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(PetscMemcpy(carr, garr, pdipm->ng * sizeof(PetscScalar)));
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(PetscMemcpy(carr, harr, pdipm->nh * sizeof(PetscScalar)));
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 sendbuf[5], recvbuf[5];
156: PetscFunctionBegin;
157: /* Creates upper and lower bounds vectors on x, if not created already */
158: PetscCall(TaoComputeVariableBounds(tao));
160: PetscCall(VecGetLocalSize(tao->XL, &n));
161: PetscCall(PetscMalloc5(n, &ixlb, n, &ixub, n, &ixfree, n, &ixfixed, n, &ixbox));
163: PetscCall(VecGetOwnershipRange(tao->XL, &low, &high));
164: PetscCall(VecGetArrayRead(tao->XL, &xl));
165: PetscCall(VecGetArrayRead(tao->XU, &xu));
166: for (i = 0; i < n; i++) {
167: idx = low + i;
168: if ((PetscRealPart(xl[i]) > PETSC_NINFINITY) && (PetscRealPart(xu[i]) < PETSC_INFINITY)) {
169: if (PetscRealPart(xl[i]) == PetscRealPart(xu[i])) {
170: ixfixed[pdipm->nxfixed++] = idx;
171: } else ixbox[pdipm->nxbox++] = idx;
172: } else {
173: if ((PetscRealPart(xl[i]) > PETSC_NINFINITY) && (PetscRealPart(xu[i]) >= PETSC_INFINITY)) {
174: ixlb[pdipm->nxlb++] = idx;
175: } else if ((PetscRealPart(xl[i]) <= PETSC_NINFINITY) && (PetscRealPart(xu[i]) < PETSC_INFINITY)) {
176: ixub[pdipm->nxlb++] = idx;
177: } else ixfree[pdipm->nxfree++] = idx;
178: }
179: }
180: PetscCall(VecRestoreArrayRead(tao->XL, &xl));
181: PetscCall(VecRestoreArrayRead(tao->XU, &xu));
183: PetscCall(PetscObjectGetComm((PetscObject)tao, &comm));
184: sendbuf[0] = pdipm->nxlb;
185: sendbuf[1] = pdipm->nxub;
186: sendbuf[2] = pdipm->nxfixed;
187: sendbuf[3] = pdipm->nxbox;
188: sendbuf[4] = pdipm->nxfree;
190: PetscCallMPI(MPIU_Allreduce(sendbuf, recvbuf, 5, MPIU_INT, MPI_SUM, comm));
191: pdipm->Nxlb = recvbuf[0];
192: pdipm->Nxub = recvbuf[1];
193: pdipm->Nxfixed = recvbuf[2];
194: pdipm->Nxbox = recvbuf[3];
195: pdipm->Nxfree = recvbuf[4];
197: if (pdipm->Nxlb) PetscCall(ISCreateGeneral(comm, pdipm->nxlb, ixlb, PETSC_COPY_VALUES, &pdipm->isxlb));
198: if (pdipm->Nxub) PetscCall(ISCreateGeneral(comm, pdipm->nxub, ixub, PETSC_COPY_VALUES, &pdipm->isxub));
199: if (pdipm->Nxfixed) PetscCall(ISCreateGeneral(comm, pdipm->nxfixed, ixfixed, PETSC_COPY_VALUES, &pdipm->isxfixed));
200: if (pdipm->Nxbox) PetscCall(ISCreateGeneral(comm, pdipm->nxbox, ixbox, PETSC_COPY_VALUES, &pdipm->isxbox));
201: if (pdipm->Nxfree) PetscCall(ISCreateGeneral(comm, pdipm->nxfree, ixfree, PETSC_COPY_VALUES, &pdipm->isxfree));
202: PetscCall(PetscFree5(ixlb, ixub, ixfixed, ixbox, ixfree));
203: PetscFunctionReturn(PETSC_SUCCESS);
204: }
206: /*
207: TaoPDIPMInitializeSolution - Initialize `TAOPDIPM` solution X = [x; lambdae; lambdai; z].
208: X consists of four subvectors in the order [x; lambdae; lambdai; z]. These
209: four subvectors need to be initialized and its values copied over to X. Instead
210: of copying, we use `VecPlaceArray()`/`VecResetArray()` functions to share the memory locations for
211: X and the subvectors
213: Collective
215: Input Parameter:
216: . tao - Tao context
218: Level: beginner
219: */
220: static PetscErrorCode TaoPDIPMInitializeSolution(Tao tao)
221: {
222: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
223: PetscScalar *Xarr, *z, *lambdai;
224: PetscInt i;
225: const PetscScalar *xarr, *h;
227: PetscFunctionBegin;
228: PetscCall(VecGetArrayWrite(pdipm->X, &Xarr));
230: /* Set Initialize X.x = tao->solution */
231: PetscCall(VecGetArrayRead(tao->solution, &xarr));
232: PetscCall(PetscMemcpy(Xarr, xarr, pdipm->nx * sizeof(PetscScalar)));
233: PetscCall(VecRestoreArrayRead(tao->solution, &xarr));
235: /* Initialize X.lambdae = 0.0 */
236: if (pdipm->lambdae) PetscCall(VecSet(pdipm->lambdae, 0.0));
238: /* Initialize X.lambdai = push_init_lambdai, X.z = push_init_slack */
239: if (pdipm->Nci) {
240: PetscCall(VecSet(pdipm->lambdai, pdipm->push_init_lambdai));
241: PetscCall(VecSet(pdipm->z, pdipm->push_init_slack));
243: /* Additional modification for X.lambdai and X.z */
244: PetscCall(VecGetArrayWrite(pdipm->lambdai, &lambdai));
245: PetscCall(VecGetArrayWrite(pdipm->z, &z));
246: if (pdipm->Nh) {
247: PetscCall(VecGetArrayRead(tao->constraints_inequality, &h));
248: for (i = 0; i < pdipm->nh; i++) {
249: if (h[i] < -pdipm->push_init_slack) z[i] = -h[i];
250: if (pdipm->mu / z[i] > pdipm->push_init_lambdai) lambdai[i] = pdipm->mu / z[i];
251: }
252: PetscCall(VecRestoreArrayRead(tao->constraints_inequality, &h));
253: }
254: PetscCall(VecRestoreArrayWrite(pdipm->lambdai, &lambdai));
255: PetscCall(VecRestoreArrayWrite(pdipm->z, &z));
256: }
258: PetscCall(VecRestoreArrayWrite(pdipm->X, &Xarr));
259: PetscFunctionReturn(PETSC_SUCCESS);
260: }
262: /*
263: TaoSNESJacobian_PDIPM - Evaluate the Hessian matrix at X
265: Input Parameter:
266: snes - SNES context
267: X - KKT Vector
268: *ctx - pdipm context
270: Output Parameter:
271: J - Hessian matrix
272: Jpre - matrix to build the preconditioner from
273: */
274: static PetscErrorCode TaoSNESJacobian_PDIPM(SNES snes, Vec X, Mat J, Mat Jpre, void *ctx)
275: {
276: Tao tao = (Tao)ctx;
277: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
278: PetscInt i, row, cols[2], Jrstart, rjstart, nc, j;
279: const PetscInt *aj, *ranges, *Jranges, *rranges, *cranges;
280: const PetscScalar *Xarr, *aa;
281: PetscScalar vals[2];
282: PetscInt proc, nx_all, *nce_all = pdipm->nce_all;
283: MPI_Comm comm;
284: PetscMPIInt rank, size;
286: PetscFunctionBegin;
287: PetscCall(PetscObjectGetComm((PetscObject)snes, &comm));
288: PetscCallMPI(MPI_Comm_rank(comm, &rank));
289: PetscCallMPI(MPI_Comm_rank(comm, &size));
291: PetscCall(MatGetOwnershipRanges(Jpre, &Jranges));
292: PetscCall(MatGetOwnershipRange(Jpre, &Jrstart, NULL));
293: PetscCall(MatGetOwnershipRangesColumn(tao->hessian, &rranges));
294: PetscCall(MatGetOwnershipRangesColumn(tao->hessian, &cranges));
296: PetscCall(VecGetArrayRead(X, &Xarr));
298: /* (1) insert Z and Ci to the 4th block of Jpre -- overwrite existing values */
299: if (pdipm->solve_symmetric_kkt) { /* 1 for eq 17 revised pdipm doc 0 for eq 18 (symmetric KKT) */
300: vals[0] = 1.0;
301: for (i = 0; i < pdipm->nci; i++) {
302: row = Jrstart + pdipm->off_z + i;
303: cols[0] = Jrstart + pdipm->off_lambdai + i;
304: cols[1] = row;
305: vals[1] = Xarr[pdipm->off_lambdai + i] / Xarr[pdipm->off_z + i];
306: PetscCall(MatSetValues(Jpre, 1, &row, 2, cols, vals, INSERT_VALUES));
307: }
308: } else {
309: for (i = 0; i < pdipm->nci; i++) {
310: row = Jrstart + pdipm->off_z + i;
311: cols[0] = Jrstart + pdipm->off_lambdai + i;
312: cols[1] = row;
313: vals[0] = Xarr[pdipm->off_z + i];
314: vals[1] = Xarr[pdipm->off_lambdai + i];
315: PetscCall(MatSetValues(Jpre, 1, &row, 2, cols, vals, INSERT_VALUES));
316: }
317: }
319: /* (2) insert 2nd row block of Jpre: [ grad g, 0, 0, 0] */
320: if (pdipm->Ng) {
321: PetscCall(MatGetOwnershipRange(tao->jacobian_equality, &rjstart, NULL));
322: for (i = 0; i < pdipm->ng; i++) {
323: row = Jrstart + pdipm->off_lambdae + i;
325: PetscCall(MatGetRow(tao->jacobian_equality, i + rjstart, &nc, &aj, &aa));
326: proc = 0;
327: for (j = 0; j < nc; j++) {
328: while (aj[j] >= cranges[proc + 1]) proc++;
329: cols[0] = aj[j] - cranges[proc] + Jranges[proc];
330: PetscCall(MatSetValue(Jpre, row, cols[0], aa[j], INSERT_VALUES));
331: }
332: PetscCall(MatRestoreRow(tao->jacobian_equality, i + rjstart, &nc, &aj, &aa));
333: if (pdipm->kkt_pd) {
334: /* add shift \delta_c */
335: PetscCall(MatSetValue(Jpre, row, row, -pdipm->deltac, INSERT_VALUES));
336: }
337: }
338: }
340: /* (3) insert 3rd row block of Jpre: [ -grad h, 0, deltac, I] */
341: if (pdipm->Nh) {
342: PetscCall(MatGetOwnershipRange(tao->jacobian_inequality, &rjstart, NULL));
343: for (i = 0; i < pdipm->nh; i++) {
344: row = Jrstart + pdipm->off_lambdai + i;
345: PetscCall(MatGetRow(tao->jacobian_inequality, i + rjstart, &nc, &aj, &aa));
346: proc = 0;
347: for (j = 0; j < nc; j++) {
348: while (aj[j] >= cranges[proc + 1]) proc++;
349: cols[0] = aj[j] - cranges[proc] + Jranges[proc];
350: PetscCall(MatSetValue(Jpre, row, cols[0], -aa[j], INSERT_VALUES));
351: }
352: PetscCall(MatRestoreRow(tao->jacobian_inequality, i + rjstart, &nc, &aj, &aa));
353: if (pdipm->kkt_pd) {
354: /* add shift \delta_c */
355: PetscCall(MatSetValue(Jpre, row, row, -pdipm->deltac, INSERT_VALUES));
356: }
357: }
358: }
360: /* (4) insert 1st row block of Jpre: [Wxx, grad g', -grad h', 0] */
361: if (pdipm->Ng) { /* grad g' */
362: PetscCall(MatTranspose(tao->jacobian_equality, MAT_REUSE_MATRIX, &pdipm->jac_equality_trans));
363: }
364: if (pdipm->Nh) { /* grad h' */
365: PetscCall(MatTranspose(tao->jacobian_inequality, MAT_REUSE_MATRIX, &pdipm->jac_inequality_trans));
366: }
368: PetscCall(VecPlaceArray(pdipm->x, Xarr));
369: PetscCall(TaoComputeHessian(tao, pdipm->x, tao->hessian, tao->hessian_pre));
370: PetscCall(VecResetArray(pdipm->x));
372: PetscCall(MatGetOwnershipRange(tao->hessian, &rjstart, NULL));
373: for (i = 0; i < pdipm->nx; i++) {
374: row = Jrstart + i;
376: /* insert Wxx = fxx + ... -- provided by user */
377: PetscCall(MatGetRow(tao->hessian, i + rjstart, &nc, &aj, &aa));
378: proc = 0;
379: for (j = 0; j < nc; j++) {
380: while (aj[j] >= cranges[proc + 1]) proc++;
381: cols[0] = aj[j] - cranges[proc] + Jranges[proc];
382: if (row == cols[0] && pdipm->kkt_pd) {
383: /* add shift deltaw to Wxx component */
384: PetscCall(MatSetValue(Jpre, row, cols[0], aa[j] + pdipm->deltaw, INSERT_VALUES));
385: } else {
386: PetscCall(MatSetValue(Jpre, row, cols[0], aa[j], INSERT_VALUES));
387: }
388: }
389: PetscCall(MatRestoreRow(tao->hessian, i + rjstart, &nc, &aj, &aa));
391: /* insert grad g' */
392: if (pdipm->ng) {
393: PetscCall(MatGetRow(pdipm->jac_equality_trans, i + rjstart, &nc, &aj, &aa));
394: PetscCall(MatGetOwnershipRanges(tao->jacobian_equality, &ranges));
395: proc = 0;
396: for (j = 0; j < nc; j++) {
397: /* find row ownership of */
398: while (aj[j] >= ranges[proc + 1]) proc++;
399: nx_all = rranges[proc + 1] - rranges[proc];
400: cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
401: PetscCall(MatSetValue(Jpre, row, cols[0], aa[j], INSERT_VALUES));
402: }
403: PetscCall(MatRestoreRow(pdipm->jac_equality_trans, i + rjstart, &nc, &aj, &aa));
404: }
406: /* insert -grad h' */
407: if (pdipm->nh) {
408: PetscCall(MatGetRow(pdipm->jac_inequality_trans, i + rjstart, &nc, &aj, &aa));
409: PetscCall(MatGetOwnershipRanges(tao->jacobian_inequality, &ranges));
410: proc = 0;
411: for (j = 0; j < nc; j++) {
412: /* find row ownership of */
413: while (aj[j] >= ranges[proc + 1]) proc++;
414: nx_all = rranges[proc + 1] - rranges[proc];
415: cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
416: PetscCall(MatSetValue(Jpre, row, cols[0], -aa[j], INSERT_VALUES));
417: }
418: PetscCall(MatRestoreRow(pdipm->jac_inequality_trans, i + rjstart, &nc, &aj, &aa));
419: }
420: }
421: PetscCall(VecRestoreArrayRead(X, &Xarr));
423: /* (6) assemble Jpre and J */
424: PetscCall(MatAssemblyBegin(Jpre, MAT_FINAL_ASSEMBLY));
425: PetscCall(MatAssemblyEnd(Jpre, MAT_FINAL_ASSEMBLY));
427: if (J != Jpre) {
428: PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
429: PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
430: }
431: PetscFunctionReturn(PETSC_SUCCESS);
432: }
434: /*
435: TaoSnesFunction_PDIPM - Evaluate KKT function at X
437: Input Parameter:
438: snes - SNES context
439: X - KKT Vector
440: *ctx - pdipm
442: Output Parameter:
443: F - Updated Lagrangian vector
444: */
445: static PetscErrorCode TaoSNESFunction_PDIPM(SNES snes, Vec X, Vec F, void *ctx)
446: {
447: Tao tao = (Tao)ctx;
448: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
449: PetscScalar *Farr;
450: Vec x, L1;
451: PetscInt i;
452: const PetscScalar *Xarr, *carr, *zarr, *larr;
454: PetscFunctionBegin;
455: PetscCall(VecSet(F, 0.0));
457: PetscCall(VecGetArrayRead(X, &Xarr));
458: PetscCall(VecGetArrayWrite(F, &Farr));
460: /* (0) Evaluate f, fx, gradG, gradH at X.x Note: pdipm->x is not changed below */
461: x = pdipm->x;
462: PetscCall(VecPlaceArray(x, Xarr));
463: PetscCall(TaoPDIPMEvaluateFunctionsAndJacobians(tao, x));
465: /* Update ce, ci, and Jci at X.x */
466: PetscCall(TaoPDIPMUpdateConstraints(tao, x));
467: PetscCall(VecResetArray(x));
469: /* (1) L1 = fx + (gradG'*DE + Jce_xfixed'*lambdae_xfixed) - (gradH'*DI + Jci_xb'*lambdai_xb) */
470: L1 = pdipm->x;
471: PetscCall(VecPlaceArray(L1, Farr)); /* L1 = 0.0 */
472: if (pdipm->Nci) {
473: if (pdipm->Nh) {
474: /* L1 += gradH'*DI. Note: tao->DI is not changed below */
475: PetscCall(VecPlaceArray(tao->DI, Xarr + pdipm->off_lambdai));
476: PetscCall(MatMultTransposeAdd(tao->jacobian_inequality, tao->DI, L1, L1));
477: PetscCall(VecResetArray(tao->DI));
478: }
480: /* L1 += Jci_xb'*lambdai_xb */
481: PetscCall(VecPlaceArray(pdipm->lambdai_xb, Xarr + pdipm->off_lambdai + pdipm->nh));
482: PetscCall(MatMultTransposeAdd(pdipm->Jci_xb, pdipm->lambdai_xb, L1, L1));
483: PetscCall(VecResetArray(pdipm->lambdai_xb));
485: /* L1 = - (gradH'*DI + Jci_xb'*lambdai_xb) */
486: PetscCall(VecScale(L1, -1.0));
487: }
489: /* L1 += fx */
490: PetscCall(VecAXPY(L1, 1.0, tao->gradient));
492: if (pdipm->Nce) {
493: if (pdipm->Ng) {
494: /* L1 += gradG'*DE. Note: tao->DE is not changed below */
495: PetscCall(VecPlaceArray(tao->DE, Xarr + pdipm->off_lambdae));
496: PetscCall(MatMultTransposeAdd(tao->jacobian_equality, tao->DE, L1, L1));
497: PetscCall(VecResetArray(tao->DE));
498: }
499: if (pdipm->Nxfixed) {
500: /* L1 += Jce_xfixed'*lambdae_xfixed */
501: PetscCall(VecPlaceArray(pdipm->lambdae_xfixed, Xarr + pdipm->off_lambdae + pdipm->ng));
502: PetscCall(MatMultTransposeAdd(pdipm->Jce_xfixed, pdipm->lambdae_xfixed, L1, L1));
503: PetscCall(VecResetArray(pdipm->lambdae_xfixed));
504: }
505: }
506: PetscCall(VecResetArray(L1));
508: /* (2) L2 = ce(x) */
509: if (pdipm->Nce) {
510: PetscCall(VecGetArrayRead(pdipm->ce, &carr));
511: for (i = 0; i < pdipm->nce; i++) Farr[pdipm->off_lambdae + i] = carr[i];
512: PetscCall(VecRestoreArrayRead(pdipm->ce, &carr));
513: }
515: if (pdipm->Nci) {
516: if (pdipm->solve_symmetric_kkt) {
517: /* (3) L3 = z - ci(x);
518: (4) L4 = Lambdai * e - mu/z *e */
519: PetscCall(VecGetArrayRead(pdipm->ci, &carr));
520: larr = Xarr + pdipm->off_lambdai;
521: zarr = Xarr + pdipm->off_z;
522: for (i = 0; i < pdipm->nci; i++) {
523: Farr[pdipm->off_lambdai + i] = zarr[i] - carr[i];
524: Farr[pdipm->off_z + i] = larr[i] - pdipm->mu / zarr[i];
525: }
526: PetscCall(VecRestoreArrayRead(pdipm->ci, &carr));
527: } else {
528: /* (3) L3 = z - ci(x);
529: (4) L4 = Z * Lambdai * e - mu * e */
530: PetscCall(VecGetArrayRead(pdipm->ci, &carr));
531: larr = Xarr + pdipm->off_lambdai;
532: zarr = Xarr + pdipm->off_z;
533: for (i = 0; i < pdipm->nci; i++) {
534: Farr[pdipm->off_lambdai + i] = zarr[i] - carr[i];
535: Farr[pdipm->off_z + i] = zarr[i] * larr[i] - pdipm->mu;
536: }
537: PetscCall(VecRestoreArrayRead(pdipm->ci, &carr));
538: }
539: }
541: PetscCall(VecRestoreArrayRead(X, &Xarr));
542: PetscCall(VecRestoreArrayWrite(F, &Farr));
543: PetscFunctionReturn(PETSC_SUCCESS);
544: }
546: /*
547: Evaluate F(X); then update tao->gnorm0, tao->step = mu,
548: tao->residual = norm2(F_x,F_z) and tao->cnorm = norm2(F_ce,F_ci).
549: */
550: static PetscErrorCode TaoSNESFunction_PDIPM_residual(SNES snes, Vec X, Vec F, void *ctx)
551: {
552: Tao tao = (Tao)ctx;
553: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
554: PetscScalar *Farr, *tmparr;
555: Vec L1;
556: PetscInt i;
557: PetscReal res[2], cnorm[2];
558: const PetscScalar *Xarr = NULL;
560: PetscFunctionBegin;
561: PetscCall(TaoSNESFunction_PDIPM(snes, X, F, (void *)tao));
562: PetscCall(VecGetArrayWrite(F, &Farr));
563: PetscCall(VecGetArrayRead(X, &Xarr));
565: /* compute res[0] = norm2(F_x) */
566: L1 = pdipm->x;
567: PetscCall(VecPlaceArray(L1, Farr));
568: PetscCall(VecNorm(L1, NORM_2, &res[0]));
569: PetscCall(VecResetArray(L1));
571: /* compute res[1] = norm2(F_z), cnorm[1] = norm2(F_ci) */
572: if (pdipm->z) {
573: if (pdipm->solve_symmetric_kkt) {
574: PetscCall(VecPlaceArray(pdipm->z, Farr + pdipm->off_z));
575: if (pdipm->Nci) {
576: PetscCall(VecGetArrayWrite(pdipm->z, &tmparr));
577: for (i = 0; i < pdipm->nci; i++) tmparr[i] *= Xarr[pdipm->off_z + i];
578: PetscCall(VecRestoreArrayWrite(pdipm->z, &tmparr));
579: }
581: PetscCall(VecNorm(pdipm->z, NORM_2, &res[1]));
583: if (pdipm->Nci) {
584: PetscCall(VecGetArrayWrite(pdipm->z, &tmparr));
585: for (i = 0; i < pdipm->nci; i++) tmparr[i] /= Xarr[pdipm->off_z + i];
586: PetscCall(VecRestoreArrayWrite(pdipm->z, &tmparr));
587: }
588: PetscCall(VecResetArray(pdipm->z));
589: } else { /* !solve_symmetric_kkt */
590: PetscCall(VecPlaceArray(pdipm->z, Farr + pdipm->off_z));
591: PetscCall(VecNorm(pdipm->z, NORM_2, &res[1]));
592: PetscCall(VecResetArray(pdipm->z));
593: }
595: PetscCall(VecPlaceArray(pdipm->ci, Farr + pdipm->off_lambdai));
596: PetscCall(VecNorm(pdipm->ci, NORM_2, &cnorm[1]));
597: PetscCall(VecResetArray(pdipm->ci));
598: } else {
599: res[1] = 0.0;
600: cnorm[1] = 0.0;
601: }
603: /* compute cnorm[0] = norm2(F_ce) */
604: if (pdipm->Nce) {
605: PetscCall(VecPlaceArray(pdipm->ce, Farr + pdipm->off_lambdae));
606: PetscCall(VecNorm(pdipm->ce, NORM_2, &cnorm[0]));
607: PetscCall(VecResetArray(pdipm->ce));
608: } else cnorm[0] = 0.0;
610: PetscCall(VecRestoreArrayWrite(F, &Farr));
611: PetscCall(VecRestoreArrayRead(X, &Xarr));
613: tao->gnorm0 = tao->residual;
614: tao->residual = PetscSqrtReal(res[0] * res[0] + res[1] * res[1]);
615: tao->cnorm = PetscSqrtReal(cnorm[0] * cnorm[0] + cnorm[1] * cnorm[1]);
616: tao->step = pdipm->mu;
617: PetscFunctionReturn(PETSC_SUCCESS);
618: }
620: /*
621: PCPostSetup_PDIPM -- called when the KKT matrix is Cholesky factored for the preconditioner. Checks the inertia of Cholesky factor of the KKT matrix.
622: If it does not match the numbers of prime and dual variables, add shifts to the KKT matrix.
623: */
624: static PetscErrorCode PCPostSetUp_PDIPM(PC pc)
625: {
626: Tao tao;
627: TAO_PDIPM *pdipm;
628: Vec X;
629: SNES snes;
630: KSP ksp;
631: Mat Factor;
632: PetscBool isCHOL;
633: PetscInt nneg, nzero, npos;
635: PetscFunctionBegin;
636: PetscCall(PCGetApplicationContext(pc, &tao));
637: pdipm = (TAO_PDIPM *)tao->data;
638: X = pdipm->X;
639: snes = pdipm->snes;
641: /* Get the inertia of Cholesky factor */
642: PetscCall(SNESGetKSP(snes, &ksp));
643: PetscCall(KSPGetPC(ksp, &pc));
644: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCCHOLESKY, &isCHOL));
645: if (!isCHOL) PetscFunctionReturn(PETSC_SUCCESS);
647: PetscCall(PCFactorGetMatrix(pc, &Factor));
648: PetscCall(MatGetInertia(Factor, &nneg, &nzero, &npos));
650: if (npos < pdipm->Nx + pdipm->Nci) {
651: pdipm->deltaw = PetscMax(pdipm->lastdeltaw / 3, 1.e-4 * PETSC_MACHINE_EPSILON);
652: 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));
653: PetscCall(TaoSNESJacobian_PDIPM(snes, X, pdipm->K, pdipm->K, tao));
654: PetscCall(PCSetPostSetUp(pc, NULL));
655: PetscCall(PCSetUp(pc));
656: PetscCall(MatGetInertia(Factor, &nneg, &nzero, &npos));
658: if (npos < pdipm->Nx + pdipm->Nci) {
659: pdipm->deltaw = pdipm->lastdeltaw; /* in case reduction update does not help, this prevents that step from impacting increasing update */
660: while (npos < pdipm->Nx + pdipm->Nci && pdipm->deltaw <= 1. / PETSC_SMALL) { /* increase deltaw */
661: 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));
662: pdipm->deltaw = PetscMin(8 * pdipm->deltaw, PetscPowReal(10, 20));
663: PetscCall(TaoSNESJacobian_PDIPM(snes, X, pdipm->K, pdipm->K, tao));
664: PetscCall(PCSetUp(pc));
665: PetscCall(MatGetInertia(Factor, &nneg, &nzero, &npos));
666: }
668: PetscCheck(pdipm->deltaw < 1. / PETSC_SMALL, PetscObjectComm((PetscObject)tao), PETSC_ERR_CONV_FAILED, "Reached maximum delta w will not converge, try different initial x0");
670: PetscCall(PetscInfo(tao, "Updated deltaw %g\n", (double)pdipm->deltaw));
671: pdipm->lastdeltaw = pdipm->deltaw;
672: pdipm->deltaw = 0.0;
673: }
674: }
676: if (nzero) { /* Jacobian is singular */
677: if (pdipm->deltac == 0.0) {
678: pdipm->deltac = PETSC_SQRT_MACHINE_EPSILON;
679: } else {
680: pdipm->deltac = pdipm->deltac * PetscPowReal(pdipm->mu, .25);
681: }
682: PetscCall(PetscInfo(tao, "Updated deltac=%g, MatInertia: nneg %" PetscInt_FMT ", nzero %" PetscInt_FMT "(!=0), npos %" PetscInt_FMT "\n", (double)pdipm->deltac, nneg, nzero, npos));
683: PetscCall(TaoSNESJacobian_PDIPM(snes, X, pdipm->K, pdipm->K, tao));
684: PetscCall(PCSetPostSetUp(pc, NULL));
685: PetscCall(PCSetUp(pc));
686: PetscCall(MatGetInertia(Factor, &nneg, &nzero, &npos));
687: }
688: PetscCall(PCSetPostSetUp(pc, PCPostSetUp_PDIPM));
689: PetscFunctionReturn(PETSC_SUCCESS);
690: }
692: /*
693: SNESLineSearch_PDIPM - Custom line search used with PDIPM.
695: Collective
697: Notes:
698: This routine employs a simple backtracking line-search to keep
699: the slack variables (z) and inequality constraints Lagrange multipliers
700: (lambdai) positive, i.e., z,lambdai >=0. It does this by calculating scalars
701: alpha_p and alpha_d to keep z,lambdai non-negative. The decision (x), and the
702: slack variables are updated as X = X - alpha_d*dx. The constraint multipliers
703: are updated as Lambdai = Lambdai + alpha_p*dLambdai. The barrier parameter mu
704: is also updated as mu = mu + z'lambdai/Nci
705: */
706: static PetscErrorCode SNESLineSearch_PDIPM(SNESLineSearch linesearch, void *ctx)
707: {
708: Tao tao = (Tao)ctx;
709: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
710: SNES snes;
711: Vec X, F, Y;
712: PetscInt i, iter;
713: PetscReal alpha_p = 1.0, alpha_d = 1.0, alpha[4];
714: PetscScalar *Xarr, *z, *lambdai, dot, *taosolarr;
715: const PetscScalar *dXarr, *dz, *dlambdai;
717: PetscFunctionBegin;
718: PetscCall(SNESLineSearchGetSNES(linesearch, &snes));
719: PetscCall(SNESGetIterationNumber(snes, &iter));
721: PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_SUCCEEDED));
722: PetscCall(SNESLineSearchGetVecs(linesearch, &X, &F, &Y, NULL, NULL));
724: PetscCall(VecGetArrayWrite(X, &Xarr));
725: PetscCall(VecGetArrayRead(Y, &dXarr));
726: z = Xarr + pdipm->off_z;
727: dz = dXarr + pdipm->off_z;
728: for (i = 0; i < pdipm->nci; i++) {
729: if (z[i] - dz[i] < 0.0) alpha_p = PetscMin(alpha_p, 0.9999 * z[i] / dz[i]);
730: }
732: lambdai = Xarr + pdipm->off_lambdai;
733: dlambdai = dXarr + pdipm->off_lambdai;
735: for (i = 0; i < pdipm->nci; i++) {
736: if (lambdai[i] - dlambdai[i] < 0.0) alpha_d = PetscMin(0.9999 * lambdai[i] / dlambdai[i], alpha_d);
737: }
739: alpha[0] = alpha_p;
740: alpha[1] = alpha_d;
741: PetscCall(VecRestoreArrayRead(Y, &dXarr));
742: PetscCall(VecRestoreArrayWrite(X, &Xarr));
744: /* alpha = min(alpha) over all processes */
745: PetscCallMPI(MPIU_Allreduce(alpha, alpha + 2, 2, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)tao)));
747: alpha_p = alpha[2];
748: alpha_d = alpha[3];
750: /* X = X - alpha * Y */
751: PetscCall(VecGetArrayWrite(X, &Xarr));
752: PetscCall(VecGetArrayRead(Y, &dXarr));
753: for (i = 0; i < pdipm->nx; i++) Xarr[i] -= alpha_p * dXarr[i];
754: for (i = 0; i < pdipm->nce; i++) Xarr[i + pdipm->off_lambdae] -= alpha_d * dXarr[i + pdipm->off_lambdae];
756: for (i = 0; i < pdipm->nci; i++) {
757: Xarr[i + pdipm->off_lambdai] -= alpha_d * dXarr[i + pdipm->off_lambdai];
758: Xarr[i + pdipm->off_z] -= alpha_p * dXarr[i + pdipm->off_z];
759: }
760: PetscCall(VecGetArrayWrite(tao->solution, &taosolarr));
761: PetscCall(PetscMemcpy(taosolarr, Xarr, pdipm->nx * sizeof(PetscScalar)));
762: PetscCall(VecRestoreArrayWrite(tao->solution, &taosolarr));
764: PetscCall(VecRestoreArrayWrite(X, &Xarr));
765: PetscCall(VecRestoreArrayRead(Y, &dXarr));
767: /* Update mu = mu_update_factor * dot(z,lambdai)/pdipm->nci at updated X */
768: if (pdipm->z) PetscCall(VecDot(pdipm->z, pdipm->lambdai, &dot));
769: else dot = 0.0;
771: /* if (PetscAbsReal(pdipm->gradL) < 0.9*pdipm->mu) */
772: pdipm->mu = pdipm->mu_update_factor * dot / pdipm->Nci;
774: /* Update F; get tao->residual and tao->cnorm */
775: PetscCall(TaoSNESFunction_PDIPM_residual(snes, X, F, (void *)tao));
777: tao->niter++;
778: PetscCall(TaoLogConvergenceHistory(tao, pdipm->obj, tao->residual, tao->cnorm, tao->niter));
779: PetscCall(TaoMonitor(tao, tao->niter, pdipm->obj, tao->residual, tao->cnorm, pdipm->mu));
781: PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
782: if (tao->reason) PetscCall(SNESSetConvergedReason(snes, SNES_CONVERGED_FNORM_ABS));
783: PetscFunctionReturn(PETSC_SUCCESS);
784: }
786: static PetscErrorCode TaoSolve_PDIPM(Tao tao)
787: {
788: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
789: SNESLineSearch linesearch; /* SNESLineSearch context */
790: Vec dummy;
792: PetscFunctionBegin;
793: 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");
795: /* Initialize all variables */
796: PetscCall(TaoPDIPMInitializeSolution(tao));
798: /* Set linesearch */
799: PetscCall(SNESGetLineSearch(pdipm->snes, &linesearch));
800: PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHSHELL));
801: PetscCall(SNESLineSearchShellSetApply(linesearch, SNESLineSearch_PDIPM, tao));
802: PetscCall(SNESLineSearchSetFromOptions(linesearch));
804: tao->reason = TAO_CONTINUE_ITERATING;
806: /* -tao_monitor for iteration 0 and check convergence */
807: PetscCall(VecDuplicate(pdipm->X, &dummy));
808: PetscCall(TaoSNESFunction_PDIPM_residual(pdipm->snes, pdipm->X, dummy, (void *)tao));
810: PetscCall(TaoLogConvergenceHistory(tao, pdipm->obj, tao->residual, tao->cnorm, tao->niter));
811: PetscCall(TaoMonitor(tao, tao->niter, pdipm->obj, tao->residual, tao->cnorm, pdipm->mu));
812: PetscCall(VecDestroy(&dummy));
813: PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
814: if (tao->reason) PetscCall(SNESSetConvergedReason(pdipm->snes, SNES_CONVERGED_FNORM_ABS));
816: while (tao->reason == TAO_CONTINUE_ITERATING) {
817: SNESConvergedReason reason;
818: PetscCall(SNESSolve(pdipm->snes, NULL, pdipm->X));
820: /* Check SNES convergence */
821: PetscCall(SNESGetConvergedReason(pdipm->snes, &reason));
822: if (reason < 0) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)pdipm->snes), "SNES solve did not converged due to reason %s\n", SNESConvergedReasons[reason]));
824: /* Check TAO convergence */
825: PetscCheck(!PetscIsInfOrNanReal(pdipm->obj), PETSC_COMM_SELF, PETSC_ERR_SUP, "User-provided compute function generated Inf or NaN");
826: }
827: PetscFunctionReturn(PETSC_SUCCESS);
828: }
830: static PetscErrorCode TaoView_PDIPM(Tao tao, PetscViewer viewer)
831: {
832: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
834: PetscFunctionBegin;
835: tao->constrained = PETSC_TRUE;
836: PetscCall(PetscViewerASCIIPushTab(viewer));
837: PetscCall(PetscViewerASCIIPrintf(viewer, "Number of prime=%" PetscInt_FMT ", Number of dual=%" PetscInt_FMT "\n", pdipm->Nx + pdipm->Nci, pdipm->Nce + pdipm->Nci));
838: if (pdipm->kkt_pd) PetscCall(PetscViewerASCIIPrintf(viewer, "KKT shifts deltaw=%g, deltac=%g\n", (double)pdipm->deltaw, (double)pdipm->deltac));
839: PetscCall(PetscViewerASCIIPopTab(viewer));
840: PetscFunctionReturn(PETSC_SUCCESS);
841: }
843: static PetscErrorCode TaoSetup_PDIPM(Tao tao)
844: {
845: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
846: MPI_Comm comm;
847: PetscMPIInt size;
848: PetscInt row, col, Jcrstart, Jcrend, k, tmp, nc, proc, *nh_all, *ng_all;
849: PetscInt offset, *xa, *xb, i, j, rstart, rend;
850: PetscScalar one = 1.0, neg_one = -1.0;
851: const PetscInt *cols, *rranges, *cranges, *aj, *ranges;
852: const PetscScalar *aa, *Xarr;
853: Mat J;
854: Mat Jce_xfixed_trans, Jci_xb_trans;
855: PetscInt *dnz, *onz, rjstart, nx_all, *nce_all, *Jranges, cols1[2];
857: PetscFunctionBegin;
858: PetscCall(PetscObjectGetComm((PetscObject)tao, &comm));
859: PetscCallMPI(MPI_Comm_size(comm, &size));
861: /* (1) Setup Bounds and create Tao vectors */
862: PetscCall(TaoPDIPMSetUpBounds(tao));
864: if (!tao->gradient) {
865: PetscCall(VecDuplicate(tao->solution, &tao->gradient));
866: PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));
867: }
869: /* (2) Get sizes */
870: /* Size of vector x - This is set by TaoSetSolution */
871: PetscCall(VecGetSize(tao->solution, &pdipm->Nx));
872: PetscCall(VecGetLocalSize(tao->solution, &pdipm->nx));
874: /* Size of equality constraints and vectors */
875: if (tao->constraints_equality) {
876: PetscCall(VecGetSize(tao->constraints_equality, &pdipm->Ng));
877: PetscCall(VecGetLocalSize(tao->constraints_equality, &pdipm->ng));
878: } else {
879: pdipm->ng = pdipm->Ng = 0;
880: }
882: pdipm->nce = pdipm->ng + pdipm->nxfixed;
883: pdipm->Nce = pdipm->Ng + pdipm->Nxfixed;
885: /* Size of inequality constraints and vectors */
886: if (tao->constraints_inequality) {
887: PetscCall(VecGetSize(tao->constraints_inequality, &pdipm->Nh));
888: PetscCall(VecGetLocalSize(tao->constraints_inequality, &pdipm->nh));
889: } else {
890: pdipm->nh = pdipm->Nh = 0;
891: }
893: pdipm->nci = pdipm->nh + pdipm->nxlb + pdipm->nxub + 2 * pdipm->nxbox;
894: pdipm->Nci = pdipm->Nh + pdipm->Nxlb + pdipm->Nxub + 2 * pdipm->Nxbox;
896: /* Full size of the KKT system to be solved */
897: pdipm->n = pdipm->nx + pdipm->nce + 2 * pdipm->nci;
898: pdipm->N = pdipm->Nx + pdipm->Nce + 2 * pdipm->Nci;
900: /* (3) Offsets for subvectors */
901: pdipm->off_lambdae = pdipm->nx;
902: pdipm->off_lambdai = pdipm->off_lambdae + pdipm->nce;
903: pdipm->off_z = pdipm->off_lambdai + pdipm->nci;
905: /* (4) Create vectors and subvectors */
906: /* Ce and Ci vectors */
907: PetscCall(VecCreate(comm, &pdipm->ce));
908: PetscCall(VecSetSizes(pdipm->ce, pdipm->nce, pdipm->Nce));
909: PetscCall(VecSetFromOptions(pdipm->ce));
911: PetscCall(VecCreate(comm, &pdipm->ci));
912: PetscCall(VecSetSizes(pdipm->ci, pdipm->nci, pdipm->Nci));
913: PetscCall(VecSetFromOptions(pdipm->ci));
915: /* X=[x; lambdae; lambdai; z] for the big KKT system */
916: PetscCall(VecCreate(comm, &pdipm->X));
917: PetscCall(VecSetSizes(pdipm->X, pdipm->n, pdipm->N));
918: PetscCall(VecSetFromOptions(pdipm->X));
920: /* Subvectors; they share local arrays with X */
921: PetscCall(VecGetArrayRead(pdipm->X, &Xarr));
922: /* x shares local array with X.x */
923: if (pdipm->Nx) PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nx, pdipm->Nx, Xarr, &pdipm->x));
925: /* lambdae shares local array with X.lambdae */
926: if (pdipm->Nce) PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nce, pdipm->Nce, Xarr + pdipm->off_lambdae, &pdipm->lambdae));
928: /* tao->DE shares local array with X.lambdae_g */
929: if (pdipm->Ng) {
930: PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->ng, pdipm->Ng, Xarr + pdipm->off_lambdae, &tao->DE));
932: PetscCall(VecCreate(comm, &pdipm->lambdae_xfixed));
933: PetscCall(VecSetSizes(pdipm->lambdae_xfixed, pdipm->nxfixed, PETSC_DECIDE));
934: PetscCall(VecSetFromOptions(pdipm->lambdae_xfixed));
935: }
937: if (pdipm->Nci) {
938: /* lambdai shares local array with X.lambdai */
939: PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nci, pdipm->Nci, Xarr + pdipm->off_lambdai, &pdipm->lambdai));
941: /* z for slack variables; it shares local array with X.z */
942: PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nci, pdipm->Nci, Xarr + pdipm->off_z, &pdipm->z));
943: }
945: /* tao->DI which shares local array with X.lambdai_h */
946: if (pdipm->Nh) PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nh, pdipm->Nh, Xarr + pdipm->off_lambdai, &tao->DI));
947: PetscCall(VecCreate(comm, &pdipm->lambdai_xb));
948: PetscCall(VecSetSizes(pdipm->lambdai_xb, pdipm->nci - pdipm->nh, PETSC_DECIDE));
949: PetscCall(VecSetFromOptions(pdipm->lambdai_xb));
951: PetscCall(VecRestoreArrayRead(pdipm->X, &Xarr));
953: /* (5) Create Jacobians Jce_xfixed and Jci */
954: /* (5.1) PDIPM Jacobian of equality bounds cebound(x) = J_nxfixed */
955: if (pdipm->Nxfixed) {
956: /* Create Jce_xfixed */
957: PetscCall(MatCreate(comm, &pdipm->Jce_xfixed));
958: PetscCall(MatSetSizes(pdipm->Jce_xfixed, pdipm->nxfixed, pdipm->nx, PETSC_DECIDE, pdipm->Nx));
959: PetscCall(MatSetFromOptions(pdipm->Jce_xfixed));
960: PetscCall(MatSeqAIJSetPreallocation(pdipm->Jce_xfixed, 1, NULL));
961: PetscCall(MatMPIAIJSetPreallocation(pdipm->Jce_xfixed, 1, NULL, 1, NULL));
963: PetscCall(MatGetOwnershipRange(pdipm->Jce_xfixed, &Jcrstart, &Jcrend));
964: PetscCall(ISGetIndices(pdipm->isxfixed, &cols));
965: k = 0;
966: for (row = Jcrstart; row < Jcrend; row++) {
967: PetscCall(MatSetValues(pdipm->Jce_xfixed, 1, &row, 1, cols + k, &one, INSERT_VALUES));
968: k++;
969: }
970: PetscCall(ISRestoreIndices(pdipm->isxfixed, &cols));
971: PetscCall(MatAssemblyBegin(pdipm->Jce_xfixed, MAT_FINAL_ASSEMBLY));
972: PetscCall(MatAssemblyEnd(pdipm->Jce_xfixed, MAT_FINAL_ASSEMBLY));
973: }
975: /* (5.2) PDIPM inequality Jacobian Jci = [tao->jacobian_inequality; ...] */
976: PetscCall(MatCreate(comm, &pdipm->Jci_xb));
977: PetscCall(MatSetSizes(pdipm->Jci_xb, pdipm->nci - pdipm->nh, pdipm->nx, PETSC_DECIDE, pdipm->Nx));
978: PetscCall(MatSetFromOptions(pdipm->Jci_xb));
979: PetscCall(MatSeqAIJSetPreallocation(pdipm->Jci_xb, 1, NULL));
980: PetscCall(MatMPIAIJSetPreallocation(pdipm->Jci_xb, 1, NULL, 1, NULL));
982: PetscCall(MatGetOwnershipRange(pdipm->Jci_xb, &Jcrstart, &Jcrend));
983: offset = Jcrstart;
984: if (pdipm->Nxub) {
985: /* Add xub to Jci_xb */
986: PetscCall(ISGetIndices(pdipm->isxub, &cols));
987: k = 0;
988: for (row = offset; row < offset + pdipm->nxub; row++) {
989: PetscCall(MatSetValues(pdipm->Jci_xb, 1, &row, 1, cols + k, &neg_one, INSERT_VALUES));
990: k++;
991: }
992: PetscCall(ISRestoreIndices(pdipm->isxub, &cols));
993: }
995: if (pdipm->Nxlb) {
996: /* Add xlb to Jci_xb */
997: PetscCall(ISGetIndices(pdipm->isxlb, &cols));
998: k = 0;
999: offset += pdipm->nxub;
1000: for (row = offset; row < offset + pdipm->nxlb; row++) {
1001: PetscCall(MatSetValues(pdipm->Jci_xb, 1, &row, 1, cols + k, &one, INSERT_VALUES));
1002: k++;
1003: }
1004: PetscCall(ISRestoreIndices(pdipm->isxlb, &cols));
1005: }
1007: /* Add xbox to Jci_xb */
1008: if (pdipm->Nxbox) {
1009: PetscCall(ISGetIndices(pdipm->isxbox, &cols));
1010: k = 0;
1011: offset += pdipm->nxlb;
1012: for (row = offset; row < offset + pdipm->nxbox; row++) {
1013: PetscCall(MatSetValues(pdipm->Jci_xb, 1, &row, 1, cols + k, &neg_one, INSERT_VALUES));
1014: tmp = row + pdipm->nxbox;
1015: PetscCall(MatSetValues(pdipm->Jci_xb, 1, &tmp, 1, cols + k, &one, INSERT_VALUES));
1016: k++;
1017: }
1018: PetscCall(ISRestoreIndices(pdipm->isxbox, &cols));
1019: }
1021: PetscCall(MatAssemblyBegin(pdipm->Jci_xb, MAT_FINAL_ASSEMBLY));
1022: PetscCall(MatAssemblyEnd(pdipm->Jci_xb, MAT_FINAL_ASSEMBLY));
1023: /* PetscCall(MatView(pdipm->Jci_xb,PETSC_VIEWER_STDOUT_WORLD)); */
1025: /* (6) Set up ISs for PC Fieldsplit */
1026: if (pdipm->solve_reduced_kkt) {
1027: PetscCall(PetscMalloc2(pdipm->nx + pdipm->nce, &xa, 2 * pdipm->nci, &xb));
1028: for (i = 0; i < pdipm->nx + pdipm->nce; i++) xa[i] = i;
1029: for (i = 0; i < 2 * pdipm->nci; i++) xb[i] = pdipm->off_lambdai + i;
1031: PetscCall(ISCreateGeneral(comm, pdipm->nx + pdipm->nce, xa, PETSC_OWN_POINTER, &pdipm->is1));
1032: PetscCall(ISCreateGeneral(comm, 2 * pdipm->nci, xb, PETSC_OWN_POINTER, &pdipm->is2));
1033: }
1035: /* (7) Gather offsets from all processes */
1036: PetscCall(PetscMalloc1(size, &pdipm->nce_all));
1038: /* Get rstart of KKT matrix */
1039: PetscCallMPI(MPI_Scan(&pdipm->n, &rstart, 1, MPIU_INT, MPI_SUM, comm));
1040: rstart -= pdipm->n;
1042: PetscCallMPI(MPI_Allgather(&pdipm->nce, 1, MPIU_INT, pdipm->nce_all, 1, MPIU_INT, comm));
1044: PetscCall(PetscMalloc3(size, &ng_all, size, &nh_all, size, &Jranges));
1045: PetscCallMPI(MPI_Allgather(&rstart, 1, MPIU_INT, Jranges, 1, MPIU_INT, comm));
1046: PetscCallMPI(MPI_Allgather(&pdipm->nh, 1, MPIU_INT, nh_all, 1, MPIU_INT, comm));
1047: PetscCallMPI(MPI_Allgather(&pdipm->ng, 1, MPIU_INT, ng_all, 1, MPIU_INT, comm));
1049: PetscCall(MatGetOwnershipRanges(tao->hessian, &rranges));
1050: PetscCall(MatGetOwnershipRangesColumn(tao->hessian, &cranges));
1052: if (pdipm->Ng) {
1053: PetscCall(TaoComputeJacobianEquality(tao, tao->solution, tao->jacobian_equality, tao->jacobian_equality_pre));
1054: PetscCall(MatTranspose(tao->jacobian_equality, MAT_INITIAL_MATRIX, &pdipm->jac_equality_trans));
1055: }
1056: if (pdipm->Nh) {
1057: PetscCall(TaoComputeJacobianInequality(tao, tao->solution, tao->jacobian_inequality, tao->jacobian_inequality_pre));
1058: PetscCall(MatTranspose(tao->jacobian_inequality, MAT_INITIAL_MATRIX, &pdipm->jac_inequality_trans));
1059: }
1061: /* Count dnz,onz for preallocation of KKT matrix */
1062: nce_all = pdipm->nce_all;
1064: if (pdipm->Nxfixed) PetscCall(MatTranspose(pdipm->Jce_xfixed, MAT_INITIAL_MATRIX, &Jce_xfixed_trans));
1065: PetscCall(MatTranspose(pdipm->Jci_xb, MAT_INITIAL_MATRIX, &Jci_xb_trans));
1067: MatPreallocateBegin(comm, pdipm->n, pdipm->n, dnz, onz);
1069: /* 1st row block of KKT matrix: [Wxx; gradCe'; -gradCi'; 0] */
1070: PetscCall(TaoPDIPMEvaluateFunctionsAndJacobians(tao, pdipm->x));
1071: PetscCall(TaoComputeHessian(tao, tao->solution, tao->hessian, tao->hessian_pre));
1073: /* Insert tao->hessian */
1074: PetscCall(MatGetOwnershipRange(tao->hessian, &rjstart, NULL));
1075: for (i = 0; i < pdipm->nx; i++) {
1076: row = rstart + i;
1078: PetscCall(MatGetRow(tao->hessian, i + rjstart, &nc, &aj, NULL));
1079: proc = 0;
1080: for (j = 0; j < nc; j++) {
1081: while (aj[j] >= cranges[proc + 1]) proc++;
1082: col = aj[j] - cranges[proc] + Jranges[proc];
1083: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1084: }
1085: PetscCall(MatRestoreRow(tao->hessian, i + rjstart, &nc, &aj, NULL));
1087: if (pdipm->ng) {
1088: /* Insert grad g' */
1089: PetscCall(MatGetRow(pdipm->jac_equality_trans, i + rjstart, &nc, &aj, NULL));
1090: PetscCall(MatGetOwnershipRanges(tao->jacobian_equality, &ranges));
1091: proc = 0;
1092: for (j = 0; j < nc; j++) {
1093: /* find row ownership of */
1094: while (aj[j] >= ranges[proc + 1]) proc++;
1095: nx_all = rranges[proc + 1] - rranges[proc];
1096: col = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
1097: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1098: }
1099: PetscCall(MatRestoreRow(pdipm->jac_equality_trans, i + rjstart, &nc, &aj, NULL));
1100: }
1102: /* Insert Jce_xfixed^T' */
1103: if (pdipm->nxfixed) {
1104: PetscCall(MatGetRow(Jce_xfixed_trans, i + rjstart, &nc, &aj, NULL));
1105: PetscCall(MatGetOwnershipRanges(pdipm->Jce_xfixed, &ranges));
1106: proc = 0;
1107: for (j = 0; j < nc; j++) {
1108: /* find row ownership of */
1109: while (aj[j] >= ranges[proc + 1]) proc++;
1110: nx_all = rranges[proc + 1] - rranges[proc];
1111: col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + ng_all[proc];
1112: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1113: }
1114: PetscCall(MatRestoreRow(Jce_xfixed_trans, i + rjstart, &nc, &aj, NULL));
1115: }
1117: if (pdipm->nh) {
1118: /* Insert -grad h' */
1119: PetscCall(MatGetRow(pdipm->jac_inequality_trans, i + rjstart, &nc, &aj, NULL));
1120: PetscCall(MatGetOwnershipRanges(tao->jacobian_inequality, &ranges));
1121: proc = 0;
1122: for (j = 0; j < nc; j++) {
1123: /* find row ownership of */
1124: while (aj[j] >= ranges[proc + 1]) proc++;
1125: nx_all = rranges[proc + 1] - rranges[proc];
1126: col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
1127: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1128: }
1129: PetscCall(MatRestoreRow(pdipm->jac_inequality_trans, i + rjstart, &nc, &aj, NULL));
1130: }
1132: /* Insert Jci_xb^T' */
1133: PetscCall(MatGetRow(Jci_xb_trans, i + rjstart, &nc, &aj, NULL));
1134: PetscCall(MatGetOwnershipRanges(pdipm->Jci_xb, &ranges));
1135: proc = 0;
1136: for (j = 0; j < nc; j++) {
1137: /* find row ownership of */
1138: while (aj[j] >= ranges[proc + 1]) proc++;
1139: nx_all = rranges[proc + 1] - rranges[proc];
1140: col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc] + nh_all[proc];
1141: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1142: }
1143: PetscCall(MatRestoreRow(Jci_xb_trans, i + rjstart, &nc, &aj, NULL));
1144: }
1146: /* 2nd Row block of KKT matrix: [grad Ce, deltac*I, 0, 0] */
1147: if (pdipm->Ng) {
1148: PetscCall(MatGetOwnershipRange(tao->jacobian_equality, &rjstart, NULL));
1149: for (i = 0; i < pdipm->ng; i++) {
1150: row = rstart + pdipm->off_lambdae + i;
1152: PetscCall(MatGetRow(tao->jacobian_equality, i + rjstart, &nc, &aj, NULL));
1153: proc = 0;
1154: for (j = 0; j < nc; j++) {
1155: while (aj[j] >= cranges[proc + 1]) proc++;
1156: col = aj[j] - cranges[proc] + Jranges[proc];
1157: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz)); /* grad g */
1158: }
1159: PetscCall(MatRestoreRow(tao->jacobian_equality, i + rjstart, &nc, &aj, NULL));
1160: }
1161: }
1162: /* Jce_xfixed */
1163: if (pdipm->Nxfixed) {
1164: PetscCall(MatGetOwnershipRange(pdipm->Jce_xfixed, &Jcrstart, NULL));
1165: for (i = 0; i < (pdipm->nce - pdipm->ng); i++) {
1166: row = rstart + pdipm->off_lambdae + pdipm->ng + i;
1168: PetscCall(MatGetRow(pdipm->Jce_xfixed, i + Jcrstart, &nc, &cols, NULL));
1169: PetscCheck(nc == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "nc != 1");
1171: proc = 0;
1172: j = 0;
1173: while (cols[j] >= cranges[proc + 1]) proc++;
1174: col = cols[j] - cranges[proc] + Jranges[proc];
1175: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1176: PetscCall(MatRestoreRow(pdipm->Jce_xfixed, i + Jcrstart, &nc, &cols, NULL));
1177: }
1178: }
1180: /* 3rd Row block of KKT matrix: [ gradCi, 0, deltac*I, -I] */
1181: if (pdipm->Nh) {
1182: PetscCall(MatGetOwnershipRange(tao->jacobian_inequality, &rjstart, NULL));
1183: for (i = 0; i < pdipm->nh; i++) {
1184: row = rstart + pdipm->off_lambdai + i;
1186: PetscCall(MatGetRow(tao->jacobian_inequality, i + rjstart, &nc, &aj, NULL));
1187: proc = 0;
1188: for (j = 0; j < nc; j++) {
1189: while (aj[j] >= cranges[proc + 1]) proc++;
1190: col = aj[j] - cranges[proc] + Jranges[proc];
1191: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz)); /* grad h */
1192: }
1193: PetscCall(MatRestoreRow(tao->jacobian_inequality, i + rjstart, &nc, &aj, NULL));
1194: }
1195: /* I */
1196: for (i = 0; i < pdipm->nh; i++) {
1197: row = rstart + pdipm->off_lambdai + i;
1198: col = rstart + pdipm->off_z + i;
1199: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1200: }
1201: }
1203: /* Jci_xb */
1204: PetscCall(MatGetOwnershipRange(pdipm->Jci_xb, &Jcrstart, NULL));
1205: for (i = 0; i < (pdipm->nci - pdipm->nh); i++) {
1206: row = rstart + pdipm->off_lambdai + pdipm->nh + i;
1208: PetscCall(MatGetRow(pdipm->Jci_xb, i + Jcrstart, &nc, &cols, NULL));
1209: PetscCheck(nc == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "nc != 1");
1210: proc = 0;
1211: for (j = 0; j < nc; j++) {
1212: while (cols[j] >= cranges[proc + 1]) proc++;
1213: col = cols[j] - cranges[proc] + Jranges[proc];
1214: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1215: }
1216: PetscCall(MatRestoreRow(pdipm->Jci_xb, i + Jcrstart, &nc, &cols, NULL));
1217: /* I */
1218: col = rstart + pdipm->off_z + pdipm->nh + i;
1219: PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1220: }
1222: /* 4-th Row block of KKT matrix: Z and Ci */
1223: for (i = 0; i < pdipm->nci; i++) {
1224: row = rstart + pdipm->off_z + i;
1225: cols1[0] = rstart + pdipm->off_lambdai + i;
1226: cols1[1] = row;
1227: PetscCall(MatPreallocateSet(row, 2, cols1, dnz, onz));
1228: }
1230: /* diagonal entry */
1231: for (i = 0; i < pdipm->n; i++) dnz[i]++; /* diagonal entry */
1233: /* Create KKT matrix */
1234: PetscCall(MatCreate(comm, &J));
1235: PetscCall(MatSetSizes(J, pdipm->n, pdipm->n, PETSC_DECIDE, PETSC_DECIDE));
1236: PetscCall(MatSetFromOptions(J));
1237: PetscCall(MatSeqAIJSetPreallocation(J, 0, dnz));
1238: PetscCall(MatMPIAIJSetPreallocation(J, 0, dnz, 0, onz));
1239: MatPreallocateEnd(dnz, onz);
1240: pdipm->K = J;
1242: /* (8) Insert constant entries to K */
1243: /* Set 0.0 to diagonal of K, so that the solver does not complain *about missing diagonal value */
1244: PetscCall(MatGetOwnershipRange(J, &rstart, &rend));
1245: for (i = rstart; i < rend; i++) PetscCall(MatSetValue(J, i, i, 0.0, INSERT_VALUES));
1246: /* In case Wxx has no diagonal entries preset set diagonal to deltaw given */
1247: if (pdipm->kkt_pd) {
1248: for (i = 0; i < pdipm->nh; i++) {
1249: row = rstart + i;
1250: PetscCall(MatSetValue(J, row, row, pdipm->deltaw, INSERT_VALUES));
1251: }
1252: }
1254: /* Row block of K: [ grad Ce, 0, 0, 0] */
1255: if (pdipm->Nxfixed) {
1256: PetscCall(MatGetOwnershipRange(pdipm->Jce_xfixed, &Jcrstart, NULL));
1257: for (i = 0; i < (pdipm->nce - pdipm->ng); i++) {
1258: row = rstart + pdipm->off_lambdae + pdipm->ng + i;
1260: PetscCall(MatGetRow(pdipm->Jce_xfixed, i + Jcrstart, &nc, &cols, &aa));
1261: proc = 0;
1262: for (j = 0; j < nc; j++) {
1263: while (cols[j] >= cranges[proc + 1]) proc++;
1264: col = cols[j] - cranges[proc] + Jranges[proc];
1265: PetscCall(MatSetValue(J, row, col, aa[j], INSERT_VALUES)); /* grad Ce */
1266: PetscCall(MatSetValue(J, col, row, aa[j], INSERT_VALUES)); /* grad Ce' */
1267: }
1268: PetscCall(MatRestoreRow(pdipm->Jce_xfixed, i + Jcrstart, &nc, &cols, &aa));
1269: }
1270: }
1272: /* Row block of K: [ -grad Ci, 0, 0, I] */
1273: PetscCall(MatGetOwnershipRange(pdipm->Jci_xb, &Jcrstart, NULL));
1274: for (i = 0; i < pdipm->nci - pdipm->nh; i++) {
1275: row = rstart + pdipm->off_lambdai + pdipm->nh + i;
1277: PetscCall(MatGetRow(pdipm->Jci_xb, i + Jcrstart, &nc, &cols, &aa));
1278: proc = 0;
1279: for (j = 0; j < nc; j++) {
1280: while (cols[j] >= cranges[proc + 1]) proc++;
1281: col = cols[j] - cranges[proc] + Jranges[proc];
1282: PetscCall(MatSetValue(J, col, row, -aa[j], INSERT_VALUES));
1283: PetscCall(MatSetValue(J, row, col, -aa[j], INSERT_VALUES));
1284: }
1285: PetscCall(MatRestoreRow(pdipm->Jci_xb, i + Jcrstart, &nc, &cols, &aa));
1287: col = rstart + pdipm->off_z + pdipm->nh + i;
1288: PetscCall(MatSetValue(J, row, col, 1, INSERT_VALUES));
1289: }
1291: for (i = 0; i < pdipm->nh; i++) {
1292: row = rstart + pdipm->off_lambdai + i;
1293: col = rstart + pdipm->off_z + i;
1294: PetscCall(MatSetValue(J, row, col, 1, INSERT_VALUES));
1295: }
1297: /* Row block of K: [ 0, 0, I, ...] */
1298: for (i = 0; i < pdipm->nci; i++) {
1299: row = rstart + pdipm->off_z + i;
1300: col = rstart + pdipm->off_lambdai + i;
1301: PetscCall(MatSetValue(J, row, col, 1, INSERT_VALUES));
1302: }
1304: if (pdipm->Nxfixed) PetscCall(MatDestroy(&Jce_xfixed_trans));
1305: PetscCall(MatDestroy(&Jci_xb_trans));
1306: PetscCall(PetscFree3(ng_all, nh_all, Jranges));
1308: /* (9) Set up nonlinear solver SNES */
1309: PetscCall(SNESSetFunction(pdipm->snes, NULL, TaoSNESFunction_PDIPM, (void *)tao));
1310: PetscCall(SNESSetJacobian(pdipm->snes, J, J, TaoSNESJacobian_PDIPM, (void *)tao));
1312: if (pdipm->solve_reduced_kkt) {
1313: PC pc;
1314: PetscCall(KSPGetPC(tao->ksp, &pc));
1315: PetscCall(PCSetType(pc, PCFIELDSPLIT));
1316: PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
1317: PetscCall(PCFieldSplitSetIS(pc, "2", pdipm->is2));
1318: PetscCall(PCFieldSplitSetIS(pc, "1", pdipm->is1));
1319: }
1320: PetscCall(SNESSetFromOptions(pdipm->snes));
1322: /* (10) Setup PCPostSetUp() for pdipm->solve_symmetric_kkt */
1323: if (pdipm->solve_symmetric_kkt) {
1324: KSP ksp;
1325: PC pc;
1326: PetscBool isCHOL;
1328: PetscCall(SNESGetKSP(pdipm->snes, &ksp));
1329: PetscCall(KSPGetPC(ksp, &pc));
1330: PetscCall(PCSetPostSetUp(pc, PCPostSetUp_PDIPM));
1332: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCCHOLESKY, &isCHOL));
1333: if (isCHOL) {
1334: Mat Factor;
1336: PetscCheck(PetscDefined(HAVE_MUMPS), PetscObjectComm((PetscObject)tao), PETSC_ERR_SUP, "Requires external package MUMPS");
1337: PetscCall(PCFactorGetMatrix(pc, &Factor));
1338: PetscCall(MatMumpsSetIcntl(Factor, 24, 1)); /* detection of null pivot rows */
1339: if (size > 1) PetscCall(MatMumpsSetIcntl(Factor, 13, 1)); /* parallelism of the root node (enable ScaLAPACK) and its splitting */
1340: }
1341: }
1342: PetscFunctionReturn(PETSC_SUCCESS);
1343: }
1345: static PetscErrorCode TaoDestroy_PDIPM(Tao tao)
1346: {
1347: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
1349: PetscFunctionBegin;
1350: /* Freeing Vectors assocaiated with KKT (X) */
1351: PetscCall(VecDestroy(&pdipm->x)); /* Solution x */
1352: PetscCall(VecDestroy(&pdipm->lambdae)); /* Equality constraints lagrangian multiplier*/
1353: PetscCall(VecDestroy(&pdipm->lambdai)); /* Inequality constraints lagrangian multiplier*/
1354: PetscCall(VecDestroy(&pdipm->z)); /* Slack variables */
1355: PetscCall(VecDestroy(&pdipm->X)); /* Big KKT system vector [x; lambdae; lambdai; z] */
1357: /* work vectors */
1358: PetscCall(VecDestroy(&pdipm->lambdae_xfixed));
1359: PetscCall(VecDestroy(&pdipm->lambdai_xb));
1361: /* Legrangian equality and inequality Vec */
1362: PetscCall(VecDestroy(&pdipm->ce)); /* Vec of equality constraints */
1363: PetscCall(VecDestroy(&pdipm->ci)); /* Vec of inequality constraints */
1365: /* Matrices */
1366: PetscCall(MatDestroy(&pdipm->Jce_xfixed));
1367: PetscCall(MatDestroy(&pdipm->Jci_xb)); /* Jacobian of inequality constraints Jci = [tao->jacobian_inequality ; J(nxub); J(nxlb); J(nxbx)] */
1368: PetscCall(MatDestroy(&pdipm->K));
1370: /* Index Sets */
1371: if (pdipm->Nxub) PetscCall(ISDestroy(&pdipm->isxub)); /* Finite upper bound only -inf < x < ub */
1373: if (pdipm->Nxlb) PetscCall(ISDestroy(&pdipm->isxlb)); /* Finite lower bound only lb <= x < inf */
1375: if (pdipm->Nxfixed) PetscCall(ISDestroy(&pdipm->isxfixed)); /* Fixed variables lb = x = ub */
1377: if (pdipm->Nxbox) PetscCall(ISDestroy(&pdipm->isxbox)); /* Boxed variables lb <= x <= ub */
1379: if (pdipm->Nxfree) PetscCall(ISDestroy(&pdipm->isxfree)); /* Free variables -inf <= x <= inf */
1381: if (pdipm->solve_reduced_kkt) {
1382: PetscCall(ISDestroy(&pdipm->is1));
1383: PetscCall(ISDestroy(&pdipm->is2));
1384: }
1386: /* SNES */
1387: PetscCall(SNESDestroy(&pdipm->snes)); /* Nonlinear solver */
1388: PetscCall(PetscFree(pdipm->nce_all));
1389: PetscCall(MatDestroy(&pdipm->jac_equality_trans));
1390: PetscCall(MatDestroy(&pdipm->jac_inequality_trans));
1392: /* Destroy pdipm */
1393: PetscCall(PetscFree(tao->data)); /* Holding locations of pdipm */
1395: /* Destroy Dual */
1396: PetscCall(VecDestroy(&tao->DE)); /* equality dual */
1397: PetscCall(VecDestroy(&tao->DI)); /* dinequality dual */
1398: PetscFunctionReturn(PETSC_SUCCESS);
1399: }
1401: static PetscErrorCode TaoSetFromOptions_PDIPM(Tao tao, PetscOptionItems PetscOptionsObject)
1402: {
1403: TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;
1405: PetscFunctionBegin;
1406: PetscOptionsHeadBegin(PetscOptionsObject, "PDIPM method for constrained optimization");
1407: 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));
1408: 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));
1409: PetscCall(PetscOptionsBool("-tao_pdipm_solve_reduced_kkt", "Solve reduced KKT system using Schur-complement", NULL, pdipm->solve_reduced_kkt, &pdipm->solve_reduced_kkt, NULL));
1410: PetscCall(PetscOptionsReal("-tao_pdipm_mu_update_factor", "Update scalar for barrier parameter (mu) update", NULL, pdipm->mu_update_factor, &pdipm->mu_update_factor, NULL));
1411: PetscCall(PetscOptionsBool("-tao_pdipm_symmetric_kkt", "Solve non reduced symmetric KKT system", NULL, pdipm->solve_symmetric_kkt, &pdipm->solve_symmetric_kkt, NULL));
1412: PetscCall(PetscOptionsBool("-tao_pdipm_kkt_shift_pd", "Add shifts to make KKT matrix positive definite", NULL, pdipm->kkt_pd, &pdipm->kkt_pd, NULL));
1413: PetscOptionsHeadEnd();
1414: PetscFunctionReturn(PETSC_SUCCESS);
1415: }
1417: /*MC
1418: TAOPDIPM - Barrier-based primal-dual interior point algorithm for generally constrained optimization.
1420: Options Database Keys:
1421: + -tao_pdipm_push_init_lambdai - parameter to push initial dual variables away from bounds (> 0)
1422: . -tao_pdipm_push_init_slack - parameter to push initial slack variables away from bounds (> 0)
1423: . -tao_pdipm_mu_update_factor - update scalar for barrier parameter (mu) update (> 0)
1424: . -tao_pdipm_symmetric_kkt - Solve non-reduced symmetric KKT system
1425: - -tao_pdipm_kkt_shift_pd - Add shifts to make KKT matrix positive definite
1427: Level: beginner
1429: .seealso: `TAOPDIPM`, `Tao`, `TaoType`
1430: M*/
1432: PETSC_EXTERN PetscErrorCode TaoCreate_PDIPM(Tao tao)
1433: {
1434: TAO_PDIPM *pdipm;
1435: PC pc;
1437: PetscFunctionBegin;
1438: tao->ops->setup = TaoSetup_PDIPM;
1439: tao->ops->solve = TaoSolve_PDIPM;
1440: tao->ops->setfromoptions = TaoSetFromOptions_PDIPM;
1441: tao->ops->view = TaoView_PDIPM;
1442: tao->ops->destroy = TaoDestroy_PDIPM;
1444: PetscCall(PetscNew(&pdipm));
1445: tao->data = (void *)pdipm;
1447: pdipm->nx = pdipm->Nx = 0;
1448: pdipm->nxfixed = pdipm->Nxfixed = 0;
1449: pdipm->nxlb = pdipm->Nxlb = 0;
1450: pdipm->nxub = pdipm->Nxub = 0;
1451: pdipm->nxbox = pdipm->Nxbox = 0;
1452: pdipm->nxfree = pdipm->Nxfree = 0;
1454: pdipm->ng = pdipm->Ng = pdipm->nce = pdipm->Nce = 0;
1455: pdipm->nh = pdipm->Nh = pdipm->nci = pdipm->Nci = 0;
1456: pdipm->n = pdipm->N = 0;
1457: pdipm->mu = 1.0;
1458: pdipm->mu_update_factor = 0.1;
1460: pdipm->deltaw = 0.0;
1461: pdipm->lastdeltaw = 3 * 1.e-4;
1462: pdipm->deltac = 0.0;
1463: pdipm->kkt_pd = PETSC_FALSE;
1465: pdipm->push_init_slack = 1.0;
1466: pdipm->push_init_lambdai = 1.0;
1467: pdipm->solve_reduced_kkt = PETSC_FALSE;
1468: pdipm->solve_symmetric_kkt = PETSC_TRUE;
1470: /* Override default settings (unless already changed) */
1471: PetscCall(TaoParametersInitialize(tao));
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: }