Actual source code: pdipm.c
petsc-3.13.6 2020-09-29
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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:   /* (1.a) Inserting updated g(x) */
     74:   if (pdipm->Ng) {
     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: {
    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:   VecSet(pdipm->lambdai,pdipm->push_init_lambdai);
    258:   VecSet(pdipm->z,pdipm->push_init_slack);

    260:   /* Additional modification for X.lambdai and X.z */
    261:   VecGetArray(pdipm->lambdai,&lambdai);
    262:   VecGetArray(pdipm->z,&z);
    263:   if (pdipm->Nh) {
    264:     VecGetArrayRead(tao->constraints_inequality,&h);
    265:     for (i=0; i < pdipm->nh; i++) {
    266:       if (h[i] < -pdipm->push_init_slack) z[i] = -h[i];
    267:       if (pdipm->mu/z[i] > pdipm->push_init_lambdai) lambdai[i] = pdipm->mu/z[i];
    268:     }
    269:     VecRestoreArrayRead(tao->constraints_inequality,&h);
    270:   }
    271:   VecRestoreArray(pdipm->lambdai,&lambdai);
    272:   VecRestoreArray(pdipm->z,&z);

    274:   VecRestoreArray(pdipm->X,&Xarr);
    275:   return(0);
    276: }

    278: /*
    279:    TaoSNESJacobian_PDIPM - Evaluate the Hessian matrix at X

    281:    Input Parameter:
    282:    snes - SNES context
    283:    X - KKT Vector
    284:    *ctx - pdipm context

    286:    Output Parameter:
    287:    J - Hessian matrix
    288:    Jpre - Preconditioner
    289: */
    290: PetscErrorCode TaoSNESJacobian_PDIPM(SNES snes,Vec X, Mat J, Mat Jpre, void *ctx)
    291: {
    292:   PetscErrorCode    ierr;
    293:   Tao               tao=(Tao)ctx;
    294:   TAO_PDIPM         *pdipm = (TAO_PDIPM*)tao->data;
    295:   PetscInt          i,row,cols[2],Jrstart,rjstart,nc,j;
    296:   const PetscInt    *aj,*ranges,*Jranges,*rranges,*cranges;
    297:   const PetscScalar *Xarr,*aa;
    298:   PetscScalar       vals[2];
    299:   PetscInt          proc,nx_all,*nce_all=pdipm->nce_all;
    300:   MPI_Comm          comm;
    301:   PetscMPIInt       rank,size;
    302:   Mat               jac_equality_trans=pdipm->jac_equality_trans,jac_inequality_trans=pdipm->jac_inequality_trans;

    305:   PetscObjectGetComm((PetscObject)snes,&comm);
    306:   MPI_Comm_rank(comm,&rank);
    307:   MPI_Comm_rank(comm,&size);

    309:   MatGetOwnershipRanges(Jpre,&Jranges);
    310:   MatGetOwnershipRange(Jpre,&Jrstart,NULL);
    311:   MatGetOwnershipRangesColumn(tao->hessian,&rranges);
    312:   MatGetOwnershipRangesColumn(tao->hessian,&cranges);

    314:   VecGetArrayRead(X,&Xarr);

    316:   /* (2) insert Z and Ci to Jpre -- overwrite existing values */
    317:   for (i=0; i < pdipm->nci; i++) {
    318:     row     = Jrstart + pdipm->off_z + i;
    319:     cols[0] = Jrstart + pdipm->off_lambdai + i;
    320:     cols[1] = row;
    321:     vals[0] = Xarr[pdipm->off_z + i];
    322:     vals[1] = Xarr[pdipm->off_lambdai + i];
    323:     MatSetValues(Jpre,1,&row,2,cols,vals,INSERT_VALUES);
    324:   }

    326:   /* (3) insert 2nd row block of Jpre: [ grad g, 0, 0, 0] */
    327:   if (pdipm->Ng) {
    328:     MatGetOwnershipRange(tao->jacobian_equality,&rjstart,NULL);
    329:     for (i=0; i<pdipm->ng; i++){
    330:       row = Jrstart + pdipm->off_lambdae + i;
    331:
    332:       MatGetRow(tao->jacobian_equality,i+rjstart,&nc,&aj,&aa);
    333:       proc = 0;
    334:       for (j=0; j < nc; j++) {
    335:         while (aj[j] >= cranges[proc+1]) proc++;
    336:         cols[0] = aj[j] - cranges[proc] + Jranges[proc];
    337:         MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
    338:       }
    339:       MatRestoreRow(tao->jacobian_equality,i+rjstart,&nc,&aj,&aa);
    340:     }
    341:   }

    343:   if (pdipm->Nh) {
    344:     /* (4) insert 3nd row block of Jpre: [ grad h, 0, 0, 0] */
    345:     MatGetOwnershipRange(tao->jacobian_inequality,&rjstart,NULL);
    346:     for (i=0; i < pdipm->nh; i++){
    347:       row = Jrstart + pdipm->off_lambdai + i;
    348:
    349:       MatGetRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,&aa);
    350:       proc = 0;
    351:       for (j=0; j < nc; j++) {
    352:         while (aj[j] >= cranges[proc+1]) proc++;
    353:         cols[0] = aj[j] - cranges[proc] + Jranges[proc];
    354:         MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
    355:       }
    356:     MatRestoreRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,&aa);
    357:     }
    358:   }

    360:   /* (5) insert Wxx, grad g' and -grad h' to Jpre */
    361:   if (pdipm->Ng) {
    362:     MatTranspose(tao->jacobian_equality,MAT_REUSE_MATRIX,&jac_equality_trans);
    363:   }
    364:   if (pdipm->Nh) {
    365:     MatTranspose(tao->jacobian_inequality,MAT_REUSE_MATRIX,&jac_inequality_trans);
    366:   }

    368:   VecPlaceArray(pdipm->x,Xarr);
    369:   TaoComputeHessian(tao,pdipm->x,tao->hessian,tao->hessian_pre);
    370:   VecResetArray(pdipm->x);

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

    376:     /* insert Wxx */
    377:     MatGetRow(tao->hessian,i+rjstart,&nc,&aj,&aa);
    378:     proc = 0;
    379:     for (j=0; j < nc; j++) {
    380:       while (aj[j] >= cranges[proc+1]) proc++;
    381:       cols[0] = aj[j] - cranges[proc] + Jranges[proc];
    382:       MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
    383:     }
    384:     MatRestoreRow(tao->hessian,i+rjstart,&nc,&aj,&aa);

    386:     if (pdipm->ng) {
    387:       /* insert grad g' */
    388:       MatGetRow(jac_equality_trans,i+rjstart,&nc,&aj,&aa);
    389:       MatGetOwnershipRanges(tao->jacobian_equality,&ranges);
    390:       proc = 0;
    391:       for (j=0; j < nc; j++) {
    392:         /* find row ownership of */
    393:         while (aj[j] >= ranges[proc+1]) proc++;
    394:         nx_all = rranges[proc+1] - rranges[proc];
    395:         cols[0] = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
    396:         MatSetValue(Jpre,row,cols[0],aa[j],INSERT_VALUES);
    397:       }
    398:       MatRestoreRow(jac_equality_trans,i+rjstart,&nc,&aj,&aa);
    399:     }

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

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

    422:   if (J != Jpre) {
    423:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
    424:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
    425:   }
    426:   return(0);
    427: }

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

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

    437:    Output Parameter:
    438:    F - Updated Lagrangian vector
    439: */
    440: PetscErrorCode TaoSNESFunction_PDIPM(SNES snes,Vec X,Vec F,void *ctx)
    441: {
    443:   Tao            tao=(Tao)ctx;
    444:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;
    445:   PetscScalar    *Farr;
    446:   Vec            x,L1;
    447:   PetscInt       i;
    448:   PetscReal      res[2],cnorm[2];
    449:   const PetscScalar *Xarr,*carr,*zarr,*larr;

    452:   VecSet(F,0.0);

    454:   VecGetArrayRead(X,&Xarr);
    455:   VecGetArray(F,&Farr);

    457:   /* (0) Evaluate f, fx, Gx, Hx at X.x Note: pdipm->x is not changed below */
    458:   x = pdipm->x;
    459:   VecPlaceArray(x,Xarr);
    460:   TaoPDIPMEvaluateFunctionsAndJacobians(tao,x);

    462:   /* Update ce, ci, and Jci at X.x */
    463:   TaoPDIPMUpdateConstraints(tao,x);
    464:   VecResetArray(x);

    466:   /* (1) L1 = fx + (gradG'*DE + Jce_xfixed'*lambdae_xfixed) - (gradH'*DI + Jci_xb'*lambdai_xb) */
    467:   L1 = pdipm->x;
    468:   VecPlaceArray(L1,Farr);
    469:   if (pdipm->Nci) {
    470:     if (pdipm->Nh) {
    471:       /* L1 += gradH'*DI. Note: tao->DI is not changed below */
    472:       VecPlaceArray(tao->DI,Xarr+pdipm->off_lambdai);
    473:       MatMultTransposeAdd(tao->jacobian_inequality,tao->DI,L1,L1);
    474:       VecResetArray(tao->DI);
    475:     }

    477:     /* L1 += Jci_xb'*lambdai_xb */
    478:     VecPlaceArray(pdipm->lambdai_xb,Xarr+pdipm->off_lambdai+pdipm->nh);
    479:     MatMultTransposeAdd(pdipm->Jci_xb,pdipm->lambdai_xb,L1,L1);
    480:     VecResetArray(pdipm->lambdai_xb);

    482:     /* (1.4) L1 = - (gradH'*DI + Jci_xb'*lambdai_xb) */
    483:     VecScale(L1,-1.0);
    484:   }

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

    489:   if (pdipm->Nce) {
    490:     if (pdipm->Ng) {
    491:       /* L1 += gradG'*DE. Note: tao->DE is not changed below */
    492:       VecPlaceArray(tao->DE,Xarr+pdipm->off_lambdae);
    493:       MatMultTransposeAdd(tao->jacobian_equality,tao->DE,L1,L1);
    494:       VecResetArray(tao->DE);
    495:     }
    496:     if (pdipm->Nxfixed) {
    497:       /* L1 += Jce_xfixed'*lambdae_xfixed */
    498:       VecPlaceArray(pdipm->lambdae_xfixed,Xarr+pdipm->off_lambdae+pdipm->ng);
    499:       MatMultTransposeAdd(pdipm->Jce_xfixed,pdipm->lambdae_xfixed,L1,L1);
    500:       VecResetArray(pdipm->lambdae_xfixed);
    501:     }
    502:   }
    503:   VecNorm(L1,NORM_2,&res[0]);
    504:   VecResetArray(L1);

    506:   /* (2) L2 = ce(x) */
    507:   if (pdipm->Nce) {
    508:     VecGetArrayRead(pdipm->ce,&carr);
    509:     for (i=0; i<pdipm->nce; i++) Farr[pdipm->off_lambdae + i] = carr[i];
    510:     VecRestoreArrayRead(pdipm->ce,&carr);
    511:   }
    512:   VecNorm(pdipm->ce,NORM_2,&cnorm[0]);

    514:   if (pdipm->Nci) {
    515:     /* (3) L3 = ci(x) - z;
    516:        (4) L4 = Z * Lambdai * e - mu * e
    517:     */
    518:     VecGetArrayRead(pdipm->ci,&carr);
    519:     larr = Xarr+pdipm->off_lambdai;
    520:     zarr = Xarr+pdipm->off_z;
    521:     for (i=0; i<pdipm->nci; i++) {
    522:       Farr[pdipm->off_lambdai + i] = carr[i] - zarr[i];
    523:       Farr[pdipm->off_z       + i] = zarr[i]*larr[i] - pdipm->mu;
    524:     }
    525:     VecRestoreArrayRead(pdipm->ci,&carr);
    526:   }

    528:   VecPlaceArray(pdipm->ci,Farr+pdipm->off_lambdai);
    529:   VecNorm(pdipm->ci,NORM_2,&cnorm[1]);
    530:   VecResetArray(pdipm->ci);

    532:   /* note: pdipm->z is not changed below */
    533:   VecPlaceArray(pdipm->z,Farr+pdipm->off_z);
    534:   VecNorm(pdipm->z,NORM_2,&res[1]);
    535:   VecResetArray(pdipm->z);

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

    540:   VecRestoreArrayRead(X,&Xarr);
    541:   VecRestoreArray(F,&Farr);
    542:   return(0);
    543: }

    545: /*
    546:    PDIPMLineSearch - Custom line search used with PDIPM.

    548:    Collective on TAO

    550:    Notes:
    551:    PDIPMLineSearch employs a simple backtracking line-search to keep
    552:    the slack variables (z) and inequality constraints lagrange multipliers
    553:    (lambdai) positive, i.e., z,lambdai >=0. It does this by calculating scalars
    554:    alpha_p and alpha_d to keep z,lambdai non-negative. The decision (x), and the
    555:    slack variables are updated as X = X + alpha_d*dx. The constraint multipliers
    556:    are updated as Lambdai = Lambdai + alpha_p*dLambdai. The barrier parameter mu
    557:    is also updated as mu = mu + z'lambdai/Nci
    558: */
    559: PetscErrorCode PDIPMLineSearch(SNESLineSearch linesearch,void *ctx)
    560: {
    562:   Tao            tao=(Tao)ctx;
    563:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;
    564:   SNES           snes;
    565:   Vec            X,F,Y,W,G;
    566:   PetscInt       i,iter;
    567:   PetscReal      alpha_p=1.0,alpha_d=1.0,alpha[4];
    568:   PetscScalar    *Xarr,*z,*lambdai,dot;
    569:   const PetscScalar *dXarr,*dz,*dlambdai;
    570:   PetscScalar    *taosolarr;

    573:   SNESLineSearchGetSNES(linesearch,&snes);
    574:   SNESGetIterationNumber(snes,&iter);

    576:   SNESLineSearchSetReason(linesearch,SNES_LINESEARCH_SUCCEEDED);
    577:   SNESLineSearchGetVecs(linesearch,&X,&F,&Y,&W,&G);

    579:   VecGetArray(X,&Xarr);
    580:   VecGetArrayRead(Y,&dXarr);
    581:   z  = Xarr + pdipm->off_z;
    582:   dz = dXarr + pdipm->off_z;
    583:   for (i=0; i < pdipm->nci; i++) {
    584:     if (z[i] - dz[i] < 0.0) {
    585:       alpha_p = PetscMin(alpha_p,0.9999*z[i]/dz[i]);
    586:     }
    587:   }

    589:   lambdai  = Xarr + pdipm->off_lambdai;
    590:   dlambdai = dXarr + pdipm->off_lambdai;

    592:   for (i=0; i<pdipm->nci; i++) {
    593:     if (lambdai[i] - dlambdai[i] < 0.0) {
    594:       alpha_d = PetscMin(0.9999*lambdai[i]/dlambdai[i],alpha_d);
    595:     }
    596:   }

    598:   alpha[0] = alpha_p;
    599:   alpha[1] = alpha_d;
    600:   VecRestoreArrayRead(Y,&dXarr);
    601:   VecRestoreArray(X,&Xarr);

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

    606:   alpha_p = alpha[2];
    607:   alpha_d = alpha[3];

    609:   VecGetArray(X,&Xarr);
    610:   VecGetArrayRead(Y,&dXarr);
    611:   for (i=0; i<pdipm->nx; i++) {
    612:     Xarr[i] = Xarr[i] - alpha_p * dXarr[i];
    613:   }

    615:   for (i=0; i<pdipm->nce; i++) {
    616:     Xarr[i+pdipm->off_lambdae] = Xarr[i+pdipm->off_lambdae] - alpha_d * dXarr[i+pdipm->off_lambdae];
    617:   }

    619:   for (i=0; i<pdipm->nci; i++) {
    620:     Xarr[i+pdipm->off_lambdai] = Xarr[i+pdipm->off_lambdai] - alpha_d * dXarr[i+pdipm->off_lambdai];
    621:   }

    623:   for (i=0; i<pdipm->nci; i++) {
    624:     Xarr[i+pdipm->off_z] = Xarr[i+pdipm->off_z] - alpha_p * dXarr[i+pdipm->off_z];
    625:   }

    627:   VecGetArray(tao->solution,&taosolarr);
    628:   PetscMemcpy(taosolarr,Xarr,pdipm->nx*sizeof(PetscScalar));
    629:   VecRestoreArray(tao->solution,&taosolarr);

    632:   VecRestoreArray(X,&Xarr);
    633:   VecRestoreArrayRead(Y,&dXarr);

    635:   /* Evaluate F at X */
    636:   SNESComputeFunction(snes,X,F);
    637:   SNESLineSearchComputeNorms(linesearch); /* must call this func, do not know why */

    639:   /* update mu = mu_update_factor * dot(z,lambdai)/pdipm->nci at updated X */
    640:   VecDot(pdipm->z,pdipm->lambdai,&dot);

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

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

    648:   tao->niter++;
    649:   TaoLogConvergenceHistory(tao,pdipm->obj,tao->residual,tao->cnorm,tao->niter);
    650:   TaoMonitor(tao,tao->niter,pdipm->obj,tao->residual,tao->cnorm,pdipm->mu);

    652:   (*tao->ops->convergencetest)(tao,tao->cnvP);
    653:   if (tao->reason) {
    654:     SNESSetConvergedReason(snes,SNES_CONVERGED_FNORM_ABS);
    655:   }
    656:   return(0);
    657: }

    659: /*
    660:    TaoSolve_PDIPM

    662:    Input Parameter:
    663:    tao - TAO context

    665:    Output Parameter:
    666:    tao - TAO context
    667: */
    668: PetscErrorCode TaoSolve_PDIPM(Tao tao)
    669: {
    670:   PetscErrorCode     ierr;
    671:   TAO_PDIPM          *pdipm = (TAO_PDIPM*)tao->data;
    672:   SNESLineSearch     linesearch;  /* SNESLineSearch context */
    673:   Vec                dummy;

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

    678:   /* Initialize all variables */
    679:   TaoPDIPMInitializeSolution(tao);

    681:   /* Set linesearch */
    682:   SNESGetLineSearch(pdipm->snes,&linesearch);
    683:   SNESLineSearchSetType(linesearch,SNESLINESEARCHSHELL);
    684:   SNESLineSearchShellSetUserFunc(linesearch,PDIPMLineSearch,tao);
    685:   SNESLineSearchSetFromOptions(linesearch);

    687:   tao->reason = TAO_CONTINUE_ITERATING;

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

    693:   TaoLogConvergenceHistory(tao,pdipm->obj,tao->residual,tao->cnorm,tao->niter);
    694:   TaoMonitor(tao,tao->niter,pdipm->obj,tao->residual,tao->cnorm,pdipm->mu);
    695:   VecDestroy(&dummy);
    696:   (*tao->ops->convergencetest)(tao,tao->cnvP);
    697:   if (tao->reason) {
    698:     SNESSetConvergedReason(pdipm->snes,SNES_CONVERGED_FNORM_ABS);
    699:   }

    701:   while (tao->reason == TAO_CONTINUE_ITERATING) {
    702:     SNESConvergedReason reason;
    703:     SNESSolve(pdipm->snes,NULL,pdipm->X);

    705:     /* Check SNES convergence */
    706:     SNESGetConvergedReason(pdipm->snes,&reason);
    707:     if (reason < 0) {
    708:       PetscPrintf(PETSC_COMM_WORLD,"SNES solve did not converged due to reason %D\n",reason);
    709:     }

    711:     /* Check TAO convergence */
    712:     if (PetscIsInfOrNanReal(pdipm->obj)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"User-provided compute function generated Inf or NaN");
    713:   }
    714:   return(0);
    715: }

    717: /*
    718:    TaoSetup_PDIPM - Sets up tao and pdipm

    720:    Input Parameter:
    721:    tao - TAO object

    723:    Output:   pdipm - initialized object
    724: */
    725: PetscErrorCode TaoSetup_PDIPM(Tao tao)
    726: {
    727:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;
    729:   MPI_Comm       comm;
    730:   PetscMPIInt    rank,size;
    731:   PetscInt       row,col,Jcrstart,Jcrend,k,tmp,nc,proc,*nh_all,*ng_all;
    732:   PetscInt       offset,*xa,*xb,i,j,rstart,rend;
    733:   PetscScalar    one=1.0,neg_one=-1.0,*Xarr;
    734:   const PetscInt    *cols,*rranges,*cranges,*aj,*ranges;
    735:   const PetscScalar *aa;
    736:   Mat            J,jac_equality_trans,jac_inequality_trans;
    737:   Mat            Jce_xfixed_trans,Jci_xb_trans;
    738:   PetscInt       *dnz,*onz,rjstart,nx_all,*nce_all,*Jranges,cols1[2];

    741:   PetscObjectGetComm((PetscObject)tao,&comm);
    742:   MPI_Comm_rank(comm,&rank);
    743:   MPI_Comm_size(comm,&size);

    745:   /* (1) Setup Bounds and create Tao vectors */
    746:   TaoPDIPMSetUpBounds(tao);

    748:   if (!tao->gradient) {
    749:     VecDuplicate(tao->solution,&tao->gradient);
    750:     VecDuplicate(tao->solution,&tao->stepdirection);
    751:   }

    753:   /* (2) Get sizes */
    754:   /* Size of vector x - This is set by TaoSetInitialVector */
    755:   VecGetSize(tao->solution,&pdipm->Nx);
    756:   VecGetLocalSize(tao->solution,&pdipm->nx);

    758:   /* Size of equality constraints and vectors */
    759:   if (tao->constraints_equality) {
    760:     VecGetSize(tao->constraints_equality,&pdipm->Ng);
    761:     VecGetLocalSize(tao->constraints_equality,&pdipm->ng);
    762:   } else {
    763:     pdipm->ng = pdipm->Ng = 0;
    764:   }

    766:   pdipm->nce = pdipm->ng + pdipm->nxfixed;
    767:   pdipm->Nce = pdipm->Ng + pdipm->Nxfixed;

    769:   /* Size of inequality constraints and vectors */
    770:   if (tao->constraints_inequality) {
    771:     VecGetSize(tao->constraints_inequality,&pdipm->Nh);
    772:     VecGetLocalSize(tao->constraints_inequality,&pdipm->nh);
    773:   } else {
    774:     pdipm->nh = pdipm->Nh = 0;
    775:   }

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

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

    784:   /* list below to TaoView_PDIPM()? */
    785:   /* PetscPrintf(PETSC_COMM_SELF,"[%d] nce %d = ng %d + nxfixed %d\n",rank,pdipm->nce,pdipm->ng,pdipm->nxfixed); */
    786:   /* PetscPrintf(PETSC_COMM_SELF,"[%d] nci %d = nh %d + nxlb %d + nxub %d + 2*nxbox %d\n",rank,pdipm->nci,pdipm->nh,pdipm->nxlb,pdipm->nxub,pdipm->nxbox); */
    787:   /* PetscPrintf(PETSC_COMM_SELF,"[%d] n %d = nx %d + nce %d + 2*nci %d\n",rank,pdipm->n,pdipm->nx,pdipm->nce,pdipm->nci); */

    789:   /* (3) Offsets for subvectors */
    790:   pdipm->off_lambdae = pdipm->nx;
    791:   pdipm->off_lambdai = pdipm->off_lambdae + pdipm->nce;
    792:   pdipm->off_z       = pdipm->off_lambdai + pdipm->nci;

    794:   /* (4) Create vectors and subvectors */
    795:   /* Ce and Ci vectors */
    796:   VecCreate(comm,&pdipm->ce);
    797:   VecSetSizes(pdipm->ce,pdipm->nce,pdipm->Nce);
    798:   VecSetFromOptions(pdipm->ce);

    800:   VecCreate(comm,&pdipm->ci);
    801:   VecSetSizes(pdipm->ci,pdipm->nci,pdipm->Nci);
    802:   VecSetFromOptions(pdipm->ci);

    804:   /* X=[x; lambdae; lambdai; z] for the big KKT system */
    805:   VecCreate(comm,&pdipm->X);
    806:   VecSetSizes(pdipm->X,pdipm->n,pdipm->N);
    807:   VecSetFromOptions(pdipm->X);

    809:   /* Subvectors; they share local arrays with X */
    810:   VecGetArray(pdipm->X,&Xarr);
    811:   /* x shares local array with X.x */
    812:   if (pdipm->Nx) {
    813:     VecCreateMPIWithArray(comm,1,pdipm->nx,pdipm->Nx,Xarr,&pdipm->x);
    814:   }

    816:   /* lambdae shares local array with X.lambdae */
    817:   if (pdipm->Nce) {
    818:     VecCreateMPIWithArray(comm,1,pdipm->nce,pdipm->Nce,Xarr+pdipm->off_lambdae,&pdipm->lambdae);
    819:   }

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

    825:     VecCreate(comm,&pdipm->lambdae_xfixed);
    826:     VecSetSizes(pdipm->lambdae_xfixed,pdipm->nxfixed,PETSC_DECIDE);
    827:     VecSetFromOptions(pdipm->lambdae_xfixed);
    828:   }

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

    834:     /* z for slack variables; it shares local array with X.z */
    835:     VecCreateMPIWithArray(comm,1,pdipm->nci,pdipm->Nci,Xarr+pdipm->off_z,&pdipm->z);
    836:   }

    838:   /* tao->DI which shares local array with X.lambdai_h */
    839:   if (pdipm->Nh) {
    840:     VecCreateMPIWithArray(comm,1,pdipm->nh,pdipm->Nh,Xarr+pdipm->off_lambdai,&tao->DI);
    841:   }

    843:   VecCreate(comm,&pdipm->lambdai_xb);
    844:   VecSetSizes(pdipm->lambdai_xb,(pdipm->nci - pdipm->nh),PETSC_DECIDE);
    845:   VecSetFromOptions(pdipm->lambdai_xb);

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

    849:   /* (5) Create Jacobians Jce_xfixed and Jci */
    850:   /* (5.1) PDIPM Jacobian of equality bounds cebound(x) = J_nxfixed */
    851:   if (pdipm->Nxfixed) {
    852:     /* Create Jce_xfixed */
    853:     MatCreate(comm,&pdipm->Jce_xfixed);
    854:     MatSetSizes(pdipm->Jce_xfixed,pdipm->nxfixed,pdipm->nx,PETSC_DECIDE,pdipm->Nx);
    855:     MatSetFromOptions(pdipm->Jce_xfixed);
    856:     MatSeqAIJSetPreallocation(pdipm->Jce_xfixed,1,NULL);
    857:     MatMPIAIJSetPreallocation(pdipm->Jce_xfixed,1,NULL,1,NULL);

    859:     MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,&Jcrend);
    860:     ISGetIndices(pdipm->isxfixed,&cols);
    861:     k = 0;
    862:     for (row = Jcrstart; row < Jcrend; row++) {
    863:       MatSetValues(pdipm->Jce_xfixed,1,&row,1,cols+k,&one,INSERT_VALUES);
    864:       k++;
    865:     }
    866:     ISRestoreIndices(pdipm->isxfixed, &cols);
    867:     MatAssemblyBegin(pdipm->Jce_xfixed,MAT_FINAL_ASSEMBLY);
    868:     MatAssemblyEnd(pdipm->Jce_xfixed,MAT_FINAL_ASSEMBLY);
    869:   }

    871:   /* (5.2) PDIPM inequality Jacobian Jci = [tao->jacobian_inequality; ...] */
    872:   MatCreate(comm,&pdipm->Jci_xb);
    873:   MatSetSizes(pdipm->Jci_xb,pdipm->nci-pdipm->nh,pdipm->nx,PETSC_DECIDE,pdipm->Nx);
    874:   MatSetFromOptions(pdipm->Jci_xb);
    875:   MatSeqAIJSetPreallocation(pdipm->Jci_xb,1,NULL);
    876:   MatMPIAIJSetPreallocation(pdipm->Jci_xb,1,NULL,1,NULL);

    878:   MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,&Jcrend);
    879:   offset = Jcrstart;
    880:   if (pdipm->Nxub) {
    881:     /* Add xub to Jci_xb */
    882:     ISGetIndices(pdipm->isxub,&cols);
    883:     k = 0;
    884:     for (row = offset; row < offset + pdipm->nxub; row++) {
    885:       MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&neg_one,INSERT_VALUES);
    886:       k++;
    887:     }
    888:     ISRestoreIndices(pdipm->isxub, &cols);
    889:   }

    891:   if (pdipm->Nxlb) {
    892:     /* Add xlb to Jci_xb */
    893:     ISGetIndices(pdipm->isxlb,&cols);
    894:     k = 0;
    895:     offset += pdipm->nxub;
    896:     for (row = offset; row < offset + pdipm->nxlb; row++) {
    897:       MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&one,INSERT_VALUES);
    898:       k++;
    899:     }
    900:     ISRestoreIndices(pdipm->isxlb, &cols);
    901:   }

    903:   /* Add xbox to Jci_xb */
    904:   if (pdipm->Nxbox) {
    905:     ISGetIndices(pdipm->isxbox,&cols);
    906:     k = 0;
    907:     offset += pdipm->nxlb;
    908:     for (row = offset; row < offset + pdipm->nxbox; row++) {
    909:       MatSetValues(pdipm->Jci_xb,1,&row,1,cols+k,&neg_one,INSERT_VALUES);
    910:       tmp = row + pdipm->nxbox;
    911:       MatSetValues(pdipm->Jci_xb,1,&tmp,1,cols+k,&one,INSERT_VALUES);
    912:       k++;
    913:     }
    914:     ISRestoreIndices(pdipm->isxbox, &cols);
    915:   }

    917:   MatAssemblyBegin(pdipm->Jci_xb,MAT_FINAL_ASSEMBLY);
    918:   MatAssemblyEnd(pdipm->Jci_xb,MAT_FINAL_ASSEMBLY);
    919:   /* MatView(pdipm->Jci_xb,PETSC_VIEWER_STDOUT_WORLD); */

    921:   /* (6) Set up ISs for PC Fieldsplit */
    922:   if (pdipm->solve_reduced_kkt) {
    923:     PetscMalloc2(pdipm->nx+pdipm->nce,&xa,2*pdipm->nci,&xb);
    924:     for(i=0; i < pdipm->nx + pdipm->nce; i++) xa[i] = i;
    925:     for(i=0; i < 2*pdipm->nci; i++) xb[i] = pdipm->off_lambdai + i;

    927:     ISCreateGeneral(comm,pdipm->nx+pdipm->nce,xa,PETSC_OWN_POINTER,&pdipm->is1);
    928:     ISCreateGeneral(comm,2*pdipm->nci,xb,PETSC_OWN_POINTER,&pdipm->is2);
    929:   }

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

    934:   /* Get rstart of KKT matrix */
    935:   MPI_Scan(&pdipm->n,&rstart,1,MPIU_INT,MPI_SUM,comm);
    936:   rstart -= pdipm->n;

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

    940:   PetscMalloc3(size,&ng_all,size,&nh_all,size,&Jranges);
    941:   MPI_Allgather(&rstart,1,MPIU_INT,Jranges,1,MPIU_INT,comm);
    942:   MPI_Allgather(&pdipm->nh,1,MPIU_INT,nh_all,1,MPIU_INT,comm);
    943:   MPI_Allgather(&pdipm->ng,1,MPIU_INT,ng_all,1,MPIU_INT,comm);

    945:   MatGetOwnershipRanges(tao->hessian,&rranges);
    946:   MatGetOwnershipRangesColumn(tao->hessian,&cranges);

    948:   if (pdipm->Ng) {
    949:     TaoComputeJacobianEquality(tao,tao->solution,tao->jacobian_equality,tao->jacobian_equality_pre);
    950:     MatTranspose(tao->jacobian_equality,MAT_INITIAL_MATRIX,&pdipm->jac_equality_trans);
    951:   }
    952:   if (pdipm->Nh) {
    953:     TaoComputeJacobianInequality(tao,tao->solution,tao->jacobian_inequality,tao->jacobian_inequality_pre);
    954:     MatTranspose(tao->jacobian_inequality,MAT_INITIAL_MATRIX,&pdipm->jac_inequality_trans);
    955:   }

    957:   /* Count dnz,onz for preallocation of KKT matrix */
    958:   jac_equality_trans   = pdipm->jac_equality_trans;
    959:   jac_inequality_trans = pdipm->jac_inequality_trans;
    960:   nce_all = pdipm->nce_all;

    962:   if (pdipm->Nxfixed) {
    963:     MatTranspose(pdipm->Jce_xfixed,MAT_INITIAL_MATRIX,&Jce_xfixed_trans);
    964:   }
    965:   MatTranspose(pdipm->Jci_xb,MAT_INITIAL_MATRIX,&Jci_xb_trans);

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

    969:   /* 1st row block of KKT matrix: [Wxx; gradCe'; -gradCi'; 0] */
    970:   TaoPDIPMEvaluateFunctionsAndJacobians(tao,pdipm->x);
    971:   TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);

    973:   /* Insert tao->hessian */
    974:   MatGetOwnershipRange(tao->hessian,&rjstart,NULL);
    975:   for (i=0; i<pdipm->nx; i++){
    976:     row = rstart + i;

    978:     MatGetRow(tao->hessian,i+rjstart,&nc,&aj,NULL);
    979:     proc = 0;
    980:     for (j=0; j < nc; j++) {
    981:       while (aj[j] >= cranges[proc+1]) proc++;
    982:       col = aj[j] - cranges[proc] + Jranges[proc];
    983:       MatPreallocateSet(row,1,&col,dnz,onz);
    984:     }
    985:     MatRestoreRow(tao->hessian,i+rjstart,&nc,&aj,NULL);

    987:     if (pdipm->ng) {
    988:       /* Insert grad g' */
    989:       MatGetRow(jac_equality_trans,i+rjstart,&nc,&aj,NULL);
    990:       MatGetOwnershipRanges(tao->jacobian_equality,&ranges);
    991:       proc = 0;
    992:       for (j=0; j < nc; j++) {
    993:         /* find row ownership of */
    994:         while (aj[j] >= ranges[proc+1]) proc++;
    995:         nx_all = rranges[proc+1] - rranges[proc];
    996:         col = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
    997:         MatPreallocateSet(row,1,&col,dnz,onz);
    998:       }
    999:       MatRestoreRow(jac_equality_trans,i+rjstart,&nc,&aj,NULL);
    1000:     }

    1002:     /* Insert Jce_xfixed^T' */
    1003:     if (pdipm->nxfixed) {
    1004:       MatGetRow(Jce_xfixed_trans,i+rjstart,&nc,&aj,NULL);
    1005:       MatGetOwnershipRanges(pdipm->Jce_xfixed,&ranges);
    1006:       proc = 0;
    1007:       for (j=0; j < nc; j++) {
    1008:         /* find row ownership of */
    1009:         while (aj[j] >= ranges[proc+1]) proc++;
    1010:         nx_all = rranges[proc+1] - rranges[proc];
    1011:         col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + ng_all[proc];
    1012:         MatPreallocateSet(row,1,&col,dnz,onz);
    1013:       }
    1014:       MatRestoreRow(Jce_xfixed_trans,i+rjstart,&nc,&aj,NULL);
    1015:     }

    1017:     if (pdipm->nh) {
    1018:       /* Insert -grad h' */
    1019:       MatGetRow(jac_inequality_trans,i+rjstart,&nc,&aj,NULL);
    1020:       MatGetOwnershipRanges(tao->jacobian_inequality,&ranges);
    1021:       proc = 0;
    1022:       for (j=0; j < nc; j++) {
    1023:         /* find row ownership of */
    1024:         while (aj[j] >= ranges[proc+1]) proc++;
    1025:         nx_all = rranges[proc+1] - rranges[proc];
    1026:         col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc];
    1027:         MatPreallocateSet(row,1,&col,dnz,onz);
    1028:       }
    1029:       MatRestoreRow(jac_inequality_trans,i+rjstart,&nc,&aj,NULL);
    1030:     }

    1032:     /* Insert Jci_xb^T' */
    1033:     MatGetRow(Jci_xb_trans,i+rjstart,&nc,&aj,NULL);
    1034:     MatGetOwnershipRanges(pdipm->Jci_xb,&ranges);
    1035:     proc = 0;
    1036:     for (j=0; j < nc; j++) {
    1037:       /* find row ownership of */
    1038:       while (aj[j] >= ranges[proc+1]) proc++;
    1039:       nx_all = rranges[proc+1] - rranges[proc];
    1040:       col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc] + nh_all[proc];
    1041:       MatPreallocateSet(row,1,&col,dnz,onz);
    1042:     }
    1043:     MatRestoreRow(Jci_xb_trans,i+rjstart,&nc,&aj,NULL);
    1044:   }

    1046:   /* 2nd Row block of KKT matrix: [grad Ce, 0, 0, 0] */
    1047:   if (pdipm->Ng) {
    1048:     MatGetOwnershipRange(tao->jacobian_equality,&rjstart,NULL);
    1049:     for (i=0; i < pdipm->ng; i++){
    1050:       row = rstart + pdipm->off_lambdae + i;

    1052:       MatGetRow(tao->jacobian_equality,i+rjstart,&nc,&aj,NULL);
    1053:       proc = 0;
    1054:       for (j=0; j < nc; j++) {
    1055:         while (aj[j] >= cranges[proc+1]) proc++;
    1056:         col = aj[j] - cranges[proc] + Jranges[proc];
    1057:         MatPreallocateSet(row,1,&col,dnz,onz); /* grad g */
    1058:       }
    1059:       MatRestoreRow(tao->jacobian_equality,i+rjstart,&nc,&aj,NULL);
    1060:     }
    1061:   }
    1062:   /* Jce_xfixed */
    1063:   if (pdipm->Nxfixed) {
    1064:     MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,NULL);
    1065:     for (i=0; i < (pdipm->nce - pdipm->ng); i++ ){
    1066:       row = rstart + pdipm->off_lambdae + pdipm->ng + i;

    1068:       MatGetRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,NULL);
    1069:       if (nc != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"nc != 1");

    1071:       proc = 0;
    1072:       j    = 0;
    1073:       while (cols[j] >= cranges[proc+1]) proc++;
    1074:       col = cols[j] - cranges[proc] + Jranges[proc];
    1075:       MatPreallocateSet(row,1,&col,dnz,onz);
    1076:       MatRestoreRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,NULL);
    1077:     }
    1078:   }

    1080:   /* 3rd Row block of KKT matrix: [ gradCi, 0, 0, -I] */
    1081:   if (pdipm->Nh) {
    1082:     MatGetOwnershipRange(tao->jacobian_inequality,&rjstart,NULL);
    1083:     for (i=0; i < pdipm->nh; i++){
    1084:       row = rstart + pdipm->off_lambdai + i;

    1086:       MatGetRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,NULL);
    1087:       proc = 0;
    1088:       for (j=0; j < nc; j++) {
    1089:         while (aj[j] >= cranges[proc+1]) proc++;
    1090:         col = aj[j] - cranges[proc] + Jranges[proc];
    1091:         MatPreallocateSet(row,1,&col,dnz,onz); /* grad h */
    1092:       }
    1093:       MatRestoreRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,NULL);
    1094:     }
    1095:     /* -I */
    1096:     for (i=0; i < pdipm->nh; i++){
    1097:       row = rstart + pdipm->off_lambdai + i;
    1098:       col = rstart + pdipm->off_z + i;
    1099:       MatPreallocateSet(row,1,&col,dnz,onz);
    1100:     }
    1101:   }

    1103:   /* Jci_xb */
    1104:   MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,NULL);
    1105:   for (i=0; i < (pdipm->nci - pdipm->nh); i++ ){
    1106:     row = rstart + pdipm->off_lambdai + pdipm->nh + i;

    1108:     MatGetRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,NULL);
    1109:     if (nc != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"nc != 1");
    1110:     proc = 0;
    1111:     for (j=0; j < nc; j++) {
    1112:       while (cols[j] >= cranges[proc+1]) proc++;
    1113:       col = cols[j] - cranges[proc] + Jranges[proc];
    1114:       MatPreallocateSet(row,1,&col,dnz,onz);
    1115:     }
    1116:     MatRestoreRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,NULL);
    1117:     /* -I */
    1118:     col = rstart + pdipm->off_z + pdipm->nh + i;
    1119:     MatPreallocateSet(row,1,&col,dnz,onz);
    1120:   }

    1122:   /* 4-th Row block of KKT matrix: Z and Ci */
    1123:   for (i=0; i < pdipm->nci; i++) {
    1124:     row     = rstart + pdipm->off_z + i;
    1125:     cols1[0] = rstart + pdipm->off_lambdai + i;
    1126:     cols1[1] = row;
    1127:     MatPreallocateSet(row,2,cols1,dnz,onz);
    1128:   }

    1130:   /* diagonal entry */
    1131:   for (i=0; i<pdipm->n; i++) dnz[i]++; /* diagonal entry */

    1133:   /* Create KKT matrix */
    1134:   MatCreate(comm,&J);
    1135:   MatSetSizes(J,pdipm->n,pdipm->n,PETSC_DECIDE,PETSC_DECIDE);
    1136:   MatSetFromOptions(J);
    1137:   MatSeqAIJSetPreallocation(J,0,dnz);
    1138:   MatMPIAIJSetPreallocation(J,0,dnz,0,onz);
    1139:   /* MatSetOption(J,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE); */
    1140:   MatPreallocateFinalize(dnz,onz);
    1141:   pdipm->K = J;

    1143:   /* (8) Set up nonlinear solver SNES */
    1144:   SNESSetFunction(pdipm->snes,NULL,TaoSNESFunction_PDIPM,(void*)tao);
    1145:   SNESSetJacobian(pdipm->snes,J,J,TaoSNESJacobian_PDIPM,(void*)tao);

    1147:   if (pdipm->solve_reduced_kkt) {
    1148:     PC pc;
    1149:     KSPGetPC(tao->ksp,&pc);
    1150:     PCSetType(pc,PCFIELDSPLIT);
    1151:     PCFieldSplitSetType(pc,PC_COMPOSITE_SCHUR);
    1152:     PCFieldSplitSetIS(pc,"2",pdipm->is2);
    1153:     PCFieldSplitSetIS(pc,"1",pdipm->is1);
    1154:   }
    1155:   SNESSetFromOptions(pdipm->snes);

    1157:   /* (9) Insert constant entries to  K */
    1158:   /* Set 0.0 to diagonal of K, so that the solver does not complain *about missing diagonal value */
    1159:   MatGetOwnershipRange(J,&rstart,&rend);
    1160:   for (i=rstart; i<rend; i++){
    1161:     MatSetValue(J,i,i,0.0,INSERT_VALUES);
    1162:   }

    1164:   /* Row block of K: [ grad Ce, 0, 0, 0] */
    1165:   if (pdipm->Nxfixed) {
    1166:     MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,NULL);
    1167:     for (i=0; i < (pdipm->nce - pdipm->ng); i++ ){
    1168:       row = rstart + pdipm->off_lambdae + pdipm->ng + i;

    1170:       MatGetRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,&aa);
    1171:       proc = 0;
    1172:       for (j=0; j < nc; j++) {
    1173:         while (cols[j] >= cranges[proc+1]) proc++;
    1174:         col = cols[j] - cranges[proc] + Jranges[proc];
    1175:         MatSetValue(J,row,col,aa[j],INSERT_VALUES); /* grad Ce */
    1176:         MatSetValue(J,col,row,aa[j],INSERT_VALUES); /* grad Ce' */
    1177:       }
    1178:       MatRestoreRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,&aa);
    1179:     }
    1180:   }

    1182:   /* Row block of K: [ grad Ci, 0, 0, -I] */
    1183:   MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,NULL);
    1184:   for (i=0; i < (pdipm->nci - pdipm->nh); i++ ){
    1185:     row = rstart + pdipm->off_lambdai + pdipm->nh + i;

    1187:     MatGetRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,&aa);
    1188:     proc = 0;
    1189:     for (j=0; j < nc; j++) {
    1190:       while (cols[j] >= cranges[proc+1]) proc++;
    1191:       col = cols[j] - cranges[proc] + Jranges[proc];
    1192:       MatSetValue(J,col,row,-aa[j],INSERT_VALUES);
    1193:       MatSetValue(J,row,col,aa[j],INSERT_VALUES);
    1194:     }
    1195:     MatRestoreRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,&aa);

    1197:     col = rstart + pdipm->off_z + pdipm->nh + i;
    1198:     MatSetValue(J,row,col,-1,INSERT_VALUES);
    1199:   }

    1201:   for (i=0; i < pdipm->nh; i++){
    1202:     row = rstart + pdipm->off_lambdai + i;
    1203:     col = rstart + pdipm->off_z + i;
    1204:     MatSetValue(J,row,col,-1,INSERT_VALUES);
    1205:   }

    1207:   if (pdipm->Nxfixed) {
    1208:     MatDestroy(&Jce_xfixed_trans);
    1209:   }
    1210:   MatDestroy(&Jci_xb_trans);
    1211:   PetscFree3(ng_all,nh_all,Jranges);
    1212:   return(0);
    1213: }

    1215: /*
    1216:    TaoDestroy_PDIPM - Destroys the pdipm object

    1218:    Input:
    1219:    full pdipm

    1221:    Output:
    1222:    Destroyed pdipm
    1223: */
    1224: PetscErrorCode TaoDestroy_PDIPM(Tao tao)
    1225: {
    1226:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;

    1230:   /* Freeing Vectors assocaiated with KKT (X) */
    1231:   VecDestroy(&pdipm->x); /* Solution x */
    1232:   VecDestroy(&pdipm->lambdae); /* Equality constraints lagrangian multiplier*/
    1233:   VecDestroy(&pdipm->lambdai); /* Inequality constraints lagrangian multiplier*/
    1234:   VecDestroy(&pdipm->z);       /* Slack variables */
    1235:   VecDestroy(&pdipm->X);       /* Big KKT system vector [x; lambdae; lambdai; z] */

    1237:   /* work vectors */
    1238:   VecDestroy(&pdipm->lambdae_xfixed);
    1239:   VecDestroy(&pdipm->lambdai_xb);

    1241:   /* Legrangian equality and inequality Vec */
    1242:   VecDestroy(&pdipm->ce); /* Vec of equality constraints */
    1243:   VecDestroy(&pdipm->ci); /* Vec of inequality constraints */

    1245:   /* Matrices */
    1246:   MatDestroy(&pdipm->Jce_xfixed);
    1247:   MatDestroy(&pdipm->Jci_xb); /* Jacobian of inequality constraints Jci = [tao->jacobian_inequality ; J(nxub); J(nxlb); J(nxbx)] */
    1248:   MatDestroy(&pdipm->K);

    1250:   /* Index Sets */
    1251:   if (pdipm->Nxub) {
    1252:     ISDestroy(&pdipm->isxub);    /* Finite upper bound only -inf < x < ub */
    1253:   }

    1255:   if (pdipm->Nxlb) {
    1256:     ISDestroy(&pdipm->isxlb);    /* Finite lower bound only  lb <= x < inf */
    1257:   }

    1259:   if (pdipm->Nxfixed) {
    1260:     ISDestroy(&pdipm->isxfixed); /* Fixed variables         lb =  x = ub */
    1261:   }

    1263:   if (pdipm->Nxbox) {
    1264:     ISDestroy(&pdipm->isxbox);   /* Boxed variables         lb <= x <= ub */
    1265:   }

    1267:   if (pdipm->Nxfree) {
    1268:     ISDestroy(&pdipm->isxfree);  /* Free variables        -inf <= x <= inf */
    1269:   }

    1271:   if (pdipm->solve_reduced_kkt) {
    1272:     ISDestroy(&pdipm->is1);
    1273:     ISDestroy(&pdipm->is2);
    1274:   }

    1276:   /* SNES */
    1277:   SNESDestroy(&pdipm->snes); /* Nonlinear solver */
    1278:   PetscFree(pdipm->nce_all);
    1279:   MatDestroy(&pdipm->jac_equality_trans);
    1280:   MatDestroy(&pdipm->jac_inequality_trans);

    1282:   /* Destroy pdipm */
    1283:   PetscFree(tao->data); /* Holding locations of pdipm */

    1285:   /* Destroy Dual */
    1286:   VecDestroy(&tao->DE); /* equality dual */
    1287:   VecDestroy(&tao->DI); /* dinequality dual */
    1288:   return(0);
    1289: }

    1291: PetscErrorCode TaoSetFromOptions_PDIPM(PetscOptionItems *PetscOptionsObject,Tao tao)
    1292: {
    1293:   TAO_PDIPM      *pdipm = (TAO_PDIPM*)tao->data;

    1297:   PetscOptionsHead(PetscOptionsObject,"PDIPM method for constrained optimization");
    1298:   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);
    1299:   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);
    1300:   PetscOptionsBool("-tao_pdipm_solve_reduced_kkt","Solve reduced KKT system using Schur-complement",NULL,pdipm->solve_reduced_kkt,&pdipm->solve_reduced_kkt,NULL);
    1301:   PetscOptionsReal("-tao_pdipm_mu_update_factor","Update scalar for barrier parameter (mu) update",NULL,pdipm->mu_update_factor,&pdipm->mu_update_factor,NULL);
    1302:   PetscOptionsTail();
    1303:   return(0);
    1304: }

    1306: /*MC
    1307:   TAOPDIPM - Barrier-based primal-dual interior point algorithm for generally constrained optimization.

    1309:   Option Database Keys:
    1310: +   -tao_pdipm_push_init_lambdai - parameter to push initial dual variables away from bounds (> 0)
    1311: .   -tao_pdipm_push_init_slack  - parameter to push initial slack variables away from bounds (> 0)
    1312: -   -tao_pdipm_mu_update_factor - update scalar for barrier parameter (mu) update (> 0)

    1314:   Level: beginner
    1315: M*/
    1316: PETSC_EXTERN PetscErrorCode TaoCreate_PDIPM(Tao tao)
    1317: {
    1318:   TAO_PDIPM      *pdipm;

    1322:   tao->ops->setup          = TaoSetup_PDIPM;
    1323:   tao->ops->solve          = TaoSolve_PDIPM;
    1324:   tao->ops->setfromoptions = TaoSetFromOptions_PDIPM;
    1325:   tao->ops->destroy        = TaoDestroy_PDIPM;

    1327:   PetscNewLog(tao,&pdipm);
    1328:   tao->data = (void*)pdipm;

    1330:   pdipm->nx      = pdipm->Nx      = 0;
    1331:   pdipm->nxfixed = pdipm->Nxfixed = 0;
    1332:   pdipm->nxlb    = pdipm->Nxlb    = 0;
    1333:   pdipm->nxub    = pdipm->Nxub    = 0;
    1334:   pdipm->nxbox   = pdipm->Nxbox   = 0;
    1335:   pdipm->nxfree  = pdipm->Nxfree  = 0;

    1337:   pdipm->ng = pdipm->Ng = pdipm->nce = pdipm->Nce = 0;
    1338:   pdipm->nh = pdipm->Nh = pdipm->nci = pdipm->Nci = 0;
    1339:   pdipm->n  = pdipm->N  = 0;
    1340:   pdipm->mu = 1.0;
    1341:   pdipm->mu_update_factor = 0.1;

    1343:   pdipm->push_init_slack   = 1.0;
    1344:   pdipm->push_init_lambdai = 1.0;
    1345:   pdipm->solve_reduced_kkt = PETSC_FALSE;

    1347:   /* Override default settings (unless already changed) */
    1348:   if (!tao->max_it_changed) tao->max_it = 200;
    1349:   if (!tao->max_funcs_changed) tao->max_funcs = 500;

    1351:   SNESCreate(((PetscObject)tao)->comm,&pdipm->snes);
    1352:   SNESSetOptionsPrefix(pdipm->snes,tao->hdr.prefix);
    1353:   SNESGetKSP(pdipm->snes,&tao->ksp);
    1354:   PetscObjectReference((PetscObject)tao->ksp);
    1355:   return(0);
    1356: }