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;

284:   PetscFunctionBegin;
285:   PetscCall(MatGetOwnershipRanges(Jpre, &Jranges));
286:   PetscCall(MatGetOwnershipRange(Jpre, &Jrstart, NULL));
287:   PetscCall(MatGetOwnershipRangesColumn(tao->hessian, &rranges));
288:   PetscCall(MatGetOwnershipRangesColumn(tao->hessian, &cranges));

290:   PetscCall(VecGetArrayRead(X, &Xarr));

292:   /* (1) insert Z and Ci to the 4th block of Jpre -- overwrite existing values */
293:   if (pdipm->solve_symmetric_kkt) { /* 1 for eq 17 revised pdipm doc 0 for eq 18 (symmetric KKT) */
294:     vals[0] = 1.0;
295:     for (i = 0; i < pdipm->nci; i++) {
296:       row     = Jrstart + pdipm->off_z + i;
297:       cols[0] = Jrstart + pdipm->off_lambdai + i;
298:       cols[1] = row;
299:       vals[1] = Xarr[pdipm->off_lambdai + i] / Xarr[pdipm->off_z + i];
300:       PetscCall(MatSetValues(Jpre, 1, &row, 2, cols, vals, INSERT_VALUES));
301:     }
302:   } else {
303:     for (i = 0; i < pdipm->nci; i++) {
304:       row     = Jrstart + pdipm->off_z + i;
305:       cols[0] = Jrstart + pdipm->off_lambdai + i;
306:       cols[1] = row;
307:       vals[0] = Xarr[pdipm->off_z + i];
308:       vals[1] = Xarr[pdipm->off_lambdai + i];
309:       PetscCall(MatSetValues(Jpre, 1, &row, 2, cols, vals, INSERT_VALUES));
310:     }
311:   }

313:   /* (2) insert 2nd row block of Jpre: [ grad g, 0, 0, 0] */
314:   if (pdipm->Ng) {
315:     PetscCall(MatGetOwnershipRange(tao->jacobian_equality, &rjstart, NULL));
316:     for (i = 0; i < pdipm->ng; i++) {
317:       row = Jrstart + pdipm->off_lambdae + i;

319:       PetscCall(MatGetRow(tao->jacobian_equality, i + rjstart, &nc, &aj, &aa));
320:       proc = 0;
321:       for (j = 0; j < nc; j++) {
322:         while (aj[j] >= cranges[proc + 1]) proc++;
323:         cols[0] = aj[j] - cranges[proc] + Jranges[proc];
324:         PetscCall(MatSetValue(Jpre, row, cols[0], aa[j], INSERT_VALUES));
325:       }
326:       PetscCall(MatRestoreRow(tao->jacobian_equality, i + rjstart, &nc, &aj, &aa));
327:       if (pdipm->kkt_pd) {
328:         /* add shift \delta_c */
329:         PetscCall(MatSetValue(Jpre, row, row, -pdipm->deltac, INSERT_VALUES));
330:       }
331:     }
332:   }

334:   /* (3) insert 3rd row block of Jpre: [ -grad h, 0, deltac, I] */
335:   if (pdipm->Nh) {
336:     PetscCall(MatGetOwnershipRange(tao->jacobian_inequality, &rjstart, NULL));
337:     for (i = 0; i < pdipm->nh; i++) {
338:       row = Jrstart + pdipm->off_lambdai + i;
339:       PetscCall(MatGetRow(tao->jacobian_inequality, i + rjstart, &nc, &aj, &aa));
340:       proc = 0;
341:       for (j = 0; j < nc; j++) {
342:         while (aj[j] >= cranges[proc + 1]) proc++;
343:         cols[0] = aj[j] - cranges[proc] + Jranges[proc];
344:         PetscCall(MatSetValue(Jpre, row, cols[0], -aa[j], INSERT_VALUES));
345:       }
346:       PetscCall(MatRestoreRow(tao->jacobian_inequality, i + rjstart, &nc, &aj, &aa));
347:       if (pdipm->kkt_pd) {
348:         /* add shift \delta_c */
349:         PetscCall(MatSetValue(Jpre, row, row, -pdipm->deltac, INSERT_VALUES));
350:       }
351:     }
352:   }

354:   /* (4) insert 1st row block of Jpre: [Wxx, grad g', -grad h', 0] */
355:   if (pdipm->Ng) { /* grad g' */
356:     PetscCall(MatTranspose(tao->jacobian_equality, MAT_REUSE_MATRIX, &pdipm->jac_equality_trans));
357:   }
358:   if (pdipm->Nh) { /* grad h' */
359:     PetscCall(MatTranspose(tao->jacobian_inequality, MAT_REUSE_MATRIX, &pdipm->jac_inequality_trans));
360:   }

362:   PetscCall(VecPlaceArray(pdipm->x, Xarr));
363:   PetscCall(TaoComputeHessian(tao, pdipm->x, tao->hessian, tao->hessian_pre));
364:   PetscCall(VecResetArray(pdipm->x));

366:   PetscCall(MatGetOwnershipRange(tao->hessian, &rjstart, NULL));
367:   for (i = 0; i < pdipm->nx; i++) {
368:     row = Jrstart + i;

370:     /* insert Wxx = fxx + ... -- provided by user */
371:     PetscCall(MatGetRow(tao->hessian, i + rjstart, &nc, &aj, &aa));
372:     proc = 0;
373:     for (j = 0; j < nc; j++) {
374:       while (aj[j] >= cranges[proc + 1]) proc++;
375:       cols[0] = aj[j] - cranges[proc] + Jranges[proc];
376:       if (row == cols[0] && pdipm->kkt_pd) {
377:         /* add shift deltaw to Wxx component */
378:         PetscCall(MatSetValue(Jpre, row, cols[0], aa[j] + pdipm->deltaw, INSERT_VALUES));
379:       } else {
380:         PetscCall(MatSetValue(Jpre, row, cols[0], aa[j], INSERT_VALUES));
381:       }
382:     }
383:     PetscCall(MatRestoreRow(tao->hessian, i + rjstart, &nc, &aj, &aa));

385:     /* insert grad g' */
386:     if (pdipm->ng) {
387:       PetscCall(MatGetRow(pdipm->jac_equality_trans, i + rjstart, &nc, &aj, &aa));
388:       PetscCall(MatGetOwnershipRanges(tao->jacobian_equality, &ranges));
389:       proc = 0;
390:       for (j = 0; j < nc; j++) {
391:         /* find row ownership of */
392:         while (aj[j] >= ranges[proc + 1]) proc++;
393:         nx_all  = rranges[proc + 1] - rranges[proc];
394:         cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
395:         PetscCall(MatSetValue(Jpre, row, cols[0], aa[j], INSERT_VALUES));
396:       }
397:       PetscCall(MatRestoreRow(pdipm->jac_equality_trans, i + rjstart, &nc, &aj, &aa));
398:     }

400:     /* insert -grad h' */
401:     if (pdipm->nh) {
402:       PetscCall(MatGetRow(pdipm->jac_inequality_trans, i + rjstart, &nc, &aj, &aa));
403:       PetscCall(MatGetOwnershipRanges(tao->jacobian_inequality, &ranges));
404:       proc = 0;
405:       for (j = 0; j < nc; j++) {
406:         /* find row ownership of */
407:         while (aj[j] >= ranges[proc + 1]) proc++;
408:         nx_all  = rranges[proc + 1] - rranges[proc];
409:         cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
410:         PetscCall(MatSetValue(Jpre, row, cols[0], -aa[j], INSERT_VALUES));
411:       }
412:       PetscCall(MatRestoreRow(pdipm->jac_inequality_trans, i + rjstart, &nc, &aj, &aa));
413:     }
414:   }
415:   PetscCall(VecRestoreArrayRead(X, &Xarr));

417:   /* (6) assemble Jpre and J */
418:   PetscCall(MatAssemblyBegin(Jpre, MAT_FINAL_ASSEMBLY));
419:   PetscCall(MatAssemblyEnd(Jpre, MAT_FINAL_ASSEMBLY));

421:   if (J != Jpre) {
422:     PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
423:     PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
424:   }
425:   PetscFunctionReturn(PETSC_SUCCESS);
426: }

428: /*
429:    TaoSnesFunction_PDIPM - Evaluate KKT function at X

431:    Input Parameter:
432:    snes - SNES context
433:    X - KKT Vector
434:    *ctx - pdipm

436:    Output Parameter:
437:    F - Updated Lagrangian vector
438: */
439: static PetscErrorCode TaoSNESFunction_PDIPM(SNES snes, Vec X, Vec F, void *ctx)
440: {
441:   Tao                tao   = (Tao)ctx;
442:   TAO_PDIPM         *pdipm = (TAO_PDIPM *)tao->data;
443:   PetscScalar       *Farr;
444:   Vec                x, L1;
445:   PetscInt           i;
446:   const PetscScalar *Xarr, *carr, *zarr, *larr;

448:   PetscFunctionBegin;
449:   PetscCall(VecSet(F, 0.0));

451:   PetscCall(VecGetArrayRead(X, &Xarr));
452:   PetscCall(VecGetArrayWrite(F, &Farr));

454:   /* (0) Evaluate f, fx, gradG, gradH at X.x Note: pdipm->x is not changed below */
455:   x = pdipm->x;
456:   PetscCall(VecPlaceArray(x, Xarr));
457:   PetscCall(TaoPDIPMEvaluateFunctionsAndJacobians(tao, x));

459:   /* Update ce, ci, and Jci at X.x */
460:   PetscCall(TaoPDIPMUpdateConstraints(tao, x));
461:   PetscCall(VecResetArray(x));

463:   /* (1) L1 = fx + (gradG'*DE + Jce_xfixed'*lambdae_xfixed) - (gradH'*DI + Jci_xb'*lambdai_xb) */
464:   L1 = pdipm->x;
465:   PetscCall(VecPlaceArray(L1, Farr)); /* L1 = 0.0 */
466:   if (pdipm->Nci) {
467:     if (pdipm->Nh) {
468:       /* L1 += gradH'*DI. Note: tao->DI is not changed below */
469:       PetscCall(VecPlaceArray(tao->DI, Xarr + pdipm->off_lambdai));
470:       PetscCall(MatMultTransposeAdd(tao->jacobian_inequality, tao->DI, L1, L1));
471:       PetscCall(VecResetArray(tao->DI));
472:     }

474:     /* L1 += Jci_xb'*lambdai_xb */
475:     PetscCall(VecPlaceArray(pdipm->lambdai_xb, Xarr + pdipm->off_lambdai + pdipm->nh));
476:     PetscCall(MatMultTransposeAdd(pdipm->Jci_xb, pdipm->lambdai_xb, L1, L1));
477:     PetscCall(VecResetArray(pdipm->lambdai_xb));

479:     /* L1 = - (gradH'*DI + Jci_xb'*lambdai_xb) */
480:     PetscCall(VecScale(L1, -1.0));
481:   }

483:   /* L1 += fx */
484:   PetscCall(VecAXPY(L1, 1.0, tao->gradient));

486:   if (pdipm->Nce) {
487:     if (pdipm->Ng) {
488:       /* L1 += gradG'*DE. Note: tao->DE is not changed below */
489:       PetscCall(VecPlaceArray(tao->DE, Xarr + pdipm->off_lambdae));
490:       PetscCall(MatMultTransposeAdd(tao->jacobian_equality, tao->DE, L1, L1));
491:       PetscCall(VecResetArray(tao->DE));
492:     }
493:     if (pdipm->Nxfixed) {
494:       /* L1 += Jce_xfixed'*lambdae_xfixed */
495:       PetscCall(VecPlaceArray(pdipm->lambdae_xfixed, Xarr + pdipm->off_lambdae + pdipm->ng));
496:       PetscCall(MatMultTransposeAdd(pdipm->Jce_xfixed, pdipm->lambdae_xfixed, L1, L1));
497:       PetscCall(VecResetArray(pdipm->lambdae_xfixed));
498:     }
499:   }
500:   PetscCall(VecResetArray(L1));

502:   /* (2) L2 = ce(x) */
503:   if (pdipm->Nce) {
504:     PetscCall(VecGetArrayRead(pdipm->ce, &carr));
505:     for (i = 0; i < pdipm->nce; i++) Farr[pdipm->off_lambdae + i] = carr[i];
506:     PetscCall(VecRestoreArrayRead(pdipm->ce, &carr));
507:   }

509:   if (pdipm->Nci) {
510:     if (pdipm->solve_symmetric_kkt) {
511:       /* (3) L3 = z - ci(x);
512:          (4) L4 = Lambdai * e - mu/z *e  */
513:       PetscCall(VecGetArrayRead(pdipm->ci, &carr));
514:       larr = Xarr + pdipm->off_lambdai;
515:       zarr = Xarr + pdipm->off_z;
516:       for (i = 0; i < pdipm->nci; i++) {
517:         Farr[pdipm->off_lambdai + i] = zarr[i] - carr[i];
518:         Farr[pdipm->off_z + i]       = larr[i] - pdipm->mu / zarr[i];
519:       }
520:       PetscCall(VecRestoreArrayRead(pdipm->ci, &carr));
521:     } else {
522:       /* (3) L3 = z - ci(x);
523:          (4) L4 = Z * Lambdai * e - mu * e  */
524:       PetscCall(VecGetArrayRead(pdipm->ci, &carr));
525:       larr = Xarr + pdipm->off_lambdai;
526:       zarr = Xarr + pdipm->off_z;
527:       for (i = 0; i < pdipm->nci; i++) {
528:         Farr[pdipm->off_lambdai + i] = zarr[i] - carr[i];
529:         Farr[pdipm->off_z + i]       = zarr[i] * larr[i] - pdipm->mu;
530:       }
531:       PetscCall(VecRestoreArrayRead(pdipm->ci, &carr));
532:     }
533:   }

535:   PetscCall(VecRestoreArrayRead(X, &Xarr));
536:   PetscCall(VecRestoreArrayWrite(F, &Farr));
537:   PetscFunctionReturn(PETSC_SUCCESS);
538: }

540: /*
541:   Evaluate F(X); then update tao->gnorm0, tao->step = mu,
542:   tao->residual = norm2(F_x,F_z) and tao->cnorm = norm2(F_ce,F_ci).
543: */
544: static PetscErrorCode TaoSNESFunction_PDIPM_residual(SNES snes, Vec X, Vec F, void *ctx)
545: {
546:   Tao                tao   = (Tao)ctx;
547:   TAO_PDIPM         *pdipm = (TAO_PDIPM *)tao->data;
548:   PetscScalar       *Farr, *tmparr;
549:   Vec                L1;
550:   PetscInt           i;
551:   PetscReal          res[2], cnorm[2];
552:   const PetscScalar *Xarr = NULL;

554:   PetscFunctionBegin;
555:   PetscCall(TaoSNESFunction_PDIPM(snes, X, F, (void *)tao));
556:   PetscCall(VecGetArrayWrite(F, &Farr));
557:   PetscCall(VecGetArrayRead(X, &Xarr));

559:   /* compute res[0] = norm2(F_x) */
560:   L1 = pdipm->x;
561:   PetscCall(VecPlaceArray(L1, Farr));
562:   PetscCall(VecNorm(L1, NORM_2, &res[0]));
563:   PetscCall(VecResetArray(L1));

565:   /* compute res[1] = norm2(F_z), cnorm[1] = norm2(F_ci) */
566:   if (pdipm->z) {
567:     if (pdipm->solve_symmetric_kkt) {
568:       PetscCall(VecPlaceArray(pdipm->z, Farr + pdipm->off_z));
569:       if (pdipm->Nci) {
570:         PetscCall(VecGetArrayWrite(pdipm->z, &tmparr));
571:         for (i = 0; i < pdipm->nci; i++) tmparr[i] *= Xarr[pdipm->off_z + i];
572:         PetscCall(VecRestoreArrayWrite(pdipm->z, &tmparr));
573:       }

575:       PetscCall(VecNorm(pdipm->z, NORM_2, &res[1]));

577:       if (pdipm->Nci) {
578:         PetscCall(VecGetArrayWrite(pdipm->z, &tmparr));
579:         for (i = 0; i < pdipm->nci; i++) tmparr[i] /= Xarr[pdipm->off_z + i];
580:         PetscCall(VecRestoreArrayWrite(pdipm->z, &tmparr));
581:       }
582:       PetscCall(VecResetArray(pdipm->z));
583:     } else { /* !solve_symmetric_kkt */
584:       PetscCall(VecPlaceArray(pdipm->z, Farr + pdipm->off_z));
585:       PetscCall(VecNorm(pdipm->z, NORM_2, &res[1]));
586:       PetscCall(VecResetArray(pdipm->z));
587:     }

589:     PetscCall(VecPlaceArray(pdipm->ci, Farr + pdipm->off_lambdai));
590:     PetscCall(VecNorm(pdipm->ci, NORM_2, &cnorm[1]));
591:     PetscCall(VecResetArray(pdipm->ci));
592:   } else {
593:     res[1]   = 0.0;
594:     cnorm[1] = 0.0;
595:   }

597:   /* compute cnorm[0] = norm2(F_ce) */
598:   if (pdipm->Nce) {
599:     PetscCall(VecPlaceArray(pdipm->ce, Farr + pdipm->off_lambdae));
600:     PetscCall(VecNorm(pdipm->ce, NORM_2, &cnorm[0]));
601:     PetscCall(VecResetArray(pdipm->ce));
602:   } else cnorm[0] = 0.0;

604:   PetscCall(VecRestoreArrayWrite(F, &Farr));
605:   PetscCall(VecRestoreArrayRead(X, &Xarr));

607:   tao->gnorm0   = tao->residual;
608:   tao->residual = PetscSqrtReal(res[0] * res[0] + res[1] * res[1]);
609:   tao->cnorm    = PetscSqrtReal(cnorm[0] * cnorm[0] + cnorm[1] * cnorm[1]);
610:   tao->step     = pdipm->mu;
611:   PetscFunctionReturn(PETSC_SUCCESS);
612: }

614: /*
615:   PCPostSetup_PDIPM -- called when the KKT matrix is Cholesky factored for the preconditioner. Checks the inertia of Cholesky factor of the KKT matrix.
616:   If it does not match the numbers of prime and dual variables, add shifts to the KKT matrix.
617: */
618: static PetscErrorCode PCPostSetUp_PDIPM(PC pc)
619: {
620:   Tao        tao;
621:   TAO_PDIPM *pdipm;
622:   Vec        X;
623:   SNES       snes;
624:   KSP        ksp;
625:   Mat        Factor;
626:   PetscBool  isCHOL;
627:   PetscInt   nneg, nzero, npos;

629:   PetscFunctionBegin;
630:   PetscCall(PCGetApplicationContext(pc, &tao));
631:   pdipm = (TAO_PDIPM *)tao->data;
632:   X     = pdipm->X;
633:   snes  = pdipm->snes;

635:   /* Get the inertia of Cholesky factor */
636:   PetscCall(SNESGetKSP(snes, &ksp));
637:   PetscCall(KSPGetPC(ksp, &pc));
638:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCCHOLESKY, &isCHOL));
639:   if (!isCHOL) PetscFunctionReturn(PETSC_SUCCESS);

641:   PetscCall(PCFactorGetMatrix(pc, &Factor));
642:   PetscCall(MatGetInertia(Factor, &nneg, &nzero, &npos));

644:   if (npos < pdipm->Nx + pdipm->Nci) {
645:     pdipm->deltaw = PetscMax(pdipm->lastdeltaw / 3, 1.e-4 * PETSC_MACHINE_EPSILON);
646:     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));
647:     PetscCall(TaoSNESJacobian_PDIPM(snes, X, pdipm->K, pdipm->K, tao));
648:     PetscCall(PCSetPostSetUp(pc, NULL));
649:     PetscCall(PCSetUp(pc));
650:     PetscCall(MatGetInertia(Factor, &nneg, &nzero, &npos));

652:     if (npos < pdipm->Nx + pdipm->Nci) {
653:       pdipm->deltaw = pdipm->lastdeltaw;                                           /* in case reduction update does not help, this prevents that step from impacting increasing update */
654:       while (npos < pdipm->Nx + pdipm->Nci && pdipm->deltaw <= 1. / PETSC_SMALL) { /* increase deltaw */
655:         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));
656:         pdipm->deltaw = PetscMin(8 * pdipm->deltaw, PetscPowReal(10, 20));
657:         PetscCall(TaoSNESJacobian_PDIPM(snes, X, pdipm->K, pdipm->K, tao));
658:         PetscCall(PCSetUp(pc));
659:         PetscCall(MatGetInertia(Factor, &nneg, &nzero, &npos));
660:       }

662:       PetscCheck(pdipm->deltaw < 1. / PETSC_SMALL, PetscObjectComm((PetscObject)tao), PETSC_ERR_CONV_FAILED, "Reached maximum delta w will not converge, try different initial x0");

664:       PetscCall(PetscInfo(tao, "Updated deltaw %g\n", (double)pdipm->deltaw));
665:       pdipm->lastdeltaw = pdipm->deltaw;
666:       pdipm->deltaw     = 0.0;
667:     }
668:   }

670:   if (nzero) { /* Jacobian is singular */
671:     if (pdipm->deltac == 0.0) {
672:       pdipm->deltac = PETSC_SQRT_MACHINE_EPSILON;
673:     } else {
674:       pdipm->deltac = pdipm->deltac * PetscPowReal(pdipm->mu, .25);
675:     }
676:     PetscCall(PetscInfo(tao, "Updated deltac=%g, MatInertia: nneg %" PetscInt_FMT ", nzero %" PetscInt_FMT "(!=0), npos %" PetscInt_FMT "\n", (double)pdipm->deltac, nneg, nzero, npos));
677:     PetscCall(TaoSNESJacobian_PDIPM(snes, X, pdipm->K, pdipm->K, tao));
678:     PetscCall(PCSetPostSetUp(pc, NULL));
679:     PetscCall(PCSetUp(pc));
680:     PetscCall(MatGetInertia(Factor, &nneg, &nzero, &npos));
681:   }
682:   PetscCall(PCSetPostSetUp(pc, PCPostSetUp_PDIPM));
683:   PetscFunctionReturn(PETSC_SUCCESS);
684: }

686: /*
687:    SNESLineSearch_PDIPM - Custom line search used with PDIPM.

689:    Collective

691:    Notes:
692:    This routine employs a simple backtracking line-search to keep
693:    the slack variables (z) and inequality constraints Lagrange multipliers
694:    (lambdai) positive, i.e., z,lambdai >=0. It does this by calculating scalars
695:    alpha_p and alpha_d to keep z,lambdai non-negative. The decision (x), and the
696:    slack variables are updated as X = X - alpha_d*dx. The constraint multipliers
697:    are updated as Lambdai = Lambdai + alpha_p*dLambdai. The barrier parameter mu
698:    is also updated as mu = mu + z'lambdai/Nci
699: */
700: static PetscErrorCode SNESLineSearch_PDIPM(SNESLineSearch linesearch, void *ctx)
701: {
702:   Tao                tao   = (Tao)ctx;
703:   TAO_PDIPM         *pdipm = (TAO_PDIPM *)tao->data;
704:   SNES               snes;
705:   Vec                X, F, Y;
706:   PetscInt           i, iter;
707:   PetscReal          alpha_p = 1.0, alpha_d = 1.0, alpha[4];
708:   PetscScalar       *Xarr, *z, *lambdai, dot, *taosolarr;
709:   const PetscScalar *dXarr, *dz, *dlambdai;

711:   PetscFunctionBegin;
712:   PetscCall(SNESLineSearchGetSNES(linesearch, &snes));
713:   PetscCall(SNESGetIterationNumber(snes, &iter));

715:   PetscCall(SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_SUCCEEDED));
716:   PetscCall(SNESLineSearchGetVecs(linesearch, &X, &F, &Y, NULL, NULL));

718:   PetscCall(VecGetArrayWrite(X, &Xarr));
719:   PetscCall(VecGetArrayRead(Y, &dXarr));
720:   z  = Xarr + pdipm->off_z;
721:   dz = dXarr + pdipm->off_z;
722:   for (i = 0; i < pdipm->nci; i++) {
723:     if (z[i] - dz[i] < 0.0) alpha_p = PetscMin(alpha_p, 0.9999 * z[i] / dz[i]);
724:   }

726:   lambdai  = Xarr + pdipm->off_lambdai;
727:   dlambdai = dXarr + pdipm->off_lambdai;

729:   for (i = 0; i < pdipm->nci; i++) {
730:     if (lambdai[i] - dlambdai[i] < 0.0) alpha_d = PetscMin(0.9999 * lambdai[i] / dlambdai[i], alpha_d);
731:   }

733:   alpha[0] = alpha_p;
734:   alpha[1] = alpha_d;
735:   PetscCall(VecRestoreArrayRead(Y, &dXarr));
736:   PetscCall(VecRestoreArrayWrite(X, &Xarr));

738:   /* alpha = min(alpha) over all processes */
739:   PetscCallMPI(MPIU_Allreduce(alpha, alpha + 2, 2, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)tao)));

741:   alpha_p = alpha[2];
742:   alpha_d = alpha[3];

744:   /* X = X - alpha * Y */
745:   PetscCall(VecGetArrayWrite(X, &Xarr));
746:   PetscCall(VecGetArrayRead(Y, &dXarr));
747:   for (i = 0; i < pdipm->nx; i++) Xarr[i] -= alpha_p * dXarr[i];
748:   for (i = 0; i < pdipm->nce; i++) Xarr[i + pdipm->off_lambdae] -= alpha_d * dXarr[i + pdipm->off_lambdae];

750:   for (i = 0; i < pdipm->nci; i++) {
751:     Xarr[i + pdipm->off_lambdai] -= alpha_d * dXarr[i + pdipm->off_lambdai];
752:     Xarr[i + pdipm->off_z] -= alpha_p * dXarr[i + pdipm->off_z];
753:   }
754:   PetscCall(VecGetArrayWrite(tao->solution, &taosolarr));
755:   PetscCall(PetscMemcpy(taosolarr, Xarr, pdipm->nx * sizeof(PetscScalar)));
756:   PetscCall(VecRestoreArrayWrite(tao->solution, &taosolarr));

758:   PetscCall(VecRestoreArrayWrite(X, &Xarr));
759:   PetscCall(VecRestoreArrayRead(Y, &dXarr));

761:   /* Update mu = mu_update_factor * dot(z,lambdai)/pdipm->nci at updated X */
762:   if (pdipm->z) PetscCall(VecDot(pdipm->z, pdipm->lambdai, &dot));
763:   else dot = 0.0;

765:   /* if (PetscAbsReal(pdipm->gradL) < 0.9*pdipm->mu)  */
766:   pdipm->mu = pdipm->mu_update_factor * dot / pdipm->Nci;

768:   /* Update F; get tao->residual and tao->cnorm */
769:   PetscCall(TaoSNESFunction_PDIPM_residual(snes, X, F, (void *)tao));

771:   tao->niter++;
772:   PetscCall(TaoLogConvergenceHistory(tao, pdipm->obj, tao->residual, tao->cnorm, tao->niter));
773:   PetscCall(TaoMonitor(tao, tao->niter, pdipm->obj, tao->residual, tao->cnorm, pdipm->mu));

775:   PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
776:   if (tao->reason) PetscCall(SNESSetConvergedReason(snes, SNES_CONVERGED_FNORM_ABS));
777:   PetscFunctionReturn(PETSC_SUCCESS);
778: }

780: static PetscErrorCode TaoSolve_PDIPM(Tao tao)
781: {
782:   TAO_PDIPM     *pdipm = (TAO_PDIPM *)tao->data;
783:   SNESLineSearch linesearch; /* SNESLineSearch context */
784:   Vec            dummy;

786:   PetscFunctionBegin;
787:   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");

789:   /* Initialize all variables */
790:   PetscCall(TaoPDIPMInitializeSolution(tao));

792:   /* Set linesearch */
793:   PetscCall(SNESGetLineSearch(pdipm->snes, &linesearch));
794:   PetscCall(SNESLineSearchSetType(linesearch, SNESLINESEARCHSHELL));
795:   PetscCall(SNESLineSearchShellSetApply(linesearch, SNESLineSearch_PDIPM, tao));
796:   PetscCall(SNESLineSearchSetFromOptions(linesearch));

798:   tao->reason = TAO_CONTINUE_ITERATING;

800:   /* -tao_monitor for iteration 0 and check convergence */
801:   PetscCall(VecDuplicate(pdipm->X, &dummy));
802:   PetscCall(TaoSNESFunction_PDIPM_residual(pdipm->snes, pdipm->X, dummy, (void *)tao));

804:   PetscCall(TaoLogConvergenceHistory(tao, pdipm->obj, tao->residual, tao->cnorm, tao->niter));
805:   PetscCall(TaoMonitor(tao, tao->niter, pdipm->obj, tao->residual, tao->cnorm, pdipm->mu));
806:   PetscCall(VecDestroy(&dummy));
807:   PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
808:   if (tao->reason) PetscCall(SNESSetConvergedReason(pdipm->snes, SNES_CONVERGED_FNORM_ABS));

810:   while (tao->reason == TAO_CONTINUE_ITERATING) {
811:     SNESConvergedReason reason;
812:     PetscCall(SNESSolve(pdipm->snes, NULL, pdipm->X));

814:     /* Check SNES convergence */
815:     PetscCall(SNESGetConvergedReason(pdipm->snes, &reason));
816:     if (reason < 0) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)pdipm->snes), "SNES solve did not converged due to reason %s\n", SNESConvergedReasons[reason]));

818:     /* Check TAO convergence */
819:     PetscCheck(!PetscIsInfOrNanReal(pdipm->obj), PETSC_COMM_SELF, PETSC_ERR_SUP, "User-provided compute function generated Inf or NaN");
820:   }
821:   PetscFunctionReturn(PETSC_SUCCESS);
822: }

824: static PetscErrorCode TaoView_PDIPM(Tao tao, PetscViewer viewer)
825: {
826:   TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;

828:   PetscFunctionBegin;
829:   tao->constrained = PETSC_TRUE;
830:   PetscCall(PetscViewerASCIIPushTab(viewer));
831:   PetscCall(PetscViewerASCIIPrintf(viewer, "Number of prime=%" PetscInt_FMT ", Number of dual=%" PetscInt_FMT "\n", pdipm->Nx + pdipm->Nci, pdipm->Nce + pdipm->Nci));
832:   if (pdipm->kkt_pd) PetscCall(PetscViewerASCIIPrintf(viewer, "KKT shifts deltaw=%g, deltac=%g\n", (double)pdipm->deltaw, (double)pdipm->deltac));
833:   PetscCall(PetscViewerASCIIPopTab(viewer));
834:   PetscFunctionReturn(PETSC_SUCCESS);
835: }

837: static PetscErrorCode TaoSetup_PDIPM(Tao tao)
838: {
839:   TAO_PDIPM         *pdipm = (TAO_PDIPM *)tao->data;
840:   MPI_Comm           comm;
841:   PetscMPIInt        size;
842:   PetscInt           row, col, Jcrstart, Jcrend, k, tmp, nc, proc, *nh_all, *ng_all;
843:   PetscInt           offset, *xa, *xb, i, j, rstart, rend;
844:   PetscScalar        one = 1.0, neg_one = -1.0;
845:   const PetscInt    *cols, *rranges, *cranges, *aj, *ranges;
846:   const PetscScalar *aa, *Xarr;
847:   Mat                J;
848:   Mat                Jce_xfixed_trans, Jci_xb_trans;
849:   PetscInt          *dnz, *onz, rjstart, nx_all, *nce_all, *Jranges, cols1[2];

851:   PetscFunctionBegin;
852:   PetscCall(PetscObjectGetComm((PetscObject)tao, &comm));
853:   PetscCallMPI(MPI_Comm_size(comm, &size));

855:   /* (1) Setup Bounds and create Tao vectors */
856:   PetscCall(TaoPDIPMSetUpBounds(tao));

858:   if (!tao->gradient) {
859:     PetscCall(VecDuplicate(tao->solution, &tao->gradient));
860:     PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));
861:   }

863:   /* (2) Get sizes */
864:   /* Size of vector x - This is set by TaoSetSolution */
865:   PetscCall(VecGetSize(tao->solution, &pdipm->Nx));
866:   PetscCall(VecGetLocalSize(tao->solution, &pdipm->nx));

868:   /* Size of equality constraints and vectors */
869:   if (tao->constraints_equality) {
870:     PetscCall(VecGetSize(tao->constraints_equality, &pdipm->Ng));
871:     PetscCall(VecGetLocalSize(tao->constraints_equality, &pdipm->ng));
872:   } else {
873:     pdipm->ng = pdipm->Ng = 0;
874:   }

876:   pdipm->nce = pdipm->ng + pdipm->nxfixed;
877:   pdipm->Nce = pdipm->Ng + pdipm->Nxfixed;

879:   /* Size of inequality constraints and vectors */
880:   if (tao->constraints_inequality) {
881:     PetscCall(VecGetSize(tao->constraints_inequality, &pdipm->Nh));
882:     PetscCall(VecGetLocalSize(tao->constraints_inequality, &pdipm->nh));
883:   } else {
884:     pdipm->nh = pdipm->Nh = 0;
885:   }

887:   pdipm->nci = pdipm->nh + pdipm->nxlb + pdipm->nxub + 2 * pdipm->nxbox;
888:   pdipm->Nci = pdipm->Nh + pdipm->Nxlb + pdipm->Nxub + 2 * pdipm->Nxbox;

890:   /* Full size of the KKT system to be solved */
891:   pdipm->n = pdipm->nx + pdipm->nce + 2 * pdipm->nci;
892:   pdipm->N = pdipm->Nx + pdipm->Nce + 2 * pdipm->Nci;

894:   /* (3) Offsets for subvectors */
895:   pdipm->off_lambdae = pdipm->nx;
896:   pdipm->off_lambdai = pdipm->off_lambdae + pdipm->nce;
897:   pdipm->off_z       = pdipm->off_lambdai + pdipm->nci;

899:   /* (4) Create vectors and subvectors */
900:   /* Ce and Ci vectors */
901:   PetscCall(VecCreate(comm, &pdipm->ce));
902:   PetscCall(VecSetSizes(pdipm->ce, pdipm->nce, pdipm->Nce));
903:   PetscCall(VecSetFromOptions(pdipm->ce));

905:   PetscCall(VecCreate(comm, &pdipm->ci));
906:   PetscCall(VecSetSizes(pdipm->ci, pdipm->nci, pdipm->Nci));
907:   PetscCall(VecSetFromOptions(pdipm->ci));

909:   /* X=[x; lambdae; lambdai; z] for the big KKT system */
910:   PetscCall(VecCreate(comm, &pdipm->X));
911:   PetscCall(VecSetSizes(pdipm->X, pdipm->n, pdipm->N));
912:   PetscCall(VecSetFromOptions(pdipm->X));

914:   /* Subvectors; they share local arrays with X */
915:   PetscCall(VecGetArrayRead(pdipm->X, &Xarr));
916:   /* x shares local array with X.x */
917:   if (pdipm->Nx) PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nx, pdipm->Nx, Xarr, &pdipm->x));

919:   /* lambdae shares local array with X.lambdae */
920:   if (pdipm->Nce) PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nce, pdipm->Nce, Xarr + pdipm->off_lambdae, &pdipm->lambdae));

922:   /* tao->DE shares local array with X.lambdae_g */
923:   if (pdipm->Ng) {
924:     PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->ng, pdipm->Ng, Xarr + pdipm->off_lambdae, &tao->DE));

926:     PetscCall(VecCreate(comm, &pdipm->lambdae_xfixed));
927:     PetscCall(VecSetSizes(pdipm->lambdae_xfixed, pdipm->nxfixed, PETSC_DECIDE));
928:     PetscCall(VecSetFromOptions(pdipm->lambdae_xfixed));
929:   }

931:   if (pdipm->Nci) {
932:     /* lambdai shares local array with X.lambdai */
933:     PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nci, pdipm->Nci, Xarr + pdipm->off_lambdai, &pdipm->lambdai));

935:     /* z for slack variables; it shares local array with X.z */
936:     PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nci, pdipm->Nci, Xarr + pdipm->off_z, &pdipm->z));
937:   }

939:   /* tao->DI which shares local array with X.lambdai_h */
940:   if (pdipm->Nh) PetscCall(VecCreateMPIWithArray(comm, 1, pdipm->nh, pdipm->Nh, Xarr + pdipm->off_lambdai, &tao->DI));
941:   PetscCall(VecCreate(comm, &pdipm->lambdai_xb));
942:   PetscCall(VecSetSizes(pdipm->lambdai_xb, pdipm->nci - pdipm->nh, PETSC_DECIDE));
943:   PetscCall(VecSetFromOptions(pdipm->lambdai_xb));

945:   PetscCall(VecRestoreArrayRead(pdipm->X, &Xarr));

947:   /* (5) Create Jacobians Jce_xfixed and Jci */
948:   /* (5.1) PDIPM Jacobian of equality bounds cebound(x) = J_nxfixed */
949:   if (pdipm->Nxfixed) {
950:     /* Create Jce_xfixed */
951:     PetscCall(MatCreate(comm, &pdipm->Jce_xfixed));
952:     PetscCall(MatSetSizes(pdipm->Jce_xfixed, pdipm->nxfixed, pdipm->nx, PETSC_DECIDE, pdipm->Nx));
953:     PetscCall(MatSetFromOptions(pdipm->Jce_xfixed));
954:     PetscCall(MatSeqAIJSetPreallocation(pdipm->Jce_xfixed, 1, NULL));
955:     PetscCall(MatMPIAIJSetPreallocation(pdipm->Jce_xfixed, 1, NULL, 1, NULL));

957:     PetscCall(MatGetOwnershipRange(pdipm->Jce_xfixed, &Jcrstart, &Jcrend));
958:     PetscCall(ISGetIndices(pdipm->isxfixed, &cols));
959:     k = 0;
960:     for (row = Jcrstart; row < Jcrend; row++) {
961:       PetscCall(MatSetValues(pdipm->Jce_xfixed, 1, &row, 1, cols + k, &one, INSERT_VALUES));
962:       k++;
963:     }
964:     PetscCall(ISRestoreIndices(pdipm->isxfixed, &cols));
965:     PetscCall(MatAssemblyBegin(pdipm->Jce_xfixed, MAT_FINAL_ASSEMBLY));
966:     PetscCall(MatAssemblyEnd(pdipm->Jce_xfixed, MAT_FINAL_ASSEMBLY));
967:   }

969:   /* (5.2) PDIPM inequality Jacobian Jci = [tao->jacobian_inequality; ...] */
970:   PetscCall(MatCreate(comm, &pdipm->Jci_xb));
971:   PetscCall(MatSetSizes(pdipm->Jci_xb, pdipm->nci - pdipm->nh, pdipm->nx, PETSC_DECIDE, pdipm->Nx));
972:   PetscCall(MatSetFromOptions(pdipm->Jci_xb));
973:   PetscCall(MatSeqAIJSetPreallocation(pdipm->Jci_xb, 1, NULL));
974:   PetscCall(MatMPIAIJSetPreallocation(pdipm->Jci_xb, 1, NULL, 1, NULL));

976:   PetscCall(MatGetOwnershipRange(pdipm->Jci_xb, &Jcrstart, &Jcrend));
977:   offset = Jcrstart;
978:   if (pdipm->Nxub) {
979:     /* Add xub to Jci_xb */
980:     PetscCall(ISGetIndices(pdipm->isxub, &cols));
981:     k = 0;
982:     for (row = offset; row < offset + pdipm->nxub; row++) {
983:       PetscCall(MatSetValues(pdipm->Jci_xb, 1, &row, 1, cols + k, &neg_one, INSERT_VALUES));
984:       k++;
985:     }
986:     PetscCall(ISRestoreIndices(pdipm->isxub, &cols));
987:   }

989:   if (pdipm->Nxlb) {
990:     /* Add xlb to Jci_xb */
991:     PetscCall(ISGetIndices(pdipm->isxlb, &cols));
992:     k = 0;
993:     offset += pdipm->nxub;
994:     for (row = offset; row < offset + pdipm->nxlb; row++) {
995:       PetscCall(MatSetValues(pdipm->Jci_xb, 1, &row, 1, cols + k, &one, INSERT_VALUES));
996:       k++;
997:     }
998:     PetscCall(ISRestoreIndices(pdipm->isxlb, &cols));
999:   }

1001:   /* Add xbox to Jci_xb */
1002:   if (pdipm->Nxbox) {
1003:     PetscCall(ISGetIndices(pdipm->isxbox, &cols));
1004:     k = 0;
1005:     offset += pdipm->nxlb;
1006:     for (row = offset; row < offset + pdipm->nxbox; row++) {
1007:       PetscCall(MatSetValues(pdipm->Jci_xb, 1, &row, 1, cols + k, &neg_one, INSERT_VALUES));
1008:       tmp = row + pdipm->nxbox;
1009:       PetscCall(MatSetValues(pdipm->Jci_xb, 1, &tmp, 1, cols + k, &one, INSERT_VALUES));
1010:       k++;
1011:     }
1012:     PetscCall(ISRestoreIndices(pdipm->isxbox, &cols));
1013:   }

1015:   PetscCall(MatAssemblyBegin(pdipm->Jci_xb, MAT_FINAL_ASSEMBLY));
1016:   PetscCall(MatAssemblyEnd(pdipm->Jci_xb, MAT_FINAL_ASSEMBLY));
1017:   /* PetscCall(MatView(pdipm->Jci_xb,PETSC_VIEWER_STDOUT_WORLD)); */

1019:   /* (6) Set up ISs for PC Fieldsplit */
1020:   if (pdipm->solve_reduced_kkt) {
1021:     PetscCall(PetscMalloc2(pdipm->nx + pdipm->nce, &xa, 2 * pdipm->nci, &xb));
1022:     for (i = 0; i < pdipm->nx + pdipm->nce; i++) xa[i] = i;
1023:     for (i = 0; i < 2 * pdipm->nci; i++) xb[i] = pdipm->off_lambdai + i;

1025:     PetscCall(ISCreateGeneral(comm, pdipm->nx + pdipm->nce, xa, PETSC_OWN_POINTER, &pdipm->is1));
1026:     PetscCall(ISCreateGeneral(comm, 2 * pdipm->nci, xb, PETSC_OWN_POINTER, &pdipm->is2));
1027:   }

1029:   /* (7) Gather offsets from all processes */
1030:   PetscCall(PetscMalloc1(size, &pdipm->nce_all));

1032:   /* Get rstart of KKT matrix */
1033:   PetscCallMPI(MPI_Scan(&pdipm->n, &rstart, 1, MPIU_INT, MPI_SUM, comm));
1034:   rstart -= pdipm->n;

1036:   PetscCallMPI(MPI_Allgather(&pdipm->nce, 1, MPIU_INT, pdipm->nce_all, 1, MPIU_INT, comm));

1038:   PetscCall(PetscMalloc3(size, &ng_all, size, &nh_all, size, &Jranges));
1039:   PetscCallMPI(MPI_Allgather(&rstart, 1, MPIU_INT, Jranges, 1, MPIU_INT, comm));
1040:   PetscCallMPI(MPI_Allgather(&pdipm->nh, 1, MPIU_INT, nh_all, 1, MPIU_INT, comm));
1041:   PetscCallMPI(MPI_Allgather(&pdipm->ng, 1, MPIU_INT, ng_all, 1, MPIU_INT, comm));

1043:   PetscCall(MatGetOwnershipRanges(tao->hessian, &rranges));
1044:   PetscCall(MatGetOwnershipRangesColumn(tao->hessian, &cranges));

1046:   if (pdipm->Ng) {
1047:     PetscCall(TaoComputeJacobianEquality(tao, tao->solution, tao->jacobian_equality, tao->jacobian_equality_pre));
1048:     PetscCall(MatTranspose(tao->jacobian_equality, MAT_INITIAL_MATRIX, &pdipm->jac_equality_trans));
1049:   }
1050:   if (pdipm->Nh) {
1051:     PetscCall(TaoComputeJacobianInequality(tao, tao->solution, tao->jacobian_inequality, tao->jacobian_inequality_pre));
1052:     PetscCall(MatTranspose(tao->jacobian_inequality, MAT_INITIAL_MATRIX, &pdipm->jac_inequality_trans));
1053:   }

1055:   /* Count dnz,onz for preallocation of KKT matrix */
1056:   nce_all = pdipm->nce_all;

1058:   if (pdipm->Nxfixed) PetscCall(MatTranspose(pdipm->Jce_xfixed, MAT_INITIAL_MATRIX, &Jce_xfixed_trans));
1059:   PetscCall(MatTranspose(pdipm->Jci_xb, MAT_INITIAL_MATRIX, &Jci_xb_trans));

1061:   MatPreallocateBegin(comm, pdipm->n, pdipm->n, dnz, onz);

1063:   /* 1st row block of KKT matrix: [Wxx; gradCe'; -gradCi'; 0] */
1064:   PetscCall(TaoPDIPMEvaluateFunctionsAndJacobians(tao, pdipm->x));
1065:   PetscCall(TaoComputeHessian(tao, tao->solution, tao->hessian, tao->hessian_pre));

1067:   /* Insert tao->hessian */
1068:   PetscCall(MatGetOwnershipRange(tao->hessian, &rjstart, NULL));
1069:   for (i = 0; i < pdipm->nx; i++) {
1070:     row = rstart + i;

1072:     PetscCall(MatGetRow(tao->hessian, i + rjstart, &nc, &aj, NULL));
1073:     proc = 0;
1074:     for (j = 0; j < nc; j++) {
1075:       while (aj[j] >= cranges[proc + 1]) proc++;
1076:       col = aj[j] - cranges[proc] + Jranges[proc];
1077:       PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1078:     }
1079:     PetscCall(MatRestoreRow(tao->hessian, i + rjstart, &nc, &aj, NULL));

1081:     if (pdipm->ng) {
1082:       /* Insert grad g' */
1083:       PetscCall(MatGetRow(pdipm->jac_equality_trans, i + rjstart, &nc, &aj, NULL));
1084:       PetscCall(MatGetOwnershipRanges(tao->jacobian_equality, &ranges));
1085:       proc = 0;
1086:       for (j = 0; j < nc; j++) {
1087:         /* find row ownership of */
1088:         while (aj[j] >= ranges[proc + 1]) proc++;
1089:         nx_all = rranges[proc + 1] - rranges[proc];
1090:         col    = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
1091:         PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1092:       }
1093:       PetscCall(MatRestoreRow(pdipm->jac_equality_trans, i + rjstart, &nc, &aj, NULL));
1094:     }

1096:     /* Insert Jce_xfixed^T' */
1097:     if (pdipm->nxfixed) {
1098:       PetscCall(MatGetRow(Jce_xfixed_trans, i + rjstart, &nc, &aj, NULL));
1099:       PetscCall(MatGetOwnershipRanges(pdipm->Jce_xfixed, &ranges));
1100:       proc = 0;
1101:       for (j = 0; j < nc; j++) {
1102:         /* find row ownership of */
1103:         while (aj[j] >= ranges[proc + 1]) proc++;
1104:         nx_all = rranges[proc + 1] - rranges[proc];
1105:         col    = aj[j] - ranges[proc] + Jranges[proc] + nx_all + ng_all[proc];
1106:         PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1107:       }
1108:       PetscCall(MatRestoreRow(Jce_xfixed_trans, i + rjstart, &nc, &aj, NULL));
1109:     }

1111:     if (pdipm->nh) {
1112:       /* Insert -grad h' */
1113:       PetscCall(MatGetRow(pdipm->jac_inequality_trans, i + rjstart, &nc, &aj, NULL));
1114:       PetscCall(MatGetOwnershipRanges(tao->jacobian_inequality, &ranges));
1115:       proc = 0;
1116:       for (j = 0; j < nc; j++) {
1117:         /* find row ownership of */
1118:         while (aj[j] >= ranges[proc + 1]) proc++;
1119:         nx_all = rranges[proc + 1] - rranges[proc];
1120:         col    = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
1121:         PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1122:       }
1123:       PetscCall(MatRestoreRow(pdipm->jac_inequality_trans, i + rjstart, &nc, &aj, NULL));
1124:     }

1126:     /* Insert Jci_xb^T' */
1127:     PetscCall(MatGetRow(Jci_xb_trans, i + rjstart, &nc, &aj, NULL));
1128:     PetscCall(MatGetOwnershipRanges(pdipm->Jci_xb, &ranges));
1129:     proc = 0;
1130:     for (j = 0; j < nc; j++) {
1131:       /* find row ownership of */
1132:       while (aj[j] >= ranges[proc + 1]) proc++;
1133:       nx_all = rranges[proc + 1] - rranges[proc];
1134:       col    = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc] + nh_all[proc];
1135:       PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1136:     }
1137:     PetscCall(MatRestoreRow(Jci_xb_trans, i + rjstart, &nc, &aj, NULL));
1138:   }

1140:   /* 2nd Row block of KKT matrix: [grad Ce, deltac*I, 0, 0] */
1141:   if (pdipm->Ng) {
1142:     PetscCall(MatGetOwnershipRange(tao->jacobian_equality, &rjstart, NULL));
1143:     for (i = 0; i < pdipm->ng; i++) {
1144:       row = rstart + pdipm->off_lambdae + i;

1146:       PetscCall(MatGetRow(tao->jacobian_equality, i + rjstart, &nc, &aj, NULL));
1147:       proc = 0;
1148:       for (j = 0; j < nc; j++) {
1149:         while (aj[j] >= cranges[proc + 1]) proc++;
1150:         col = aj[j] - cranges[proc] + Jranges[proc];
1151:         PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz)); /* grad g */
1152:       }
1153:       PetscCall(MatRestoreRow(tao->jacobian_equality, i + rjstart, &nc, &aj, NULL));
1154:     }
1155:   }
1156:   /* Jce_xfixed */
1157:   if (pdipm->Nxfixed) {
1158:     PetscCall(MatGetOwnershipRange(pdipm->Jce_xfixed, &Jcrstart, NULL));
1159:     for (i = 0; i < (pdipm->nce - pdipm->ng); i++) {
1160:       row = rstart + pdipm->off_lambdae + pdipm->ng + i;

1162:       PetscCall(MatGetRow(pdipm->Jce_xfixed, i + Jcrstart, &nc, &cols, NULL));
1163:       PetscCheck(nc == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "nc != 1");

1165:       proc = 0;
1166:       j    = 0;
1167:       while (cols[j] >= cranges[proc + 1]) proc++;
1168:       col = cols[j] - cranges[proc] + Jranges[proc];
1169:       PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1170:       PetscCall(MatRestoreRow(pdipm->Jce_xfixed, i + Jcrstart, &nc, &cols, NULL));
1171:     }
1172:   }

1174:   /* 3rd Row block of KKT matrix: [ gradCi, 0, deltac*I, -I] */
1175:   if (pdipm->Nh) {
1176:     PetscCall(MatGetOwnershipRange(tao->jacobian_inequality, &rjstart, NULL));
1177:     for (i = 0; i < pdipm->nh; i++) {
1178:       row = rstart + pdipm->off_lambdai + i;

1180:       PetscCall(MatGetRow(tao->jacobian_inequality, i + rjstart, &nc, &aj, NULL));
1181:       proc = 0;
1182:       for (j = 0; j < nc; j++) {
1183:         while (aj[j] >= cranges[proc + 1]) proc++;
1184:         col = aj[j] - cranges[proc] + Jranges[proc];
1185:         PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz)); /* grad h */
1186:       }
1187:       PetscCall(MatRestoreRow(tao->jacobian_inequality, i + rjstart, &nc, &aj, NULL));
1188:     }
1189:     /* I */
1190:     for (i = 0; i < pdipm->nh; i++) {
1191:       row = rstart + pdipm->off_lambdai + i;
1192:       col = rstart + pdipm->off_z + i;
1193:       PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1194:     }
1195:   }

1197:   /* Jci_xb */
1198:   PetscCall(MatGetOwnershipRange(pdipm->Jci_xb, &Jcrstart, NULL));
1199:   for (i = 0; i < (pdipm->nci - pdipm->nh); i++) {
1200:     row = rstart + pdipm->off_lambdai + pdipm->nh + i;

1202:     PetscCall(MatGetRow(pdipm->Jci_xb, i + Jcrstart, &nc, &cols, NULL));
1203:     PetscCheck(nc == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "nc != 1");
1204:     proc = 0;
1205:     for (j = 0; j < nc; j++) {
1206:       while (cols[j] >= cranges[proc + 1]) proc++;
1207:       col = cols[j] - cranges[proc] + Jranges[proc];
1208:       PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1209:     }
1210:     PetscCall(MatRestoreRow(pdipm->Jci_xb, i + Jcrstart, &nc, &cols, NULL));
1211:     /* I */
1212:     col = rstart + pdipm->off_z + pdipm->nh + i;
1213:     PetscCall(MatPreallocateSet(row, 1, &col, dnz, onz));
1214:   }

1216:   /* 4-th Row block of KKT matrix: Z and Ci */
1217:   for (i = 0; i < pdipm->nci; i++) {
1218:     row      = rstart + pdipm->off_z + i;
1219:     cols1[0] = rstart + pdipm->off_lambdai + i;
1220:     cols1[1] = row;
1221:     PetscCall(MatPreallocateSet(row, 2, cols1, dnz, onz));
1222:   }

1224:   /* diagonal entry */
1225:   for (i = 0; i < pdipm->n; i++) dnz[i]++; /* diagonal entry */

1227:   /* Create KKT matrix */
1228:   PetscCall(MatCreate(comm, &J));
1229:   PetscCall(MatSetSizes(J, pdipm->n, pdipm->n, PETSC_DECIDE, PETSC_DECIDE));
1230:   PetscCall(MatSetFromOptions(J));
1231:   PetscCall(MatSeqAIJSetPreallocation(J, 0, dnz));
1232:   PetscCall(MatMPIAIJSetPreallocation(J, 0, dnz, 0, onz));
1233:   MatPreallocateEnd(dnz, onz);
1234:   pdipm->K = J;

1236:   /* (8) Insert constant entries to  K */
1237:   /* Set 0.0 to diagonal of K, so that the solver does not complain *about missing diagonal value */
1238:   PetscCall(MatGetOwnershipRange(J, &rstart, &rend));
1239:   for (i = rstart; i < rend; i++) PetscCall(MatSetValue(J, i, i, 0.0, INSERT_VALUES));
1240:   /* In case Wxx has no diagonal entries preset set diagonal to deltaw given */
1241:   if (pdipm->kkt_pd) {
1242:     for (i = 0; i < pdipm->nh; i++) {
1243:       row = rstart + i;
1244:       PetscCall(MatSetValue(J, row, row, pdipm->deltaw, INSERT_VALUES));
1245:     }
1246:   }

1248:   /* Row block of K: [ grad Ce, 0, 0, 0] */
1249:   if (pdipm->Nxfixed) {
1250:     PetscCall(MatGetOwnershipRange(pdipm->Jce_xfixed, &Jcrstart, NULL));
1251:     for (i = 0; i < (pdipm->nce - pdipm->ng); i++) {
1252:       row = rstart + pdipm->off_lambdae + pdipm->ng + i;

1254:       PetscCall(MatGetRow(pdipm->Jce_xfixed, i + Jcrstart, &nc, &cols, &aa));
1255:       proc = 0;
1256:       for (j = 0; j < nc; j++) {
1257:         while (cols[j] >= cranges[proc + 1]) proc++;
1258:         col = cols[j] - cranges[proc] + Jranges[proc];
1259:         PetscCall(MatSetValue(J, row, col, aa[j], INSERT_VALUES)); /* grad Ce */
1260:         PetscCall(MatSetValue(J, col, row, aa[j], INSERT_VALUES)); /* grad Ce' */
1261:       }
1262:       PetscCall(MatRestoreRow(pdipm->Jce_xfixed, i + Jcrstart, &nc, &cols, &aa));
1263:     }
1264:   }

1266:   /* Row block of K: [ -grad Ci, 0, 0, I] */
1267:   PetscCall(MatGetOwnershipRange(pdipm->Jci_xb, &Jcrstart, NULL));
1268:   for (i = 0; i < pdipm->nci - pdipm->nh; i++) {
1269:     row = rstart + pdipm->off_lambdai + pdipm->nh + i;

1271:     PetscCall(MatGetRow(pdipm->Jci_xb, i + Jcrstart, &nc, &cols, &aa));
1272:     proc = 0;
1273:     for (j = 0; j < nc; j++) {
1274:       while (cols[j] >= cranges[proc + 1]) proc++;
1275:       col = cols[j] - cranges[proc] + Jranges[proc];
1276:       PetscCall(MatSetValue(J, col, row, -aa[j], INSERT_VALUES));
1277:       PetscCall(MatSetValue(J, row, col, -aa[j], INSERT_VALUES));
1278:     }
1279:     PetscCall(MatRestoreRow(pdipm->Jci_xb, i + Jcrstart, &nc, &cols, &aa));

1281:     col = rstart + pdipm->off_z + pdipm->nh + i;
1282:     PetscCall(MatSetValue(J, row, col, 1, INSERT_VALUES));
1283:   }

1285:   for (i = 0; i < pdipm->nh; i++) {
1286:     row = rstart + pdipm->off_lambdai + i;
1287:     col = rstart + pdipm->off_z + i;
1288:     PetscCall(MatSetValue(J, row, col, 1, INSERT_VALUES));
1289:   }

1291:   /* Row block of K: [ 0, 0, I, ...] */
1292:   for (i = 0; i < pdipm->nci; i++) {
1293:     row = rstart + pdipm->off_z + i;
1294:     col = rstart + pdipm->off_lambdai + i;
1295:     PetscCall(MatSetValue(J, row, col, 1, INSERT_VALUES));
1296:   }

1298:   if (pdipm->Nxfixed) PetscCall(MatDestroy(&Jce_xfixed_trans));
1299:   PetscCall(MatDestroy(&Jci_xb_trans));
1300:   PetscCall(PetscFree3(ng_all, nh_all, Jranges));

1302:   /* (9) Set up nonlinear solver SNES */
1303:   PetscCall(SNESSetFunction(pdipm->snes, NULL, TaoSNESFunction_PDIPM, (void *)tao));
1304:   PetscCall(SNESSetJacobian(pdipm->snes, J, J, TaoSNESJacobian_PDIPM, (void *)tao));

1306:   if (pdipm->solve_reduced_kkt) {
1307:     PC pc;
1308:     PetscCall(KSPGetPC(tao->ksp, &pc));
1309:     PetscCall(PCSetType(pc, PCFIELDSPLIT));
1310:     PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
1311:     PetscCall(PCFieldSplitSetIS(pc, "2", pdipm->is2));
1312:     PetscCall(PCFieldSplitSetIS(pc, "1", pdipm->is1));
1313:   }
1314:   PetscCall(SNESSetFromOptions(pdipm->snes));

1316:   /* (10) Setup PCPostSetUp() for pdipm->solve_symmetric_kkt */
1317:   if (pdipm->solve_symmetric_kkt) {
1318:     KSP       ksp;
1319:     PC        pc;
1320:     PetscBool isCHOL;

1322:     PetscCall(SNESGetKSP(pdipm->snes, &ksp));
1323:     PetscCall(KSPGetPC(ksp, &pc));
1324:     PetscCall(PCSetPostSetUp(pc, PCPostSetUp_PDIPM));

1326:     PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCCHOLESKY, &isCHOL));
1327:     if (isCHOL) {
1328:       Mat Factor;

1330:       PetscCheck(PetscDefined(HAVE_MUMPS), PetscObjectComm((PetscObject)tao), PETSC_ERR_SUP, "Requires external package MUMPS");
1331:       PetscCall(PCFactorGetMatrix(pc, &Factor));
1332:       PetscCall(MatMumpsSetIcntl(Factor, 24, 1));               /* detection of null pivot rows */
1333:       if (size > 1) PetscCall(MatMumpsSetIcntl(Factor, 13, 1)); /* parallelism of the root node (enable ScaLAPACK) and its splitting */
1334:     }
1335:   }
1336:   PetscFunctionReturn(PETSC_SUCCESS);
1337: }

1339: static PetscErrorCode TaoDestroy_PDIPM(Tao tao)
1340: {
1341:   TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;

1343:   PetscFunctionBegin;
1344:   /* Freeing Vectors assocaiated with KKT (X) */
1345:   PetscCall(VecDestroy(&pdipm->x));       /* Solution x */
1346:   PetscCall(VecDestroy(&pdipm->lambdae)); /* Equality constraints lagrangian multiplier*/
1347:   PetscCall(VecDestroy(&pdipm->lambdai)); /* Inequality constraints lagrangian multiplier*/
1348:   PetscCall(VecDestroy(&pdipm->z));       /* Slack variables */
1349:   PetscCall(VecDestroy(&pdipm->X));       /* Big KKT system vector [x; lambdae; lambdai; z] */

1351:   /* work vectors */
1352:   PetscCall(VecDestroy(&pdipm->lambdae_xfixed));
1353:   PetscCall(VecDestroy(&pdipm->lambdai_xb));

1355:   /* Legrangian equality and inequality Vec */
1356:   PetscCall(VecDestroy(&pdipm->ce)); /* Vec of equality constraints */
1357:   PetscCall(VecDestroy(&pdipm->ci)); /* Vec of inequality constraints */

1359:   /* Matrices */
1360:   PetscCall(MatDestroy(&pdipm->Jce_xfixed));
1361:   PetscCall(MatDestroy(&pdipm->Jci_xb)); /* Jacobian of inequality constraints Jci = [tao->jacobian_inequality ; J(nxub); J(nxlb); J(nxbx)] */
1362:   PetscCall(MatDestroy(&pdipm->K));

1364:   /* Index Sets */
1365:   if (pdipm->Nxub) PetscCall(ISDestroy(&pdipm->isxub)); /* Finite upper bound only -inf < x < ub */

1367:   if (pdipm->Nxlb) PetscCall(ISDestroy(&pdipm->isxlb)); /* Finite lower bound only  lb <= x < inf */

1369:   if (pdipm->Nxfixed) PetscCall(ISDestroy(&pdipm->isxfixed)); /* Fixed variables         lb =  x = ub */

1371:   if (pdipm->Nxbox) PetscCall(ISDestroy(&pdipm->isxbox)); /* Boxed variables         lb <= x <= ub */

1373:   if (pdipm->Nxfree) PetscCall(ISDestroy(&pdipm->isxfree)); /* Free variables        -inf <= x <= inf */

1375:   if (pdipm->solve_reduced_kkt) {
1376:     PetscCall(ISDestroy(&pdipm->is1));
1377:     PetscCall(ISDestroy(&pdipm->is2));
1378:   }

1380:   /* SNES */
1381:   PetscCall(SNESDestroy(&pdipm->snes)); /* Nonlinear solver */
1382:   PetscCall(PetscFree(pdipm->nce_all));
1383:   PetscCall(MatDestroy(&pdipm->jac_equality_trans));
1384:   PetscCall(MatDestroy(&pdipm->jac_inequality_trans));

1386:   /* Destroy pdipm */
1387:   PetscCall(PetscFree(tao->data)); /* Holding locations of pdipm */

1389:   /* Destroy Dual */
1390:   PetscCall(VecDestroy(&tao->DE)); /* equality dual */
1391:   PetscCall(VecDestroy(&tao->DI)); /* dinequality dual */
1392:   PetscFunctionReturn(PETSC_SUCCESS);
1393: }

1395: static PetscErrorCode TaoSetFromOptions_PDIPM(Tao tao, PetscOptionItems PetscOptionsObject)
1396: {
1397:   TAO_PDIPM *pdipm = (TAO_PDIPM *)tao->data;

1399:   PetscFunctionBegin;
1400:   PetscOptionsHeadBegin(PetscOptionsObject, "PDIPM method for constrained optimization");
1401:   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));
1402:   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));
1403:   PetscCall(PetscOptionsBool("-tao_pdipm_solve_reduced_kkt", "Solve reduced KKT system using Schur-complement", NULL, pdipm->solve_reduced_kkt, &pdipm->solve_reduced_kkt, NULL));
1404:   PetscCall(PetscOptionsReal("-tao_pdipm_mu_update_factor", "Update scalar for barrier parameter (mu) update", NULL, pdipm->mu_update_factor, &pdipm->mu_update_factor, NULL));
1405:   PetscCall(PetscOptionsBool("-tao_pdipm_symmetric_kkt", "Solve non reduced symmetric KKT system", NULL, pdipm->solve_symmetric_kkt, &pdipm->solve_symmetric_kkt, NULL));
1406:   PetscCall(PetscOptionsBool("-tao_pdipm_kkt_shift_pd", "Add shifts to make KKT matrix positive definite", NULL, pdipm->kkt_pd, &pdipm->kkt_pd, NULL));
1407:   PetscOptionsHeadEnd();
1408:   PetscFunctionReturn(PETSC_SUCCESS);
1409: }

1411: /*MC
1412:   TAOPDIPM - Barrier-based primal-dual interior point algorithm for generally constrained optimization.

1414:   Options Database Keys:
1415: +   -tao_pdipm_push_init_lambdai - parameter to push initial dual variables away from bounds (> 0)
1416: .   -tao_pdipm_push_init_slack   - parameter to push initial slack variables away from bounds (> 0)
1417: .   -tao_pdipm_mu_update_factor  - update scalar for barrier parameter (mu) update (> 0)
1418: .   -tao_pdipm_symmetric_kkt     - Solve non-reduced symmetric KKT system
1419: -   -tao_pdipm_kkt_shift_pd      - Add shifts to make KKT matrix positive definite

1421:   Level: beginner

1423: .seealso: `TAOPDIPM`, `Tao`, `TaoType`
1424: M*/

1426: PETSC_EXTERN PetscErrorCode TaoCreate_PDIPM(Tao tao)
1427: {
1428:   TAO_PDIPM *pdipm;
1429:   PC         pc;

1431:   PetscFunctionBegin;
1432:   tao->ops->setup          = TaoSetup_PDIPM;
1433:   tao->ops->solve          = TaoSolve_PDIPM;
1434:   tao->ops->setfromoptions = TaoSetFromOptions_PDIPM;
1435:   tao->ops->view           = TaoView_PDIPM;
1436:   tao->ops->destroy        = TaoDestroy_PDIPM;

1438:   PetscCall(PetscNew(&pdipm));
1439:   tao->data = (void *)pdipm;

1441:   pdipm->nx = pdipm->Nx = 0;
1442:   pdipm->nxfixed = pdipm->Nxfixed = 0;
1443:   pdipm->nxlb = pdipm->Nxlb = 0;
1444:   pdipm->nxub = pdipm->Nxub = 0;
1445:   pdipm->nxbox = pdipm->Nxbox = 0;
1446:   pdipm->nxfree = pdipm->Nxfree = 0;

1448:   pdipm->ng = pdipm->Ng = pdipm->nce = pdipm->Nce = 0;
1449:   pdipm->nh = pdipm->Nh = pdipm->nci = pdipm->Nci = 0;
1450:   pdipm->n = pdipm->N     = 0;
1451:   pdipm->mu               = 1.0;
1452:   pdipm->mu_update_factor = 0.1;

1454:   pdipm->deltaw     = 0.0;
1455:   pdipm->lastdeltaw = 3 * 1.e-4;
1456:   pdipm->deltac     = 0.0;
1457:   pdipm->kkt_pd     = PETSC_FALSE;

1459:   pdipm->push_init_slack     = 1.0;
1460:   pdipm->push_init_lambdai   = 1.0;
1461:   pdipm->solve_reduced_kkt   = PETSC_FALSE;
1462:   pdipm->solve_symmetric_kkt = PETSC_TRUE;

1464:   /* Override default settings (unless already changed) */
1465:   PetscCall(TaoParametersInitialize(tao));
1466:   PetscObjectParameterSetDefault(tao, max_it, 200);
1467:   PetscObjectParameterSetDefault(tao, max_funcs, 500);

1469:   PetscCall(SNESCreate(((PetscObject)tao)->comm, &pdipm->snes));
1470:   PetscCall(SNESSetOptionsPrefix(pdipm->snes, tao->hdr.prefix));
1471:   PetscCall(SNESGetKSP(pdipm->snes, &tao->ksp));
1472:   PetscCall(PetscObjectReference((PetscObject)tao->ksp));
1473:   PetscCall(KSPGetPC(tao->ksp, &pc));
1474:   PetscCall(PCSetApplicationContext(pc, (void *)tao));
1475:   PetscFunctionReturn(PETSC_SUCCESS);
1476: }