoutine()`, using
1426: `PETSC_NINFINITY` and `PETSC_INFINITY` entries for unbounded variables.
1428: .seealso: `TAOPDIPM`, `Tao`, `TaoType`, `TaoSetVariableBounds()`, `TaoSetVariableBoundsRoutine()`
1429: M*/
1431: PETSC_EXTERN PetscErrorCode TaoCreate_PDIPM(Tao tao)
1432: {
1433: TAO_PDIPM *pdipm;
1434: PC pc;
1436: PetscFunctionBegin;
1437: tao->ops->setup = TaoSetup_PDIPM;
1438: tao->ops->solve = TaoSolve_PDIPM;
1439: tao->ops->setfromoptions = TaoSetFromOptions_PDIPM;
1440: tao->ops->view = TaoView_PDIPM;
1441: tao->ops->destroy = TaoDestroy_PDIPM;
1442: tao->uses_gradient = PETSC_TRUE;
1443: tao->uses_hessian_matrices = PETSC_TRUE;
1445: PetscCall(PetscNew(&pdipm));
1446: tao->data = (void *)pdipm;
1448: pdipm->nx = pdipm->Nx = 0;
1449: pdipm->nxfixed = pdipm->Nxfixed = 0;
1450: pdipm->nxlb = pdipm->Nxlb = 0;
1451: pdipm->nxub = pdipm->Nxub = 0;
1452: pdipm->nxbox = pdipm->Nxbox = 0;
1453: pdipm->nxfree = pdipm->Nxfree = 0;
1455: pdipm->ng = pdipm->Ng = pdipm->nce = pdipm->Nce = 0;
1456: pdipm->nh = pdipm->Nh = pdipm->nci = pdipm->Nci = 0;
1457: pdipm->n = pdipm->N = 0;
1458: pdipm->mu = 1.0;
1459: pdipm->mu_update_factor = 0.1;
1461: pdipm->deltaw = 0.0;
1462: pdipm->lastdeltaw = 3 * 1.e-4;
1463: pdipm->deltac = 0.0;
1464: pdipm->kkt_pd = PETSC_FALSE;
1466: pdipm->push_init_slack = 1.0;
1467: pdipm->push_init_lambdai = 1.0;
1468: pdipm->solve_reduced_kkt = PETSC_FALSE;
1469: pdipm->solve_symmetric_kkt = PETSC_TRUE;
1471: /* Override default settings (unless already changed) */
1472: PetscObjectParameterSetDefault(tao, max_it, 200);
1473: PetscObjectParameterSetDefault(tao, max_funcs, 500);
1475: PetscCall(SNESCreate(((PetscObject)tao)->comm, &pdipm->snes));
1476: PetscCall(SNESSetOptionsPrefix(pdipm->snes, tao->hdr.prefix));
1477: PetscCall(SNESGetKSP(pdipm->snes, &tao->ksp));
1478: PetscCall(PetscObjectReference((PetscObject)tao->ksp));
1479: PetscCall(KSPGetPC(tao->ksp, &pc));
1480: PetscCall(PCSetApplicationContext(pc, (void *)tao));
1481: PetscFunctionReturn(PETSC_SUCCESS);
1482: }