Actual source code: pdipm.c
petsc-3.15.0 2021-03-30
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      1: #include <petsctaolinesearch.h>
      2: #include <../src/tao/constrained/impls/ipm/pdipm.h>
      3: #include <petscsnes.h>

      5: /*
      6:    TaoPDIPMEvaluateFunctionsAndJacobians - Evaluate the objective function f, gradient fx, constraints, and all the Jacobians at current vector

      8:    Collective on tao

     10:    Input Parameter:
     11: +  tao - solver context
     12: -  x - vector at which all objects to be evaluated

     14:    Level: beginner

     16: .seealso: TaoPDIPMUpdateConstraints(), TaoPDIPMSetUpBounds()
     17: */
     18: PetscErrorCode TaoPDIPMEvaluateFunctionsAndJacobians(Tao tao,Vec x)
     19: {
     21:   TAO_PDIPM      *pdipm=(TAO_PDIPM*)tao->data;

     24:   /* Compute user objective function and gradient */
     25:   TaoComputeObjectiveAndGradient(tao,x,&pdipm->obj,tao->gradient);

     27:   /* Equality constraints and Jacobian */
     28:   if (pdipm->Ng) {
     29:     TaoComputeEqualityConstraints(tao,x,tao->constraints_equality);
     30:     TaoComputeJacobianEquality(tao,x,tao->jacobian_equality,tao->jacobian_equality_pre);
     31:   }

     33:   /* Inequality constraints and Jacobian */
     34:   if (pdipm->Nh) {
     35:     TaoComputeInequalityConstraints(tao,x,tao->constraints_inequality);
     36:     TaoComputeJacobianInequality(tao,x,tao->jacobian_inequality,tao->jacobian_inequality_pre);
     37:   }
     38:   return(0);
     39: }

     41: /*
     42:   TaoPDIPMUpdateConstraints - Update the vectors ce and ci at x

     44:   Collective

     46:   Input Parameter:
     47: + tao - Tao context
     48: - x - vector at which constraints to be evaluted

     50:    Level: beginner

     52: .seealso: TaoPDIPMEvaluateFunctionsAndJacobians()
     53: */
     54: PetscErrorCode TaoPDIPMUpdateConstraints(Tao tao,Vec x)
     55: {
     56:   PetscErrorCode    ierr;
     57:   TAO_PDIPM         *pdipm=(TAO_PDIPM*)tao->data;
     58:   PetscInt          i,offset,offset1,k,xstart;
     59:   PetscScalar       *carr;
     60:   const PetscInt    *ubptr,*lbptr,*bxptr,*fxptr;
     61:   const PetscScalar *xarr,*xuarr,*xlarr,*garr,*harr;

     64:   VecGetOwnershipRange(x,&xstart,NULL);

     66:   VecGetArrayRead(x,&xarr);
     67:   VecGetArrayRead(tao->XU,&xuarr);
     68:   VecGetArrayRead(tao->XL,&xlarr);

     70:   /* (1) Update ce vector */
     71:   VecGetArray(pdipm->ce,&carr);

     73:   if (pdipm->Ng) {
     74:     /* (1.a) Inserting updated g(x) */
     75:     VecGetArrayRead(tao->constraints_equality,&garr);
     76:     PetscMemcpy(carr,garr,pdipm->ng*sizeof(PetscScalar));
     77:     VecRestoreArrayRead(tao->constraints_equality,&garr);
     78:   }

     80:   /* (1.b) Update xfixed */
     81:   if (pdipm->Nxfixed) {
     82:     offset = pdipm->ng;
     83:     ISGetIndices(pdipm->isxfixed,&fxptr); /* global indices in x */
     84:     for (k=0;k < pdipm->nxfixed;k++){
     85:       i = fxptr[k]-xstart;
     86:       carr[offset + k] = xarr[i] - xuarr[i];
     87:     }
     88:   }
     89:   VecRestoreArray(pdipm->ce,&carr);

     91:   /* (2) Update ci vector */
     92:   VecGetArray(pdipm->ci,&carr);

     94:   if (pdipm->Nh) {
     95:     /* (2.a) Inserting updated h(x) */
     96:     VecGetArrayRead(tao->constraints_inequality,&harr);
     97:     PetscMemcpy(carr,harr,pdipm->nh*sizeof(PetscScalar));
     98:     VecRestoreArrayRead(tao->constraints_inequality,&harr);
     99:   }

    101:   /* (2.b) Update xub */
    102:   offset = pdipm->nh;
    103:   if (pdipm->Nxub) {
    104:     ISGetIndices(pdipm->isxub,&ubptr);
    105:     for (k=0; k<pdipm->nxub; k++){
    106:       i = ubptr[k]-xstart;
    107:       carr[offset + k] = xuarr[i] - xarr[i];
    108:     }
    109:   }

    111:   if (pdipm->Nxlb) {
    112:     /* (2.c) Update xlb */
    113:     offset += pdipm->nxub;
    114:     ISGetIndices(pdipm->isxlb,&lbptr); /* global indices in x */
    115:     for (k=0; k<pdipm->nxlb; k++){
    116:       i = lbptr[k]-xstart;
    117:       carr[offset + k] = xarr[i] - xlarr[i];
    118:     }
    119:   }

    121:   if (pdipm->Nxbox) {
    122:     /* (2.d) Update xbox */
    123:     offset += pdipm->nxlb;
    124:     offset1 = offset + pdipm->nxbox;
    125:     ISGetIndices(pdipm->isxbox,&bxptr); /* global indices in x */
    126:     for (k=0; k<pdipm->nxbox; k++){
    127:       i = bxptr[k]-xstart; /* local indices in x */
    128:       carr[offset+k]  = xuarr[i] - xarr[i];
    129:       carr[offset1+k] = xarr[i]  - xlarr[i];
    130:     }
    131:   }
    132:   VecRestoreArray(pdipm->ci,&carr);

    134:   /* Restoring Vectors */
    135:   VecRestoreArrayRead(x,&xarr);
    136:   VecRestoreArrayRead(tao->XU,&xuarr);
    137:   VecRestoreArrayRead(tao->XL,&xlarr);
    138:   return(0);
    139: }

    141: /*
    142:    TaoPDIPMSetUpBounds - Create upper and lower bound vectors of x

    144:    Collective

    146:    Input Parameter:
    147: .  tao - holds pdipm and XL & XU

    149:    Level: beginner

    151: .seealso: TaoPDIPMUpdateConstraints
    152: */
    153: PetscErrorCode TaoPDIPMSetUpBounds(Tao tao)
    154: {
    155:   PetscErrorCode    ierr;
    156:   TAO_PDIPM         *pdipm=(TAO_PDIPM*)tao->data;
    157:   const PetscScalar *xl,*xu;
    158:   PetscInt          n,*ixlb,*ixub,*ixfixed,*ixfree,*ixbox,i,low,high,idx;
    159:   MPI_Comm          comm;
    160:   PetscInt          sendbuf[5],recvbuf[5];

    163:   /* Creates upper and lower bounds vectors on x, if not created already */
    164:   TaoComputeVariableBounds(tao);

    166:   VecGetLocalSize(tao->XL,&n);
    167:   PetscMalloc5(n,&ixlb,n,&ixub,n,&ixfree,n,&ixfixed,n,&ixbox);

    169:   VecGetOwnershipRange(tao->XL,&low,&high);
    170:   VecGetArrayRead(tao->XL,&xl);
    171:   VecGetArrayRead(tao->XU,&xu);
    172:   for (i=0; i<n; i++) {
    173:     idx = low + i;
    174:     if ((PetscRealPart(xl[i]) > PETSC_NINFINITY) && (PetscRealPart(xu[i]) < PETSC_INFINITY)) {
    175:       if (PetscRealPart(xl[i]) == PetscRealPart(xu[i])) {
    176:         ixfixed[pdipm->nxfixed++]  = idx;
    177:       } else ixbox[pdipm->nxbox++] = idx;
    178:     } else {
    179:       if ((PetscRealPart(xl[i]) > PETSC_NINFINITY) && (PetscRealPart(xu[i]) >= PETSC_INFINITY)) {
    180:         ixlb[pdipm->nxlb++] = idx;
    181:       } else if ((PetscRealPart(xl[i]) <= PETSC_NINFINITY) && (PetscRealPart(xu[i]) < PETSC_INFINITY)) {
    182:         ixub[pdipm->nxlb++] = idx;
    183:       } else  ixfree[pdipm->nxfree++] = idx;
    184:     }
    185:   }
    186:   VecRestoreArrayRead(tao->XL,&xl);
    187:   VecRestoreArrayRead(tao->XU,&xu);

    189:   PetscObjectGetComm((PetscObject)tao,&comm);
    190:   sendbuf[0] = pdipm->nxlb;
    191:   sendbuf[1] = pdipm->nxub;
    192:   sendbuf[2] = pdipm->nxfixed;
    193:   sendbuf[3] = pdipm->nxbox;
    194:   sendbuf[4] = pdipm->nxfree;

    196:   MPI_Allreduce(sendbuf,recvbuf,5,MPIU_INT,MPI_SUM,comm);
    197:   pdipm->Nxlb    = recvbuf[0];
    198:   pdipm->Nxub    = recvbuf[1];
    199:   pdipm->Nxfixed = recvbuf[2];
    200:   pdipm->Nxbox   = recvbuf[3];
    201:   pdipm->Nxfree  = recvbuf[4];

    203:   if (pdipm->Nxlb) {
    204:     ISCreateGeneral(comm,pdipm->nxlb,ixlb,PETSC_COPY_VALUES,&pdipm->isxlb);
    205:   }
    206:   if (pdipm->Nxub) {
    207:     ISCreateGeneral(comm,pdipm->nxub,ixub,PETSC_COPY_VALUES,&pdipm->isxub);
    208:   }
    209:   if (pdipm->Nxfixed) {
    210:     ISCreateGeneral(comm,pdipm->nxfixed,ixfixed,PETSC_COPY_VALUES,&pdipm->isxfixed);
    211:   }
    212:   if (pdipm->Nxbox) {
    213:     ISCreateGeneral(comm,pdipm->nxbox,ixbox,PETSC_COPY_VALUES,&pdipm->isxbox);
    214:   }
    215:   if (pdipm->Nxfree) {
    216:     ISCreateGeneral(comm,pdipm->nxfree,ixfree,PETSC_COPY_VALUES,&pdipm->isxfree);
    217:   }
    218:   PetscFree5(ixlb,ixub,ixfixed,ixbox,ixfree);
    219:   return(0);
    220: }

    222: /*
    223:    TaoPDIPMInitializeSolution - Initialize PDIPM solution X = [x; lambdae; lambdai; z].
    224:    X consists of four subvectors in the order [x; lambdae; lambdai; z]. These
    225:      four subvectors need to be initialized and its values copied over to X. Instead
    226:      of copying, we use VecPlace/ResetArray functions to share the memory locations for
    227:      X and the subvectors

    229:    Collective

    231:    Input Parameter:
    232: .  tao - Tao context

    234:    Level: beginner
    235: */
    236: PetscErrorCode TaoPDIPMInitializeSolution(Tao tao)
    237: {
    238:   PetscErrorCode    ierr;
    239:   TAO_PDIPM         *pdipm = (TAO_PDIPM*)tao->data;
    240:   PetscScalar       *Xarr,*z,*lambdai;
    241:   PetscInt          i;
    242:   const PetscScalar *xarr,*h;

    245:   VecGetArray(pdipm->X,&Xarr);

    247:   /* Set Initialize X.x = tao->solution */
    248:   VecGetArrayRead(tao->solution,&xarr);
    249:   PetscMemcpy(Xarr,xarr,pdipm->nx*sizeof(PetscScalar));
    250:   VecRestoreArrayRead(tao->solution,&xarr);

    252:   /* Initialize X.lambdae = 0.0 */
    253:   if (pdipm->lambdae) {
    254:     VecSet(pdipm->lambdae,0.0);
    255:   }
    256:   /* Initialize X.lambdai = push_init_lambdai, X.z = push_init_slack */
    257:   if (pdipm->lambdai) {
    258:     VecSet(pdipm->lambdai,pdipm->push_init_lambdai);
    259:   }
    260:   if (pdipm->z) {
    261:     VecSet(pdipm->z,pdipm->push_init_slack);
    262:   }

    264:   /* Additional modification for X.lambdai and X.z */
    265:   if (pdipm->lambdai) {
    266:     VecGetArray(pdipm->lambdai,&lambdai);
    267:   }
    268:   if (pdipm->z) {
    269:     VecGetArray(pdipm->z,&z);
    270:   }
    271:   if (pdipm->Nh) {
    272:     VecGetArrayRead(tao->constraints_inequality,&h);
    273:     for (i=0; i < pdipm->nh; i++) {
    274:       if (h[i] < -pdipm->push_init_slack) z[i] = -h[i];
    275:       if (pdipm->mu/z[i] > pdipm->push_init_lambdai) lambdai[i] = pdipm->mu/z[i];
    276:     }
    277:     VecRestoreArrayRead(tao->constraints_inequality,&h);
    278:   }
    279:   if (pdipm->lambdai) {
    280:     VecRestoreArray(pdipm->lambdai,&lambdai);
    281:   }
    282:   if (pdipm->z) {
    283:     VecRestoreArray(pdipm->z,&z);
    284:   }

    286:   VecRestoreArray(pdipm->X,&Xarr);
    287:   return(0);
    288: }

    290: /*
    291:    TaoSNESJacobian_PDIPM - Evaluate the Hessian matrix at X

    293:    Input Parameter:
    294:    snes - SNES context
    295:    X - KKT Vector
    296:    *ctx - pdipm context

    298:    Output Parameter:
    299:    J - Hessian matrix
    300:    Jpre - Preconditioner
    301: */
    302: PetscErrorCode TaoSNESJacobian_PDIPM(SNES snes,Vec X, Mat J, Mat Jpre, void *ctx)
    303: {
    304:   PetscErrorCode    ierr;
    305:   Tao               tao=(Tao)ctx;
    306:   TAO_PDIPM         *pdipm = (TAO_PDIPM*)tao->data;
    307:   PetscInt          i,row,cols[2],Jrstart,rjstart,nc,j;
    308:   const PetscInt    *aj,*ranges,*Jranges,*rranges,*cranges;
    309:   const PetscScalar *Xarr,*aa;
    310:   PetscScalar       vals[2];
    311:   PetscInt          proc,nx_all,*nce_all=pdipm->nce_all;
    312:   MPI_Comm          comm;
    313:   PetscMPIInt       rank,size;
    314:   Mat               jac_equality_trans=pdipm->jac_equality_trans,jac_inequality_trans=pdipm->jac_inequality_trans;

    317:   PetscObjectGetComm((PetscObject)snes,&comm);
    318:   MPI_Comm_rank(comm,&rank);
    319:   MPI_Comm_rank(comm,&size);

    321:   MatGetOwnershipRanges(Jpre,&Jranges);
    322:   MatGetOwnershipRange(Jpre,&Jrstart,NULL);
    323:   MatGetOwnershipRangesColumn(tao->hessian,&rranges);
    324:   MatGetOwnershipRangesColumn(tao->hessian,&cranges);

    326:   VecGetArrayRead(X,&Xarr);

    328:   if (pdipm->solve_symmetric_kkt) { /* 1 for eq 17 revised pdipm doc 0 for eq 18 (symmetric KKT) */
    329:     vals[0] = 1.0;
    330:     for (i=0; i < pdipm->nci; i++) {
    331:         row     = Jrstart + pdipm->off_z + i;
    332:         cols[0] = Jrstart + pdipm->off_lambdai + i;
    333:         cols[1] = row;
    334:         vals[1] = Xarr[pdipm->off_lambdai + i]/Xarr[pdipm->off_z + i];
    335:         MatSetValues(Jpre,1,&row,2,cols,vals,INSERT_VALUES);
    336:     }
    337:   } else {
    338:     /* (2) insert Z and Ci to Jpre -- overwrite existing values */
    339:     for (i=0; i < pdipm->nci; i++) {
    340:       row     = Jrstart + pdipm->off_z + i;
    341:       cols[0] = Jrstart + pdipm->off_lambdai + i;
    342:       cols[1] = row;
    343:       vals[0] = Xarr[pdipm->off_z + i];
    344:       vals[1] = Xarr[pdipm->off_lambdai + i];
    345:       MatSetValues(Jpre,1,&row,2,cols,vals,INSERT_VALUES);
    346:     }
    347:   }

    349:   /* (3) insert 2nd row block of Jpre: [ grad g, 0, 0, 0] */
    350:   if (pdipm->Ng) {
    351:     MatGetOwnershipRange(tao->jacobian_equality,&rjstart,NULL);
    352:     for (i=0; i<pdipm->ng; i++){
    353:       row = Jrstart + pdipm->off_lambdae + i;

    355:       MatGetRow(tao->jacobian_equality,i+rjstart,&nc,&aj,&aa);
    356:       proc = 0;
    357:       for (j=0; j < nc; j++) {
    358:         while (aj[j] >= cranges[proc+1]) proc++;
    359:         cols[0] = aj[j] - cranges[proc] + Jranges[proc];
    360:         MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
    361:       }
    362:       MatRestoreRow(tao->jacobian_equality,i+rjstart,&nc,&aj,&aa);
    363:       if (pdipm->kkt_pd) {
    364:         /* (3) insert 2nd row block of Jpre: [ grad g, \delta_c*I, 0, 0] */
    365:         MatSetValue(Jpre,row,row,-pdipm->deltac,INSERT_VALUES);
    366:       }
    367:     }
    368:   }

    370:   if (pdipm->Nh) {
    371:     /* (4) insert 3nd row block of Jpre: [ -grad h, 0, deltac, I] */
    372:     MatGetOwnershipRange(tao->jacobian_inequality,&rjstart,NULL);
    373:     for (i=0; i < pdipm->nh; i++){
    374:       row = Jrstart + pdipm->off_lambdai + i;
    375:       MatGetRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,&aa);
    376:       proc = 0;
    377:       for (j=0; j < nc; j++) {
    378:         while (aj[j] >= cranges[proc+1]) proc++;
    379:         cols[0] = aj[j] - cranges[proc] + Jranges[proc];
    380:         MatSetValue(Jpre,row,cols[0],-aa[j],INSERT_VALUES);
    381:       }
    382:       MatRestoreRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,&aa);
    383:       if (pdipm->kkt_pd) {
    384:         MatSetValue(Jpre,row,row,-pdipm->deltac,INSERT_VALUES);
    385:       }
    386:     }
    387:   }

    389:   /* (5) insert Wxx, grad g' and -grad h' to Jpre */
    390:   if (pdipm->Ng) {
    391:     MatTranspose(tao->jacobian_equality,MAT_REUSE_MATRIX,&jac_equality_trans);
    392:   }
    393:   if (pdipm->Nh) {
    394:     MatTranspose(tao->jacobian_inequality,MAT_REUSE_MATRIX,&jac_inequality_trans);
    395:   }

    397:   VecPlaceArray(pdipm->x,Xarr);
    398:   TaoComputeHessian(tao,pdipm->x,tao->hessian,tao->hessian_pre);
    399:   VecResetArray(pdipm->x);

    401:   MatGetOwnershipRange(tao->hessian,&rjstart,NULL);
    402:   for (i=0; i<pdipm->nx; i++) {
    403:     row = Jrstart + i;

    405:     /* insert Wxx */
    406:     MatGetRow(tao->hessian,i+rjstart,&nc,&aj,&aa);
    407:     proc = 0;
    408:     for (j=0; j < nc; j++) {
    409:       while (aj[j] >= cranges[proc+1]) proc++;
    410:       cols[0] = aj[j] - cranges[proc] + Jranges[proc];
    411:       if (row == cols[0] && pdipm->kkt_pd) {
    412:         /* add diagonal shift to Wxx component */
    413:         MatSetValue(Jpre,row,cols[0],aa[j]+pdipm->deltaw,INSERT_VALUES);
    414:       } else {
    415:         MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
    416:       }
    417:     }
    418:     MatRestoreRow(tao->hessian,i+rjstart,&nc,&aj,&aa);

    420:     if (pdipm->ng) {
    421:       /* insert grad g' */
    422:       MatGetRow(jac_equality_trans,i+rjstart,&nc,&aj,&aa);
    423:       MatGetOwnershipRanges(tao->jacobian_equality,&ranges);
    424:       proc = 0;
    425:       for (j=0; j < nc; j++) {
    426:         /* find row ownership of */
    427:         while (aj[j] >= ranges[proc+1]) proc++;
    428:         nx_all = rranges[proc+1] - rranges[proc];
    429:         cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
    430:         MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
    431:       }
    432:       MatRestoreRow(jac_equality_trans,i+rjstart,&nc,&aj,&aa);
    433:     }

    435:     if (pdipm->nh) {
    436:       /* insert -grad h' */
    437:       MatGetRow(jac_inequality_trans,i+rjstart,&nc,&aj,&aa);
    438:       MatGetOwnershipRanges(tao->jacobian_inequality,&ranges);
    439:       proc = 0;
    440:       for (j=0; j < nc; j++) {
    441:         /* find row ownership of */
    442:         while (aj[j] >= ranges[proc+1]) proc++;
    443:         nx_all = rranges[proc+1] - rranges[proc];
    444:         cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
    445:         MatSetValue(Jpre,row,cols[0],-aa[j],INSERT_VALUES);
    446:       }
    447:       MatRestoreRow(jac_inequality_trans,i+rjstart,&nc,&aj,&aa);
    448:     }
    449:   }
    450:   VecRestoreArrayRead(X,&Xarr);

    452:   /* (6) assemble Jpre and J */
    453:   MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
    454:   MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);

    456:   if (J != Jpre) {
    457:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
    458:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
    459:   }
    460:   return(0);
    461: }

    463: /*
    464:    TaoSnesFunction_PDIPM - Evaluate KKT function at X

    466:    Input Parameter:
    467:    snes - SNES context
    468:    X - KKT Vector
    469:    *ctx - pdipm

    471:    Output Parameter:
    472:    F - Updated Lagrangian vector
    473: */
    474: PetscErrorCode TaoSNESFunction_PDIPM(SNES snes,Vec X,Vec F,void *ctx)
    475: {
    476:   PetscErrorCode    ierr;
    477:   Tao               tao=(Tao)ctx;
    478:   TAO_PDIPM         *pdipm = (TAO_PDIPM*)tao->data;
    479:   PetscScalar       *Farr,*tmparr;
    480:   Vec               x,L1;
    481:   PetscInt          i;
    482:   PetscReal         res[2],cnorm[2];
    483:   const PetscScalar *Xarr,*carr,*zarr,*larr;

    486:   VecSet(F,0.0);

    488:   VecGetArrayRead(X,&Xarr);
    489:   VecGetArray(F,&Farr);

    491:   /* (0) Evaluate f, fx, Gx, Hx at X.x Note: pdipm->x is not changed below */
    492:   x = pdipm->x;
    493:   VecPlaceArray(x,Xarr);
    494:   TaoPDIPMEvaluateFunctionsAndJacobians(tao,x);

    496:   /* Update ce, ci, and Jci at X.x */
    497:   TaoPDIPMUpdateConstraints(tao,x);
    498:   VecResetArray(x);

    500:   /* (1) L1 = fx + (gradG'*DE + Jce_xfixed'*lambdae_xfixed) - (gradH'*DI + Jci_xb'*lambdai_xb) */
    501:   L1 = pdipm->x;
    502:   VecPlaceArray(L1,Farr);
    503:   if (pdipm->Nci) {
    504:     if (pdipm->Nh) {
    505:       /* L1 += gradH'*DI. Note: tao->DI is not changed below */
    506:       VecPlaceArray(tao->DI,Xarr+pdipm->off_lambdai);
    507:       MatMultTransposeAdd(tao->jacobian_inequality,tao->DI,L1,L1);
    508:       VecResetArray(tao->DI);
    509:     }

    511:     /* L1 += Jci_xb'*lambdai_xb */
    512:     VecPlaceArray(pdipm->lambdai_xb,Xarr+pdipm->off_lambdai+pdipm->nh);
    513:     MatMultTransposeAdd(pdipm->Jci_xb,pdipm->lambdai_xb,L1,L1);
    514:     VecResetArray(pdipm->lambdai_xb);

    516:     /* (1.4) L1 = - (gradH'*DI + Jci_xb'*lambdai_xb) */
    517:     VecScale(L1,-1.0);
    518:   }

    520:   /* L1 += fx */
    521:   VecAXPY(L1,1.0,tao->gradient);

    523:   if (pdipm->Nce) {
    524:     if (pdipm->Ng) {
    525:       /* L1 += gradG'*DE. Note: tao->DE is not changed below */
    526:       VecPlaceArray(tao->DE,Xarr+pdipm->off_lambdae);
    527:       MatMultTransposeAdd(tao->jacobian_equality,tao->DE,L1,L1);
    528:       VecResetArray(tao->DE);
    529:     }
    530:     if (pdipm->Nxfixed) {
    531:       /* L1 += Jce_xfixed'*lambdae_xfixed */
    532:       VecPlaceArray(pdipm->lambdae_xfixed,Xarr+pdipm->off_lambdae+pdipm->ng);
    533:       MatMultTransposeAdd(pdipm->Jce_xfixed,pdipm->lambdae_xfixed,L1,L1);
    534:       VecResetArray(pdipm->lambdae_xfixed);
    535:     }
    536:   }
    537:   VecNorm(L1,NORM_2,&res[0]);
    538:   VecResetArray(L1);

    540:   /* (2) L2 = ce(x) */
    541:   if (pdipm->Nce) {
    542:     VecGetArrayRead(pdipm->ce,&carr);
    543:     for (i=0; i<pdipm->nce; i++) Farr[pdipm->off_lambdae + i] = carr[i];
    544:     VecRestoreArrayRead(pdipm->ce,&carr);
    545:   }
    546:   VecNorm(pdipm->ce,NORM_2,&cnorm[0]);

    548:   if (pdipm->Nci) {
    549:     if (pdipm->solve_symmetric_kkt) {
    550:       /* (3) L3 = ci(x) - z;
    551:          (4) L4 = Lambdai * e - mu/z *e
    552:       */
    553:       VecGetArrayRead(pdipm->ci,&carr);
    554:       larr = Xarr+pdipm->off_lambdai;
    555:       zarr = Xarr+pdipm->off_z;
    556:       for (i=0; i<pdipm->nci; i++) {
    557:         Farr[pdipm->off_lambdai + i] = zarr[i] - carr[i];
    558:         Farr[pdipm->off_z       + i] = larr[i] - pdipm->mu/zarr[i];
    559:       }
    560:       VecRestoreArrayRead(pdipm->ci,&carr);
    561:     } else {
    562:       /* (3) L3 = ci(x) - z;
    563:          (4) L4 = Z * Lambdai * e - mu * e
    564:       */
    565:       VecGetArrayRead(pdipm->ci,&carr);
    566:       larr = Xarr+pdipm->off_lambdai;
    567:       zarr = Xarr+pdipm->off_z;
    568:       for (i=0; i<pdipm->nci; i++) {
    569:         Farr[pdipm->off_lambdai + i] = zarr[i] - carr[i];
    570:         Farr[pdipm->off_z       + i] = zarr[i]*larr[i] - pdipm->mu;
    571:       }
    572:       VecRestoreArrayRead(pdipm->ci,&carr);
    573:     }
    574:   }

    576:   VecPlaceArray(pdipm->ci,Farr+pdipm->off_lambdai);
    577:   VecNorm(pdipm->ci,NORM_2,&cnorm[1]);
    578:   VecResetArray(pdipm->ci);

    580:   /* note: pdipm->z is not changed below */
    581:   if (pdipm->z) {
    582:     if (pdipm->solve_symmetric_kkt) {
    583:       VecPlaceArray(pdipm->z,Farr+pdipm->off_z);
    584:       if (pdipm->Nci) {
    585:         zarr = Xarr+pdipm->off_z;
    586:         VecGetArrayWrite(pdipm->z,&tmparr);
    587:         for (i=0; i<pdipm->nci; i++) tmparr[i] *= Xarr[pdipm->off_z + i];
    588:         VecRestoreArrayWrite(pdipm->z,&tmparr);
    589:       }

    591:       VecNorm(pdipm->z,NORM_2,&res[1]);
    592:       if (pdipm->Nci) {
    593:         zarr = Xarr+pdipm->off_z;
    594:         VecGetArray(pdipm->z,&tmparr);
    595:         for (i=0; i<pdipm->nci; i++) {
    596:           tmparr[i] /= Xarr[pdipm->off_z + i];
    597:         }
    598:         VecRestoreArray(pdipm->z,&tmparr);
    599:       }
    600:       VecResetArray(pdipm->z);
    601:     } else {
    602:       VecPlaceArray(pdipm->z,Farr+pdipm->off_z);
    603:       VecNorm(pdipm->z,NORM_2,&res[1]);
    604:       VecResetArray(pdipm->z);
    605:     }
    606:   } else res[1] = 0.0;

    608:   tao->residual = PetscSqrtReal(res[0]*res[0] + res[1]*res[1]);
    609:   tao->cnorm    = PetscSqrtReal(cnorm[0]*cnorm[0] + cnorm[1]*cnorm[1]);

    611:   VecRestoreArrayRead(X,&Xarr);
    612:   VecRestoreArray(F,&Farr);
    613:   return(0);
    614: }

    616: #include <petsc/private/matimpl.h>
    617: /*
    618:    PDIPMLineSearch - Custom line search used with PDIPM.

    620:    Collective on TAO

    622:    Notes:
    623:    PDIPMLineSearch employs a simple backtracking line-search to keep
    624:    the slack variables (z) and inequality constraints lagrange multipliers
    625:    (lambdai) positive, i.e., z,lambdai >=0. It does this by calculating scalars
    626:    alpha_p and alpha_d to keep z,lambdai non-negative. The decision (x), and the
    627:    slack variables are updated as X = X + alpha_d*dx. The constraint multipliers
    628:    are updated as Lambdai = Lambdai + alpha_p*dLambdai. The barrier parameter mu
    629:    is also updated as mu = mu + z'lambdai/Nci
    630: */
    631: PetscErrorCode PDIPMLineSearch(SNESLineSearch linesearch,void *ctx)
    632: {
    633:   PetscErrorCode    ierr;
    634:   Tao               tao=(Tao)ctx;
    635:   TAO_PDIPM         *pdipm = (TAO_PDIPM*)tao->data;
    636:   SNES              snes;
    637:   KSP               ksp;
    638:   PC                pc;
    639:   PCType            ptype;
    640:   Mat               Factor;
    641:   Vec               X,F,Y,W,G;
    642:   PetscInt          i,iter,nneg,nzero,npos;
    643:   PetscReal         alpha_p=1.0,alpha_d=1.0,alpha[4];
    644:   PetscScalar       *Xarr,*z,*lambdai,dot,*taosolarr;
    645:   const PetscScalar *dXarr,*dz,*dlambdai;
    646:   PetscBool         isCHOL;

    649:   SNESLineSearchGetSNES(linesearch,&snes);
    650:   SNESGetIterationNumber(snes,&iter);

    652:   SNESLineSearchSetReason(linesearch,SNES_LINESEARCH_SUCCEEDED);
    653:   SNESLineSearchGetVecs(linesearch,&X,&F,&Y,&W,&G);

    655:   VecGetArray(X,&Xarr);
    656:   VecGetArrayRead(Y,&dXarr);
    657:   z  = Xarr + pdipm->off_z;
    658:   dz = dXarr + pdipm->off_z;
    659:   for (i=0; i < pdipm->nci; i++) {
    660:     if (z[i] - dz[i] < 0.0) {
    661:       alpha_p = PetscMin(alpha_p,0.9999*z[i]/dz[i]);
    662:     }
    663:   }

    665:   lambdai  = Xarr + pdipm->off_lambdai;
    666:   dlambdai = dXarr + pdipm->off_lambdai;

    668:   for (i=0; i<pdipm->nci; i++) {
    669:     if (lambdai[i] - dlambdai[i] < 0.0) {
    670:       alpha_d = PetscMin(0.9999*lambdai[i]/dlambdai[i],alpha_d);
    671:     }
    672:   }

    674:   alpha[0] = alpha_p;
    675:   alpha[1] = alpha_d;
    676:   VecRestoreArrayRead(Y,&dXarr);
    677:   VecRestoreArray(X,&Xarr);

    679:   /* alpha = min(alpha) over all processes */
    680:   MPI_Allreduce(alpha,alpha+2,2,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)tao));

    682:   alpha_p = alpha[2];
    683:   alpha_d = alpha[3];

    685:   VecGetArray(X,&Xarr);
    686:   VecGetArrayRead(Y,&dXarr);
    687:   for (i=0; i<pdipm->nx; i++) {
    688:     Xarr[i] = Xarr[i] - alpha_p * dXarr[i];
    689:   }

    691:   for (i=0; i<pdipm->nce; i++) {
    692:     Xarr[i+pdipm->off_lambdae] = Xarr[i+pdipm->off_lambdae] - alpha_d * dXarr[i+pdipm->off_lambdae];
    693:   }

    695:   for (i=0; i<pdipm->nci; i++) {
    696:     Xarr[i+pdipm->off_lambdai] = Xarr[i+pdipm->off_lambdai] - alpha_d * dXarr[i+pdipm->off_lambdai];
    697:   }

    699:   for (i=0; i<pdipm->nci; i++) {
    700:     Xarr[i+pdipm->off_z] = Xarr[i+pdipm->off_z] - alpha_p * dXarr[i+pdipm->off_z];
    701:   }

    703:   VecGetArray(tao->solution,&taosolarr);
    704:   PetscMemcpy(taosolarr,Xarr,pdipm->nx*sizeof(PetscScalar));
    705:   VecRestoreArray(tao->solution,&taosolarr);

    708:   VecRestoreArray(X,&Xarr);
    709:   VecRestoreArrayRead(Y,&dXarr);

    711:   /* Evaluate F at X */
    712:   SNESComputeFunction(snes,X,F);
    713:   SNESLineSearchComputeNorms(linesearch); /* must call this func, do not know why */

    715:   /* update mu = mu_update_factor * dot(z,lambdai)/pdipm->nci at updated X */
    716:   if (pdipm->z) {
    717:     VecDot(pdipm->z,pdipm->lambdai,&dot);
    718:   } else dot = 0.0;

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

    723:   /* Update F; get tao->residual and tao->cnorm */
    724:   TaoSNESFunction_PDIPM(snes,X,F,(void*)tao);

    726:   tao->niter++;
    727:   TaoLogConvergenceHistory(tao,pdipm->obj,tao->residual,tao->cnorm,tao->niter);
    728:   TaoMonitor(tao,tao->niter,pdipm->obj,tao->residual,tao->cnorm,pdipm->mu);

    730:   (*tao->ops->convergencetest)(tao,tao->cnvP);
    731:   if (tao->reason) {
    732:     SNESSetConvergedReason(snes,SNES_CONVERGED_FNORM_ABS);
    733:   }

    735:   if (!pdipm->kkt_pd) return(0);

    737:   /* Get the inertia of Cholesky factor to set shifts for next SNES interation */
    738:   SNESGetKSP(snes,&ksp);
    739:   KSPGetPC(ksp,&pc);
    740:   PCGetType(pc,&ptype);
    741:   PetscObjectTypeCompare((PetscObject)pc,PCCHOLESKY,&isCHOL);

    743:   if (isCHOL) {
    744:     PetscMPIInt       size;
    745:     PCFactorGetMatrix(pc,&Factor);
    746:     MPI_Comm_size(PetscObjectComm((PetscObject)Factor),&size);
    747:     if (Factor->ops->getinertia) {
    748: #if defined(PETSC_HAVE_MUMPS)
    749:       MatSolverType     stype;
    750:       PetscBool         isMUMPS;
    751:       PCFactorGetMatSolverType(pc,&stype);
    752:       PetscStrcmp(stype, MATSOLVERMUMPS, &isMUMPS);
    753:       if (isMUMPS) { /* must set mumps ICNTL(13)=1 and ICNTL(24)=1 to call MatGetInertia() */
    754:         MatMumpsSetIcntl(Factor,24,1);
    755:         if (size > 1) {
    756:           MatMumpsSetIcntl(Factor,13,1);
    757:         }
    758:       }
    759: #else
    760:       if (size > 1) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_SUP,"Requires external package MUMPS");
    761: #endif
    762:       MatGetInertia(Factor,&nneg,&nzero,&npos);

    764:       if (npos < pdipm->Nx+pdipm->Nci) {
    765:         pdipm->deltaw = PetscMax(pdipm->lastdeltaw/3, 1.e-4*PETSC_MACHINE_EPSILON);
    766:         PetscInfo5(tao,"Test reduced deltaw=%g; previous MatInertia: nneg %d, nzero %d, npos %d(<%d)\n",pdipm->deltaw,nneg,nzero,npos,pdipm->Nx+pdipm->Nci);
    767:         TaoSNESJacobian_PDIPM(snes,X, pdipm->K, pdipm->K, tao);
    768:         PCSetUp(pc);
    769:         MatGetInertia(Factor,&nneg,&nzero,&npos);

    771:         if (npos < pdipm->Nx+pdipm->Nci) {
    772:           pdipm->deltaw = pdipm->lastdeltaw; /* in case reduction update does not help, this prevents that step from impacting increasing update */
    773:           while (npos < pdipm->Nx+pdipm->Nci && pdipm->deltaw <= 1.e10) { /* increase deltaw */
    774:             PetscInfo5(tao,"  deltaw=%g fails, MatInertia: nneg %d, nzero %d, npos %d(<%d)\n",pdipm->deltaw,nneg,nzero,npos,pdipm->Nx+pdipm->Nci);
    775:             pdipm->deltaw = PetscMin(8*pdipm->deltaw,PetscPowReal(10,20));
    776:             TaoSNESJacobian_PDIPM(snes,X, pdipm->K, pdipm->K, tao);
    777:             PCSetUp(pc);
    778:             MatGetInertia(Factor,&nneg,&nzero,&npos);
    779:           }

    781:           if (pdipm->deltaw >= 1.e10) {
    782:             SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_CONV_FAILED,"Reached maximum delta w will not converge, try different inital x0");
    783:           }
    784:           PetscInfo1(tao,"Updated deltaw %g\n",pdipm->deltaw);
    785:           pdipm->lastdeltaw = pdipm->deltaw;
    786:           pdipm->deltaw     = 0.0;
    787:         }
    788:       }

    790:       if (nzero) { /* Jacobian is singular */
    791:         if (pdipm->deltac == 0.0) {
    792:           pdipm->deltac = 1.e8*PETSC_MACHINE_EPSILON;
    793:         } else {
    794:           pdipm->deltac = pdipm->deltac*PetscPowReal(pdipm->mu,.25);
    795:         }
    796:         PetscInfo4(tao,"Updated deltac=%g, MatInertia: nneg %D, nzero %D(!=0), npos %D\n",pdipm->deltac,nneg,nzero,npos);
    797:       }
    798:     } else
    799:       SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_SUP,"Requires an external package that supports MatGetInertia()");
    800:   }
    801:   return(0);
    802: }

    804: /*
    805:    TaoSolve_PDIPM

    807:    Input Parameter:
    808:    tao - TAO context

    810:    Output Parameter:
    811:    tao - TAO context
    812: */
    813: PetscErrorCode TaoSolve_PDIPM(Tao tao)
    814: {
    815:   PetscErrorCode     ierr;
    816:   TAO_PDIPM          *pdipm = (TAO_PDIPM*)tao->data;
    817:   SNESLineSearch     linesearch; /* SNESLineSearch context */
    818:   Vec                dummy;

    821:   if (!tao->constraints_equality && !tao->constraints_inequality) SETERRQ(PetscObjectComm((PetscObject)tao),PETSC_ERR_ARG_NULL,"Equality and inequality constraints are not set. Either set them or switch to a different algorithm");

    823:   /* Initialize all variables */
    824:   TaoPDIPMInitializeSolution(tao);

    826:   /* Set linesearch */
    827:   SNESGetLineSearch(pdipm->snes,&linesearch);
    828:   SNESLineSearchSetType(linesearch,SNESLINESEARCHSHELL);
    829:   SNESLineSearchShellSetUserFunc(linesearch,PDIPMLineSearch,tao);
    830:   SNESLineSearchSetFromOptions(linesearch);

    832:   tao->reason = TAO_CONTINUE_ITERATING;

    834:   /* -tao_monitor for iteration 0 and check convergence */
    835:   VecDuplicate(pdipm->X,&dummy);
    836:   TaoSNESFunction_PDIPM(pdipm->snes,pdipm->X,dummy,(void*)tao);

    838:   TaoLogConvergenceHistory(tao,pdipm->obj,tao->residual,tao->cnorm,tao->niter);
    839:   TaoMonitor(tao,tao->niter,pdipm->obj,tao->residual,tao->cnorm,pdipm->mu);
    840:   VecDestroy(&dummy);
    841:   (*tao->ops->convergencetest)(tao,tao->cnvP);
    842:   if (tao->reason) {
    843:     SNESSetConvergedReason(pdipm->snes,SNES_CONVERGED_FNORM_ABS);
    844:   }

    846:   while (tao->reason == TAO_CONTINUE_ITERATING) {
    847:     SNESConvergedReason reason;
    848:     SNESSolve(pdipm->snes,NULL,pdipm->X);

    850:     /* Check SNES convergence */
    851:     SNESGetConvergedReason(pdipm->snes,&reason);
    852:     if (reason < 0) {
    853:       PetscPrintf(PetscObjectComm((PetscObject)pdipm->snes),"SNES solve did not converged due to reason %D\n",reason);
    854:     }

    856:     /* Check TAO convergence */
    857:     if (PetscIsInfOrNanReal(pdipm->obj)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"User-provided compute function generated Inf or NaN");
    858:   }
    859:   return(0);
    860: }

    862: /*
    863:   TaoView_PDIPM - View PDIPM

    865:    Input Parameter:
    866:     tao - TAO object
    867:     viewer - PetscViewer

    869:    Output:
    870: */
    871: PetscErrorCode TaoView_PDIPM(Tao tao,PetscViewer viewer)
    872: {
    873:   TAO_PDIPM      *pdipm = (TAO_PDIPM *)tao->data;

    877:   tao->constrained = PETSC_TRUE;
    878:   PetscViewerASCIIPushTab(viewer);
    879:   PetscViewerASCIIPrintf(viewer,"Number of prime=%D, Number of dual=%D\n",pdipm->Nx+pdipm->Nci,pdipm->Nce + pdipm->Nci);
    880:   if (pdipm->kkt_pd) {
    881:     PetscViewerASCIIPrintf(viewer,"KKT shifts deltaw=%g, deltac=%g\n",pdipm->deltaw,pdipm->deltac);
    882:   }
    883:   PetscViewerASCIIPopTab(viewer);
    884:   return(0);
    885: }

    887: /*
    888:    TaoSetup_PDIPM - Sets up tao and pdipm

    890:    Input Parameter:
    891:    tao - TAO object

    893:    Output:   pdipm - initialized object
    894: */
    895: PetscErrorCode TaoSetup_PDIPM(Tao tao)
    896: {
    897:   TAO_PDIPM         *pdipm = (TAO_PDIPM*)tao->data;
    898:   PetscErrorCode    ierr;
    899:   MPI_Comm          comm;
    900:   PetscMPIInt       rank,size;
    901:   PetscInt          row,col,Jcrstart,Jcrend,k,tmp,nc,proc,*nh_all,*ng_all;
    902:   PetscInt          offset,*xa,*xb,i,j,rstart,rend;
    903:   PetscScalar       one=1.0,neg_one=-1.0,*Xarr;
    904:   const PetscInt    *cols,*rranges,*cranges,*aj,*ranges;
    905:   const PetscScalar *aa;
    906:   Mat               J,jac_equality_trans,jac_inequality_trans;
    907:   Mat               Jce_xfixed_trans,Jci_xb_trans;
    908:   PetscInt          *dnz,*onz,rjstart,nx_all,*nce_all,*Jranges,cols1[2];

    911:   PetscObjectGetComm((PetscObject)tao,&comm);
    912:   MPI_Comm_rank(comm,&rank);
    913:   MPI_Comm_size(comm,&size);

    915:   /* (1) Setup Bounds and create Tao vectors */
    916:   TaoPDIPMSetUpBounds(tao);

    918:   if (!tao->gradient) {
    919:     VecDuplicate(tao->solution,&tao->gradient);
    920:     VecDuplicate(tao->solution,&tao->stepdirection);
    921:   }

    923:   /* (2) Get sizes */
    924:   /* Size of vector x - This is set by TaoSetInitialVector */
    925:   VecGetSize(tao->solution,&pdipm->Nx);
    926:   VecGetLocalSize(tao->solution,&pdipm->nx);

    928:   /* Size of equality constraints and vectors */
    929:   if (tao->constraints_equality) {
    930:     VecGetSize(tao->constraints_equality,&pdipm->Ng);
    931:     VecGetLocalSize(tao->constraints_equality,&pdipm->ng);
    932:   } else {
    933:     pdipm->ng = pdipm->Ng = 0;
    934:   }

    936:   pdipm->nce = pdipm->ng + pdipm->nxfixed;
    937:   pdipm->Nce = pdipm->Ng + pdipm->Nxfixed;

    939:   /* Size of inequality constraints and vectors */
    940:   if (tao->constraints_inequality) {
    941:     VecGetSize(tao->constraints_inequality,&pdipm->Nh);
    942:     VecGetLocalSize(tao->constraints_inequality,&pdipm->nh);
    943:   } else {
    944:     pdipm->nh = pdipm->Nh = 0;
    945:   }

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

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

    954:   /* (3) Offsets for subvectors */
    955:   pdipm->off_lambdae = pdipm->nx;
    956:   pdipm->off_lambdai = pdipm->off_lambdae + pdipm->nce;
    957:   pdipm->off_z       = pdipm->off_lambdai + pdipm->nci;

    959:   /* (4) Create vectors and subvectors */
    960:   /* Ce and Ci vectors */
    961:   VecCreate(comm,&pdipm->ce);
    962:   VecSetSizes(pdipm->ce,pdipm->nce,pdipm->Nce);
    963:   VecSetFromOptions(pdipm->ce);

    965:   VecCreate(comm,&pdipm->ci);
    966:   VecSetSizes(pdipm->ci,pdipm->nci,pdipm->Nci);
    967:   VecSetFromOptions(pdipm->ci);

    969:   /* X=[x; lambdae; lambdai; z] for the big KKT system */
    970:   VecCreate(comm,&pdipm->X);
    971:   VecSetSizes(pdipm->X,pdipm->n,pdipm->N);
    972:   VecSetFromOptions(pdipm->X);

    974:   /* Subvectors; they share local arrays with X */
    975:   VecGetArray(pdipm->X,&Xarr);
    976:   /* x shares local array with X.x */
    977:   if (pdipm->Nx) {
    978:     VecCreateMPIWithArray(comm,1,pdipm->nx,pdipm->Nx,Xarr,&pdipm->x);
    979:   }

    981:   /* lambdae shares local array with X.lambdae */
    982:   if (pdipm->Nce) {
    983:     VecCreateMPIWithArray(comm,1,pdipm->nce,pdipm->Nce,Xarr+pdipm->off_lambdae,&pdipm->lambdae);
    984:   }

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

    990:     VecCreate(comm,&pdipm->lambdae_xfixed);
    991:     VecSetSizes(pdipm->lambdae_xfixed,pdipm->nxfixed,PETSC_DECIDE);
    992:     VecSetFromOptions(pdipm->lambdae_xfixed);
    993:   }

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

    999:     /* z for slack variables; it shares local array with X.z */
    1000:     VecCreateMPIWithArray(comm,1,pdipm->nci,pdipm->Nci,Xarr+pdipm->off_z,&pdipm->z);
    1001:   }

    1003:   /* tao->DI which shares local array with X.lambdai_h */
    1004:   if (pdipm->Nh) {
    1005:     VecCreateMPIWithArray(comm,1,pdipm->nh,pdipm->Nh,Xarr+pdipm->off_lambdai,&tao->DI);
    1006:   }

    1008:   VecCreate(comm,&pdipm->lambdai_xb);
    1009:   VecSetSizes(pdipm->lambdai_xb,(pdipm->nci - pdipm->nh),PETSC_DECIDE);
    1010:   VecSetFromOptions(pdipm->lambdai_xb);

    1012:   VecRestoreArray(pdipm->X,&Xarr);

    1014:   /* (5) Create Jacobians Jce_xfixed and Jci */
    1015:   /* (5.1) PDIPM Jacobian of equality bounds cebound(x) = J_nxfixed */
    1016:   if (pdipm->Nxfixed) {
    1017:     /* Create Jce_xfixed */
    1018:     MatCreate(comm,&pdipm->Jce_xfixed);
    1019:     MatSetSizes(pdipm->Jce_xfixed,pdipm->nxfixed,pdipm->nx,PETSC_DECIDE,pdipm->Nx);
    1020:     MatSetFromOptions(pdipm->Jce_xfixed);
    1021:     MatSeqAIJSetPreallocation(pdipm->Jce_xfixed,1,NULL);
    1022:     MatMPIAIJSetPreallocation(pdipm->Jce_xfixed,1,NULL,1,NULL);

    1024:     MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,&Jcrend);
    1025:     ISGetIndices(pdipm->isxfixed,&cols);
    1026:     k = 0;
    1027:     for (row = Jcrstart; row < Jcrend; row++) {
    1028:       MatSetValues(pdipm->Jce_xfixed,1,&row,1,cols+k,&one,INSERT_VALUES);
    1029:       k++;
    1030:     }
    1031:     ISRestoreIndices(pdipm->isxfixed, &cols);
    1032:     MatAssemblyBegin(pdipm->Jce_xfixed,MAT_FINAL_ASSEMBLY);
    1033:     MatAssemblyEnd(pdipm->Jce_xfixed,MAT_FINAL_ASSEMBLY);
    1034:   }

    1036:   /* (5.2) PDIPM inequality Jacobian Jci = [tao->jacobian_inequality; ...] */
    1037:   MatCreate(comm,&pdipm->Jci_xb);
    1038:   MatSetSizes(pdipm->Jci_xb,pdipm->nci-pdipm->nh,pdipm->nx,PETSC_DECIDE,pdipm->Nx);
    1039:   MatSetFromOptions(pdipm->Jci_xb);
    1040:   MatSeqAIJSetPreallocation(pdipm->Jci_xb,1,NULL);
    1041:   MatMPIAIJSetPreallocation(pdipm->Jci_xb,1,NULL,1,NULL);

    1043:   MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,&Jcrend);
    1044:   offset = Jcrstart;
    1045:   if (pdipm->Nxub) {
    1046:     /* Add xub to Jci_xb */
    1047:     ISGetIndices(pdipm->isxub,&cols);
    1048:     k = 0;
    1049:     for (row = offset; row < offset + pdipm->nxub; row++) {
    1050:       MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&neg_one,INSERT_VALUES);
    1051:       k++;
    1052:     }
    1053:     ISRestoreIndices(pdipm->isxub, &cols);
    1054:   }

    1056:   if (pdipm->Nxlb) {
    1057:     /* Add xlb to Jci_xb */
    1058:     ISGetIndices(pdipm->isxlb,&cols);
    1059:     k = 0;
    1060:     offset += pdipm->nxub;
    1061:     for (row = offset; row < offset + pdipm->nxlb; row++) {
    1062:       MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&one,INSERT_VALUES);
    1063:       k++;
    1064:     }
    1065:     ISRestoreIndices(pdipm->isxlb, &cols);
    1066:   }

    1068:   /* Add xbox to Jci_xb */
    1069:   if (pdipm->Nxbox) {
    1070:     ISGetIndices(pdipm->isxbox,&cols);
    1071:     k = 0;
    1072:     offset += pdipm->nxlb;
    1073:     for (row = offset; row < offset + pdipm->nxbox; row++) {
    1074:       MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&neg_one,INSERT_VALUES);
    1075:       tmp = row + pdipm->nxbox;
    1076:       MatSetValues(pdipm->Jci_xb,1,&tmp,1,cols+k,&one,INSERT_VALUES);
    1077:       k++;
    1078:     }
    1079:     ISRestoreIndices(pdipm->isxbox, &cols);
    1080:   }

    1082:   MatAssemblyBegin(pdipm->Jci_xb,MAT_FINAL_ASSEMBLY);
    1083:   MatAssemblyEnd(pdipm->Jci_xb,MAT_FINAL_ASSEMBLY);
    1084:   /* MatView(pdipm->Jci_xb,PETSC_VIEWER_STDOUT_WORLD); */

    1086:   /* (6) Set up ISs for PC Fieldsplit */
    1087:   if (pdipm->solve_reduced_kkt) {
    1088:     PetscMalloc2(pdipm->nx+pdipm->nce,&xa,2*pdipm->nci,&xb);
    1089:     for (i=0; i < pdipm->nx + pdipm->nce; i++) xa[i] = i;
    1090:     for (i=0; i < 2*pdipm->nci; i++) xb[i] = pdipm->off_lambdai + i;

    1092:     ISCreateGeneral(comm,pdipm->nx+pdipm->nce,xa,PETSC_OWN_POINTER,&pdipm->is1);
    1093:     ISCreateGeneral(comm,2*pdipm->nci,xb,PETSC_OWN_POINTER,&pdipm->is2);
    1094:   }

    1096:   /* (7) Gather offsets from all processes */
    1097:   PetscMalloc1(size,&pdipm->nce_all);

    1099:   /* Get rstart of KKT matrix */
    1100:   MPI_Scan(&pdipm->n,&rstart,1,MPIU_INT,MPI_SUM,comm);
    1101:   rstart -= pdipm->n;

    1103:   MPI_Allgather(&pdipm->nce,1,MPIU_INT,pdipm->nce_all,1,MPIU_INT,comm);

    1105:   PetscMalloc3(size,&ng_all,size,&nh_all,size,&Jranges);
    1106:   MPI_Allgather(&rstart,1,MPIU_INT,Jranges,1,MPIU_INT,comm);
    1107:   MPI_Allgather(&pdipm->nh,1,MPIU_INT,nh_all,1,MPIU_INT,comm);
    1108:   MPI_Allgather(&pdipm->ng,1,MPIU_INT,ng_all,1,MPIU_INT,comm);

    1110:   MatGetOwnershipRanges(tao->hessian,&rranges);
    1111:   MatGetOwnershipRangesColumn(tao->hessian,&cranges);

    1113:   if (pdipm->Ng) {
    1114:     TaoComputeJacobianEquality(tao,tao->solution,tao->jacobian_equality,tao->jacobian_equality_pre);
    1115:     MatTranspose(tao->jacobian_equality,MAT_INITIAL_MATRIX,&pdipm->jac_equality_trans);
    1116:   }
    1117:   if (pdipm->Nh) {
    1118:     TaoComputeJacobianInequality(tao,tao->solution,tao->jacobian_inequality,tao->jacobian_inequality_pre);
    1119:     MatTranspose(tao->jacobian_inequality,MAT_INITIAL_MATRIX,&pdipm->jac_inequality_trans);
    1120:   }

    1122:   /* Count dnz,onz for preallocation of KKT matrix */
    1123:   jac_equality_trans   = pdipm->jac_equality_trans;
    1124:   jac_inequality_trans = pdipm->jac_inequality_trans;
    1125:   nce_all = pdipm->nce_all;

    1127:   if (pdipm->Nxfixed) {
    1128:     MatTranspose(pdipm->Jce_xfixed,MAT_INITIAL_MATRIX,&Jce_xfixed_trans);
    1129:   }
    1130:   MatTranspose(pdipm->Jci_xb,MAT_INITIAL_MATRIX,&Jci_xb_trans);

    1132:   MatPreallocateInitialize(comm,pdipm->n,pdipm->n,dnz,onz);

    1134:   /* 1st row block of KKT matrix: [Wxx; gradCe'; -gradCi'; 0] */
    1135:   TaoPDIPMEvaluateFunctionsAndJacobians(tao,pdipm->x);
    1136:   TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);

    1138:   /* Insert tao->hessian */
    1139:   MatGetOwnershipRange(tao->hessian,&rjstart,NULL);
    1140:   for (i=0; i<pdipm->nx; i++){
    1141:     row = rstart + i;

    1143:     MatGetRow(tao->hessian,i+rjstart,&nc,&aj,NULL);
    1144:     proc = 0;
    1145:     for (j=0; j < nc; j++) {
    1146:       while (aj[j] >= cranges[proc+1]) proc++;
    1147:       col = aj[j] - cranges[proc] + Jranges[proc];
    1148:       MatPreallocateSet(row,1,&col,dnz,onz);
    1149:     }
    1150:     MatRestoreRow(tao->hessian,i+rjstart,&nc,&aj,NULL);

    1152:     if (pdipm->ng) {
    1153:       /* Insert grad g' */
    1154:       MatGetRow(jac_equality_trans,i+rjstart,&nc,&aj,NULL);
    1155:       MatGetOwnershipRanges(tao->jacobian_equality,&ranges);
    1156:       proc = 0;
    1157:       for (j=0; j < nc; j++) {
    1158:         /* find row ownership of */
    1159:         while (aj[j] >= ranges[proc+1]) proc++;
    1160:         nx_all = rranges[proc+1] - rranges[proc];
    1161:         col = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
    1162:         MatPreallocateSet(row,1,&col,dnz,onz);
    1163:       }
    1164:       MatRestoreRow(jac_equality_trans,i+rjstart,&nc,&aj,NULL);
    1165:     }

    1167:     /* Insert Jce_xfixed^T' */
    1168:     if (pdipm->nxfixed) {
    1169:       MatGetRow(Jce_xfixed_trans,i+rjstart,&nc,&aj,NULL);
    1170:       MatGetOwnershipRanges(pdipm->Jce_xfixed,&ranges);
    1171:       proc = 0;
    1172:       for (j=0; j < nc; j++) {
    1173:         /* find row ownership of */
    1174:         while (aj[j] >= ranges[proc+1]) proc++;
    1175:         nx_all = rranges[proc+1] - rranges[proc];
    1176:         col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + ng_all[proc];
    1177:         MatPreallocateSet(row,1,&col,dnz,onz);
    1178:       }
    1179:       MatRestoreRow(Jce_xfixed_trans,i+rjstart,&nc,&aj,NULL);
    1180:     }

    1182:     if (pdipm->nh) {
    1183:       /* Insert -grad h' */
    1184:       MatGetRow(jac_inequality_trans,i+rjstart,&nc,&aj,NULL);
    1185:       MatGetOwnershipRanges(tao->jacobian_inequality,&ranges);
    1186:       proc = 0;
    1187:       for (j=0; j < nc; j++) {
    1188:         /* find row ownership of */
    1189:         while (aj[j] >= ranges[proc+1]) proc++;
    1190:         nx_all = rranges[proc+1] - rranges[proc];
    1191:         col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
    1192:         MatPreallocateSet(row,1,&col,dnz,onz);
    1193:       }
    1194:       MatRestoreRow(jac_inequality_trans,i+rjstart,&nc,&aj,NULL);
    1195:     }

    1197:     /* Insert Jci_xb^T' */
    1198:     MatGetRow(Jci_xb_trans,i+rjstart,&nc,&aj,NULL);
    1199:     MatGetOwnershipRanges(pdipm->Jci_xb,&ranges);
    1200:     proc = 0;
    1201:     for (j=0; j < nc; j++) {
    1202:       /* find row ownership of */
    1203:       while (aj[j] >= ranges[proc+1]) proc++;
    1204:       nx_all = rranges[proc+1] - rranges[proc];
    1205:       col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc] + nh_all[proc];
    1206:       MatPreallocateSet(row,1,&col,dnz,onz);
    1207:     }
    1208:     MatRestoreRow(Jci_xb_trans,i+rjstart,&nc,&aj,NULL);
    1209:   }

    1211:   /* 2nd Row block of KKT matrix: [grad Ce, deltac*I, 0, 0] */
    1212:   if (pdipm->Ng) {
    1213:     MatGetOwnershipRange(tao->jacobian_equality,&rjstart,NULL);
    1214:     for (i=0; i < pdipm->ng; i++){
    1215:       row = rstart + pdipm->off_lambdae + i;

    1217:       MatGetRow(tao->jacobian_equality,i+rjstart,&nc,&aj,NULL);
    1218:       proc = 0;
    1219:       for (j=0; j < nc; j++) {
    1220:         while (aj[j] >= cranges[proc+1]) proc++;
    1221:         col = aj[j] - cranges[proc] + Jranges[proc];
    1222:         MatPreallocateSet(row,1,&col,dnz,onz); /* grad g */
    1223:       }
    1224:       MatRestoreRow(tao->jacobian_equality,i+rjstart,&nc,&aj,NULL);
    1225:     }
    1226:   }
    1227:   /* Jce_xfixed */
    1228:   if (pdipm->Nxfixed) {
    1229:     MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,NULL);
    1230:     for (i=0; i < (pdipm->nce - pdipm->ng); i++){
    1231:       row = rstart + pdipm->off_lambdae + pdipm->ng + i;

    1233:       MatGetRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,NULL);
    1234:       if (nc != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"nc != 1");

    1236:       proc = 0;
    1237:       j    = 0;
    1238:       while (cols[j] >= cranges[proc+1]) proc++;
    1239:       col = cols[j] - cranges[proc] + Jranges[proc];
    1240:       MatPreallocateSet(row,1,&col,dnz,onz);
    1241:       MatRestoreRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,NULL);
    1242:     }
    1243:   }

    1245:   /* 3rd Row block of KKT matrix: [ gradCi, 0, deltac*I, -I] */
    1246:   if (pdipm->Nh) {
    1247:     MatGetOwnershipRange(tao->jacobian_inequality,&rjstart,NULL);
    1248:     for (i=0; i < pdipm->nh; i++){
    1249:       row = rstart + pdipm->off_lambdai + i;

    1251:       MatGetRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,NULL);
    1252:       proc = 0;
    1253:       for (j=0; j < nc; j++) {
    1254:         while (aj[j] >= cranges[proc+1]) proc++;
    1255:         col = aj[j] - cranges[proc] + Jranges[proc];
    1256:         MatPreallocateSet(row,1,&col,dnz,onz); /* grad h */
    1257:       }
    1258:       MatRestoreRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,NULL);
    1259:     }
    1260:     /* I */
    1261:     for (i=0; i < pdipm->nh; i++){
    1262:       row = rstart + pdipm->off_lambdai + i;
    1263:       col = rstart + pdipm->off_z + i;
    1264:       MatPreallocateSet(row,1,&col,dnz,onz);
    1265:     }
    1266:   }

    1268:   /* Jci_xb */
    1269:   MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,NULL);
    1270:   for (i=0; i < (pdipm->nci - pdipm->nh); i++){
    1271:     row = rstart + pdipm->off_lambdai + pdipm->nh + i;

    1273:     MatGetRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,NULL);
    1274:     if (nc != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"nc != 1");
    1275:     proc = 0;
    1276:     for (j=0; j < nc; j++) {
    1277:       while (cols[j] >= cranges[proc+1]) proc++;
    1278:       col = cols[j] - cranges[proc] + Jranges[proc];
    1279:       MatPreallocateSet(row,1,&col,dnz,onz);
    1280:     }
    1281:     MatRestoreRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,NULL);
    1282:     /* I */
    1283:     col = rstart + pdipm->off_z + pdipm->nh + i;
    1284:     MatPreallocateSet(row,1,&col,dnz,onz);
    1285:   }

    1287:   /* 4-th Row block of KKT matrix: Z and Ci */
    1288:   for (i=0; i < pdipm->nci; i++) {
    1289:     row     = rstart + pdipm->off_z + i;
    1290:     cols1[0] = rstart + pdipm->off_lambdai + i;
    1291:     cols1[1] = row;
    1292:     MatPreallocateSet(row,2,cols1,dnz,onz);
    1293:   }

    1295:   /* diagonal entry */
    1296:   for (i=0; i<pdipm->n; i++) dnz[i]++; /* diagonal entry */

    1298:   /* Create KKT matrix */
    1299:   MatCreate(comm,&J);
    1300:   MatSetSizes(J,pdipm->n,pdipm->n,PETSC_DECIDE,PETSC_DECIDE);
    1301:   MatSetFromOptions(J);
    1302:   MatSeqAIJSetPreallocation(J,0,dnz);
    1303:   MatMPIAIJSetPreallocation(J,0,dnz,0,onz);
    1304:   /* MatSetOption(J,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE); */
    1305:   MatPreallocateFinalize(dnz,onz);
    1306:   pdipm->K = J;

    1308:   /* (8) Set up nonlinear solver SNES */
    1309:   SNESSetFunction(pdipm->snes,NULL,TaoSNESFunction_PDIPM,(void*)tao);
    1310:   SNESSetJacobian(pdipm->snes,J,J,TaoSNESJacobian_PDIPM,(void*)tao);

    1312:   if (pdipm->solve_reduced_kkt) {
    1313:     PC pc;
    1314:     KSPGetPC(tao->ksp,&pc);
    1315:     PCSetType(pc,PCFIELDSPLIT);
    1316:     PCFieldSplitSetType(pc,PC_COMPOSITE_SCHUR);
    1317:     PCFieldSplitSetIS(pc,"2",pdipm->is2);
    1318:     PCFieldSplitSetIS(pc,"1",pdipm->is1);
    1319:   }
    1320:   SNESSetFromOptions(pdipm->snes);

    1322:   /* (9) Insert constant entries to  K */
    1323:   /* Set 0.0 to diagonal of K, so that the solver does not complain *about missing diagonal value */
    1324:   MatGetOwnershipRange(J,&rstart,&rend);
    1325:   for (i=rstart; i<rend; i++){
    1326:     MatSetValue(J,i,i,0.0,INSERT_VALUES);
    1327:   }
    1328:   /* In case Wxx has no diagonal entries preset set diagonal to deltaw given */
    1329:   if (pdipm->kkt_pd){
    1330:       for (i=0; i<pdipm->nh; i++){
    1331:         row  = rstart + i;
    1332:         MatSetValue(J,row,row,pdipm->deltaw,INSERT_VALUES);
    1333:       }
    1334:   }

    1336:   /* Row block of K: [ grad Ce, 0, 0, 0] */
    1337:   if (pdipm->Nxfixed) {
    1338:     MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,NULL);
    1339:     for (i=0; i < (pdipm->nce - pdipm->ng); i++){
    1340:       row = rstart + pdipm->off_lambdae + pdipm->ng + i;

    1342:       MatGetRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,&aa);
    1343:       proc = 0;
    1344:       for (j=0; j < nc; j++) {
    1345:         while (cols[j] >= cranges[proc+1]) proc++;
    1346:         col = cols[j] - cranges[proc] + Jranges[proc];
    1347:         MatSetValue(J,row,col,aa[j],INSERT_VALUES); /* grad Ce */
    1348:         MatSetValue(J,col,row,aa[j],INSERT_VALUES); /* grad Ce' */
    1349:       }
    1350:       MatRestoreRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,&aa);
    1351:     }
    1352:   }

    1354:   /* Row block of K: [ -grad Ci, 0, 0, I] */
    1355:   MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,NULL);
    1356:   for (i=0; i < pdipm->nci - pdipm->nh; i++){
    1357:     row = rstart + pdipm->off_lambdai + pdipm->nh + i;

    1359:     MatGetRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,&aa);
    1360:     proc = 0;
    1361:     for (j=0; j < nc; j++) {
    1362:       while (cols[j] >= cranges[proc+1]) proc++;
    1363:       col = cols[j] - cranges[proc] + Jranges[proc];
    1364:       MatSetValue(J,col,row,-aa[j],INSERT_VALUES);
    1365:       MatSetValue(J,row,col,-aa[j],INSERT_VALUES);
    1366:     }
    1367:     MatRestoreRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,&aa);

    1369:     col = rstart + pdipm->off_z + pdipm->nh + i;
    1370:     MatSetValue(J,row,col,1,INSERT_VALUES);
    1371:   }

    1373:   for (i=0; i < pdipm->nh; i++){
    1374:     row = rstart + pdipm->off_lambdai + i;
    1375:     col = rstart + pdipm->off_z + i;
    1376:     MatSetValue(J,row,col,1,INSERT_VALUES);
    1377:   }

    1379:   /* Row block of K: [ 0, 0, I, ...] */
    1380:   for (i=0; i < pdipm->nci; i++){
    1381:     row = rstart + pdipm->off_z + i;
    1382:     col = rstart + pdipm->off_lambdai + i;
    1383:     MatSetValue(J,row,col,1,INSERT_VALUES);
    1384:   }

    1386:   if (pdipm->Nxfixed) {
    1387:     MatDestroy(&Jce_xfixed_trans);
    1388:   }
    1389:   MatDestroy(&Jci_xb_trans);
    1390:   PetscFree3(ng_all,nh_all,Jranges);
    1391:   return(0);
    1392: }

    1394: /*
    1395:    TaoDestroy_PDIPM - Destroys the pdipm object

    1397:    Input:
    1398:    full pdipm

    1400:    Output:
    1401:    Destroyed pdipm
    1402: */
    1403: PetscErrorCode TaoDestroy_PDIPM(Tao tao)
    1404: {
    1405:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;

    1409:   /* Freeing Vectors assocaiated with KKT (X) */
    1410:   VecDestroy(&pdipm->x); /* Solution x */
    1411:   VecDestroy(&pdipm->lambdae); /* Equality constraints lagrangian multiplier*/
    1412:   VecDestroy(&pdipm->lambdai); /* Inequality constraints lagrangian multiplier*/
    1413:   VecDestroy(&pdipm->z);       /* Slack variables */
    1414:   VecDestroy(&pdipm->X);       /* Big KKT system vector [x; lambdae; lambdai; z] */

    1416:   /* work vectors */
    1417:   VecDestroy(&pdipm->lambdae_xfixed);
    1418:   VecDestroy(&pdipm->lambdai_xb);

    1420:   /* Legrangian equality and inequality Vec */
    1421:   VecDestroy(&pdipm->ce); /* Vec of equality constraints */
    1422:   VecDestroy(&pdipm->ci); /* Vec of inequality constraints */

    1424:   /* Matrices */
    1425:   MatDestroy(&pdipm->Jce_xfixed);
    1426:   MatDestroy(&pdipm->Jci_xb); /* Jacobian of inequality constraints Jci = [tao->jacobian_inequality ; J(nxub); J(nxlb); J(nxbx)] */
    1427:   MatDestroy(&pdipm->K);

    1429:   /* Index Sets */
    1430:   if (pdipm->Nxub) {
    1431:     ISDestroy(&pdipm->isxub);    /* Finite upper bound only -inf < x < ub */
    1432:   }

    1434:   if (pdipm->Nxlb) {
    1435:     ISDestroy(&pdipm->isxlb);    /* Finite lower bound only  lb <= x < inf */
    1436:   }

    1438:   if (pdipm->Nxfixed) {
    1439:     ISDestroy(&pdipm->isxfixed); /* Fixed variables         lb =  x = ub */
    1440:   }

    1442:   if (pdipm->Nxbox) {
    1443:     ISDestroy(&pdipm->isxbox);   /* Boxed variables         lb <= x <= ub */
    1444:   }

    1446:   if (pdipm->Nxfree) {
    1447:     ISDestroy(&pdipm->isxfree);  /* Free variables        -inf <= x <= inf */
    1448:   }

    1450:   if (pdipm->solve_reduced_kkt) {
    1451:     ISDestroy(&pdipm->is1);
    1452:     ISDestroy(&pdipm->is2);
    1453:   }

    1455:   /* SNES */
    1456:   SNESDestroy(&pdipm->snes); /* Nonlinear solver */
    1457:   PetscFree(pdipm->nce_all);
    1458:   MatDestroy(&pdipm->jac_equality_trans);
    1459:   MatDestroy(&pdipm->jac_inequality_trans);

    1461:   /* Destroy pdipm */
    1462:   PetscFree(tao->data); /* Holding locations of pdipm */

    1464:   /* Destroy Dual */
    1465:   VecDestroy(&tao->DE); /* equality dual */
    1466:   VecDestroy(&tao->DI); /* dinequality dual */
    1467:   return(0);
    1468: }

    1470: PetscErrorCode TaoSetFromOptions_PDIPM(PetscOptionItems *PetscOptionsObject,Tao tao)
    1471: {
    1472:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;

    1476:   PetscOptionsHead(PetscOptionsObject,"PDIPM method for constrained optimization");
    1477:   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);
    1478:   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);
    1479:   PetscOptionsBool("-tao_pdipm_solve_reduced_kkt","Solve reduced KKT system using Schur-complement",NULL,pdipm->solve_reduced_kkt,&pdipm->solve_reduced_kkt,NULL);
    1480:   PetscOptionsReal("-tao_pdipm_mu_update_factor","Update scalar for barrier parameter (mu) update",NULL,pdipm->mu_update_factor,&pdipm->mu_update_factor,NULL);
    1481:   PetscOptionsBool("-tao_pdipm_symmetric_kkt","Solve non reduced symmetric KKT system",NULL,pdipm->solve_symmetric_kkt,&pdipm->solve_symmetric_kkt,NULL);
    1482:   PetscOptionsBool("-tao_pdipm_kkt_shift_pd","Add shifts to make KKT matrix positive definite",NULL,pdipm->kkt_pd,&pdipm->kkt_pd,NULL);
    1483:   PetscOptionsTail();
    1484:   return(0);
    1485: }

    1487: /*MC
    1488:   TAOPDIPM - Barrier-based primal-dual interior point algorithm for generally constrained optimization.

    1490:   Option Database Keys:
    1491: +   -tao_pdipm_push_init_lambdai - parameter to push initial dual variables away from bounds (> 0)
    1492: .   -tao_pdipm_push_init_slack - parameter to push initial slack variables away from bounds (> 0)
    1493: .   -tao_pdipm_mu_update_factor - update scalar for barrier parameter (mu) update (> 0)
    1494: .   -tao_pdipm_symmetric_kkt - Solve non-reduced symmetric KKT system
    1495: -   -tao_pdipm_kkt_shift_pd - Add shifts to make KKT matrix positive definite

    1497:   Level: beginner
    1498: M*/
    1499: PETSC_EXTERN PetscErrorCode TaoCreate_PDIPM(Tao tao)
    1500: {
    1501:   TAO_PDIPM      *pdipm;

    1505:   tao->ops->setup          = TaoSetup_PDIPM;
    1506:   tao->ops->solve          = TaoSolve_PDIPM;
    1507:   tao->ops->setfromoptions = TaoSetFromOptions_PDIPM;
    1508:   tao->ops->view           = TaoView_PDIPM;
    1509:   tao->ops->destroy        = TaoDestroy_PDIPM;

    1511:   PetscNewLog(tao,&pdipm);
    1512:   tao->data = (void*)pdipm;

    1514:   pdipm->nx      = pdipm->Nx      = 0;
    1515:   pdipm->nxfixed = pdipm->Nxfixed = 0;
    1516:   pdipm->nxlb    = pdipm->Nxlb    = 0;
    1517:   pdipm->nxub    = pdipm->Nxub    = 0;
    1518:   pdipm->nxbox   = pdipm->Nxbox   = 0;
    1519:   pdipm->nxfree  = pdipm->Nxfree  = 0;

    1521:   pdipm->ng = pdipm->Ng = pdipm->nce = pdipm->Nce = 0;
    1522:   pdipm->nh = pdipm->Nh = pdipm->nci = pdipm->Nci = 0;
    1523:   pdipm->n  = pdipm->N  = 0;
    1524:   pdipm->mu = 1.0;
    1525:   pdipm->mu_update_factor = 0.1;

    1527:   pdipm->deltaw     = 0.0;
    1528:   pdipm->lastdeltaw = 3*1.e-4;
    1529:   pdipm->deltac     = 0.0;
    1530:   pdipm->kkt_pd     = PETSC_FALSE;

    1532:   pdipm->push_init_slack     = 1.0;
    1533:   pdipm->push_init_lambdai   = 1.0;
    1534:   pdipm->solve_reduced_kkt   = PETSC_FALSE;
    1535:   pdipm->solve_symmetric_kkt = PETSC_TRUE;

    1537:   /* Override default settings (unless already changed) */
    1538:   if (!tao->max_it_changed) tao->max_it = 200;
    1539:   if (!tao->max_funcs_changed) tao->max_funcs = 500;

    1541:   SNESCreate(((PetscObject)tao)->comm,&pdipm->snes);
    1542:   SNESSetOptionsPrefix(pdipm->snes,tao->hdr.prefix);
    1543:   SNESGetKSP(pdipm->snes,&tao->ksp);
    1544:   PetscObjectReference((PetscObject)tao->ksp);
    1545:   return(0);
    1546: }