impls/ipm/ipm.c

#include <petsctaolinesearch.h>
#include <../src/tao/constrained/impls/ipm/ipm.h> /*I "ipm.h" I*/

/*
   x,d in R^n
   f in R
   nb = mi + nlb+nub
   s in R^nb is slack vector CI(x) / x-XL / -x+XU
   bin in R^mi (tao->constraints_inequality)
   beq in R^me (tao->constraints_equality)
   lambdai in R^nb (ipmP->lambdai)
   lambdae in R^me (ipmP->lambdae)
   Jeq in R^(me x n) (tao->jacobian_equality)
   Jin in R^(mi x n) (tao->jacobian_inequality)
   Ai in  R^(nb x n) (ipmP->Ai)
   H in R^(n x n) (tao->hessian)
   min f=(1/2)*x'*H*x + d'*x
   s.t.  CE(x) == 0
         CI(x) >= 0
         x >= tao->XL
         -x >= -tao->XU
*/

static PetscErrorCode IPMComputeKKT(Tao tao);
static PetscErrorCode IPMPushInitialPoint(Tao tao);
static PetscErrorCode IPMEvaluate(Tao tao);
static PetscErrorCode IPMUpdateK(Tao tao);
static PetscErrorCode IPMUpdateAi(Tao tao);
static PetscErrorCode IPMGatherRHS(Tao tao, Vec, Vec, Vec, Vec, Vec);
static PetscErrorCode IPMScatterStep(Tao tao, Vec, Vec, Vec, Vec, Vec);
static PetscErrorCode IPMInitializeBounds(Tao tao);

static PetscErrorCode TaoSolve_IPM(Tao tao)
{
  TAO_IPM    *ipmP = (TAO_IPM *)tao->data;
  PetscInt    its, i;
  PetscScalar stepsize = 1.0;
  PetscScalar step_s, step_l, alpha, tau, sigma, phi_target;

  PetscFunctionBegin;
  /* Push initial point away from bounds */
  PetscCall(IPMInitializeBounds(tao));
  PetscCall(IPMPushInitialPoint(tao));
  PetscCall(VecCopy(tao->solution, ipmP->rhs_x));
  PetscCall(IPMEvaluate(tao));
  PetscCall(IPMComputeKKT(tao));

  tao->reason = TAO_CONTINUE_ITERATING;
  PetscCall(TaoLogConvergenceHistory(tao, ipmP->kkt_f, ipmP->phi, 0.0, tao->ksp_its));
  PetscCall(TaoMonitor(tao, tao->niter, ipmP->kkt_f, ipmP->phi, 0.0, 1.0));
  PetscUseTypeMethod(tao, convergencetest, tao->cnvP);

  while (tao->reason == TAO_CONTINUE_ITERATING) {
    /* Call general purpose update function */
    PetscTryTypeMethod(tao, update, tao->niter, tao->user_update);

    tao->ksp_its = 0;
    PetscCall(IPMUpdateK(tao));
    /*
       rhs.x    = -rd
       rhs.lame = -rpe
       rhs.lami = -rpi
       rhs.com  = -com
    */

    PetscCall(VecCopy(ipmP->rd, ipmP->rhs_x));
    if (ipmP->me > 0) PetscCall(VecCopy(ipmP->rpe, ipmP->rhs_lambdae));
    if (ipmP->nb > 0) {
      PetscCall(VecCopy(ipmP->rpi, ipmP->rhs_lambdai));
      PetscCall(VecCopy(ipmP->complementarity, ipmP->rhs_s));
    }
    PetscCall(IPMGatherRHS(tao, ipmP->bigrhs, ipmP->rhs_x, ipmP->rhs_lambdae, ipmP->rhs_lambdai, ipmP->rhs_s));
    PetscCall(VecScale(ipmP->bigrhs, -1.0));

    /* solve K * step = rhs */
    PetscCall(KSPSetOperators(tao->ksp, ipmP->K, ipmP->K));
    PetscCall(KSPSolve(tao->ksp, ipmP->bigrhs, ipmP->bigstep));

    PetscCall(IPMScatterStep(tao, ipmP->bigstep, tao->stepdirection, ipmP->ds, ipmP->dlambdae, ipmP->dlambdai));
    PetscCall(KSPGetIterationNumber(tao->ksp, &its));
    tao->ksp_its += its;
    tao->ksp_tot_its += its;
    /* Find distance along step direction to closest bound */
    if (ipmP->nb > 0) {
      PetscCall(VecStepBoundInfo(ipmP->s, ipmP->ds, ipmP->Zero_nb, ipmP->Inf_nb, &step_s, NULL, NULL));
      PetscCall(VecStepBoundInfo(ipmP->lambdai, ipmP->dlambdai, ipmP->Zero_nb, ipmP->Inf_nb, &step_l, NULL, NULL));
      alpha        = PetscMin(step_s, step_l);
      alpha        = PetscMin(alpha, 1.0);
      ipmP->alpha1 = alpha;
    } else {
      ipmP->alpha1 = alpha = 1.0;
    }

    /* x_aff = x + alpha*d */
    PetscCall(VecCopy(tao->solution, ipmP->save_x));
    if (ipmP->me > 0) PetscCall(VecCopy(ipmP->lambdae, ipmP->save_lambdae));
    if (ipmP->nb > 0) {
      PetscCall(VecCopy(ipmP->lambdai, ipmP->save_lambdai));
      PetscCall(VecCopy(ipmP->s, ipmP->save_s));
    }

    PetscCall(VecAXPY(tao->solution, alpha, tao->stepdirection));
    if (ipmP->me > 0) PetscCall(VecAXPY(ipmP->lambdae, alpha, ipmP->dlambdae));
    if (ipmP->nb > 0) {
      PetscCall(VecAXPY(ipmP->lambdai, alpha, ipmP->dlambdai));
      PetscCall(VecAXPY(ipmP->s, alpha, ipmP->ds));
    }

    /* Recompute kkt to find centering parameter sigma = (new_mu/old_mu)^3 */
    if (ipmP->mu == 0.0) {
      sigma = 0.0;
    } else {
      sigma = 1.0 / ipmP->mu;
    }
    PetscCall(IPMComputeKKT(tao));
    sigma *= ipmP->mu;
    sigma *= sigma * sigma;

    /* revert kkt info */
    PetscCall(VecCopy(ipmP->save_x, tao->solution));
    if (ipmP->me > 0) PetscCall(VecCopy(ipmP->save_lambdae, ipmP->lambdae));
    if (ipmP->nb > 0) {
      PetscCall(VecCopy(ipmP->save_lambdai, ipmP->lambdai));
      PetscCall(VecCopy(ipmP->save_s, ipmP->s));
    }
    PetscCall(IPMComputeKKT(tao));

    /* update rhs with new complementarity vector */
    if (ipmP->nb > 0) {
      PetscCall(VecCopy(ipmP->complementarity, ipmP->rhs_s));
      PetscCall(VecScale(ipmP->rhs_s, -1.0));
      PetscCall(VecShift(ipmP->rhs_s, sigma * ipmP->mu));
    }
    PetscCall(IPMGatherRHS(tao, ipmP->bigrhs, NULL, NULL, NULL, ipmP->rhs_s));

    /* solve K * step = rhs */
    PetscCall(KSPSetOperators(tao->ksp, ipmP->K, ipmP->K));
    PetscCall(KSPSolve(tao->ksp, ipmP->bigrhs, ipmP->bigstep));

    PetscCall(IPMScatterStep(tao, ipmP->bigstep, tao->stepdirection, ipmP->ds, ipmP->dlambdae, ipmP->dlambdai));
    PetscCall(KSPGetIterationNumber(tao->ksp, &its));
    tao->ksp_its += its;
    tao->ksp_tot_its += its;
    if (ipmP->nb > 0) {
      /* Get max step size and apply frac-to-boundary */
      tau = PetscMax(ipmP->taumin, 1.0 - ipmP->mu);
      tau = PetscMin(tau, 1.0);
      if (tau != 1.0) {
        PetscCall(VecScale(ipmP->s, tau));
        PetscCall(VecScale(ipmP->lambdai, tau));
      }
      PetscCall(VecStepBoundInfo(ipmP->s, ipmP->ds, ipmP->Zero_nb, ipmP->Inf_nb, &step_s, NULL, NULL));
      PetscCall(VecStepBoundInfo(ipmP->lambdai, ipmP->dlambdai, ipmP->Zero_nb, ipmP->Inf_nb, &step_l, NULL, NULL));
      if (tau != 1.0) {
        PetscCall(VecCopy(ipmP->save_s, ipmP->s));
        PetscCall(VecCopy(ipmP->save_lambdai, ipmP->lambdai));
      }
      alpha = PetscMin(step_s, step_l);
      alpha = PetscMin(alpha, 1.0);
    } else {
      alpha = 1.0;
    }
    ipmP->alpha2 = alpha;
    /* TODO make phi_target meaningful */
    phi_target = ipmP->dec * ipmP->phi;
    for (i = 0; i < 11; i++) {
      PetscCall(VecAXPY(tao->solution, alpha, tao->stepdirection));
      if (ipmP->nb > 0) {
        PetscCall(VecAXPY(ipmP->s, alpha, ipmP->ds));
        PetscCall(VecAXPY(ipmP->lambdai, alpha, ipmP->dlambdai));
      }
      if (ipmP->me > 0) PetscCall(VecAXPY(ipmP->lambdae, alpha, ipmP->dlambdae));

      /* update dual variables */
      if (ipmP->me > 0) PetscCall(VecCopy(ipmP->lambdae, tao->DE));

      PetscCall(IPMEvaluate(tao));
      PetscCall(IPMComputeKKT(tao));
      if (ipmP->phi <= phi_target) break;
      alpha /= 2.0;
    }

    PetscCall(TaoLogConvergenceHistory(tao, ipmP->kkt_f, ipmP->phi, 0.0, tao->ksp_its));
    PetscCall(TaoMonitor(tao, tao->niter, ipmP->kkt_f, ipmP->phi, 0.0, stepsize));
    PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
    tao->niter++;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoSetup_IPM(Tao tao)
{
  TAO_IPM *ipmP = (TAO_IPM *)tao->data;

  PetscFunctionBegin;
  ipmP->nb = ipmP->mi = ipmP->me = 0;
  ipmP->K                        = NULL;
  PetscCall(VecGetSize(tao->solution, &ipmP->n));
  if (!tao->gradient) {
    PetscCall(VecDuplicate(tao->solution, &tao->gradient));
    PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));
    PetscCall(VecDuplicate(tao->solution, &ipmP->rd));
    PetscCall(VecDuplicate(tao->solution, &ipmP->rhs_x));
    PetscCall(VecDuplicate(tao->solution, &ipmP->work));
    PetscCall(VecDuplicate(tao->solution, &ipmP->save_x));
  }
  if (tao->constraints_equality) {
    PetscCall(VecGetSize(tao->constraints_equality, &ipmP->me));
    PetscCall(VecDuplicate(tao->constraints_equality, &ipmP->lambdae));
    PetscCall(VecDuplicate(tao->constraints_equality, &ipmP->dlambdae));
    PetscCall(VecDuplicate(tao->constraints_equality, &ipmP->rhs_lambdae));
    PetscCall(VecDuplicate(tao->constraints_equality, &ipmP->save_lambdae));
    PetscCall(VecDuplicate(tao->constraints_equality, &ipmP->rpe));
    PetscCall(VecDuplicate(tao->constraints_equality, &tao->DE));
  }
  if (tao->constraints_inequality) PetscCall(VecDuplicate(tao->constraints_inequality, &tao->DI));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode IPMInitializeBounds(Tao tao)
{
  TAO_IPM        *ipmP = (TAO_IPM *)tao->data;
  Vec             xtmp;
  PetscInt        xstart, xend;
  PetscInt        ucstart, ucend;   /* user ci */
  PetscInt        ucestart, uceend; /* user ce */
  PetscInt        sstart = 0, send = 0;
  PetscInt        bigsize;
  PetscInt        i, counter, nloc;
  PetscInt       *cind, *xind, *ucind, *uceind, *stepind;
  VecType         vtype;
  const PetscInt *xli, *xui;
  PetscInt        xl_offset, xu_offset;
  IS              bigxl, bigxu, isuc, isc, isx, sis, is1;
  MPI_Comm        comm;

  PetscFunctionBegin;
  cind = xind = ucind = uceind = stepind = NULL;
  ipmP->mi                               = 0;
  ipmP->nxlb                             = 0;
  ipmP->nxub                             = 0;
  ipmP->nb                               = 0;
  ipmP->nslack                           = 0;

  PetscCall(VecDuplicate(tao->solution, &xtmp));
  PetscCall(TaoComputeVariableBounds(tao));
  if (tao->XL) {
    PetscCall(VecSet(xtmp, PETSC_NINFINITY));
    PetscCall(VecWhichGreaterThan(tao->XL, xtmp, &ipmP->isxl));
    PetscCall(ISGetSize(ipmP->isxl, &ipmP->nxlb));
  } else {
    ipmP->nxlb = 0;
  }
  if (tao->XU) {
    PetscCall(VecSet(xtmp, PETSC_INFINITY));
    PetscCall(VecWhichLessThan(tao->XU, xtmp, &ipmP->isxu));
    PetscCall(ISGetSize(ipmP->isxu, &ipmP->nxub));
  } else {
    ipmP->nxub = 0;
  }
  PetscCall(VecDestroy(&xtmp));
  if (tao->constraints_inequality) {
    PetscCall(VecGetSize(tao->constraints_inequality, &ipmP->mi));
  } else {
    ipmP->mi = 0;
  }
  ipmP->nb = ipmP->nxlb + ipmP->nxub + ipmP->mi;

  PetscCall(PetscObjectGetComm((PetscObject)tao->solution, &comm));

  bigsize = ipmP->n + 2 * ipmP->nb + ipmP->me;
  PetscCall(PetscMalloc1(bigsize, &stepind));
  PetscCall(PetscMalloc1(ipmP->n, &xind));
  PetscCall(PetscMalloc1(ipmP->me, &uceind));
  PetscCall(VecGetOwnershipRange(tao->solution, &xstart, &xend));

  if (ipmP->nb > 0) {
    PetscCall(VecCreate(comm, &ipmP->s));
    PetscCall(VecSetSizes(ipmP->s, PETSC_DECIDE, ipmP->nb));
    PetscCall(VecSetFromOptions(ipmP->s));
    PetscCall(VecDuplicate(ipmP->s, &ipmP->ds));
    PetscCall(VecDuplicate(ipmP->s, &ipmP->rhs_s));
    PetscCall(VecDuplicate(ipmP->s, &ipmP->complementarity));
    PetscCall(VecDuplicate(ipmP->s, &ipmP->ci));

    PetscCall(VecDuplicate(ipmP->s, &ipmP->lambdai));
    PetscCall(VecDuplicate(ipmP->s, &ipmP->dlambdai));
    PetscCall(VecDuplicate(ipmP->s, &ipmP->rhs_lambdai));
    PetscCall(VecDuplicate(ipmP->s, &ipmP->save_lambdai));

    PetscCall(VecDuplicate(ipmP->s, &ipmP->save_s));
    PetscCall(VecDuplicate(ipmP->s, &ipmP->rpi));
    PetscCall(VecDuplicate(ipmP->s, &ipmP->Zero_nb));
    PetscCall(VecSet(ipmP->Zero_nb, 0.0));
    PetscCall(VecDuplicate(ipmP->s, &ipmP->One_nb));
    PetscCall(VecSet(ipmP->One_nb, 1.0));
    PetscCall(VecDuplicate(ipmP->s, &ipmP->Inf_nb));
    PetscCall(VecSet(ipmP->Inf_nb, PETSC_INFINITY));

    PetscCall(PetscMalloc1(ipmP->nb, &cind));
    PetscCall(PetscMalloc1(ipmP->mi, &ucind));
    PetscCall(VecGetOwnershipRange(ipmP->s, &sstart, &send));

    if (ipmP->mi > 0) {
      PetscCall(VecGetOwnershipRange(tao->constraints_inequality, &ucstart, &ucend));
      counter = 0;
      for (i = ucstart; i < ucend; i++) cind[counter++] = i;
      PetscCall(ISCreateGeneral(comm, counter, cind, PETSC_COPY_VALUES, &isuc));
      PetscCall(ISCreateGeneral(comm, counter, cind, PETSC_COPY_VALUES, &isc));
      PetscCall(VecScatterCreate(tao->constraints_inequality, isuc, ipmP->ci, isc, &ipmP->ci_scat));

      PetscCall(ISDestroy(&isuc));
      PetscCall(ISDestroy(&isc));
    }
    /* need to know how may xbound indices are on each process */
    /* TODO better way */
    if (ipmP->nxlb) {
      PetscCall(ISAllGather(ipmP->isxl, &bigxl));
      PetscCall(ISGetIndices(bigxl, &xli));
      /* find offsets for this processor */
      xl_offset = ipmP->mi;
      for (i = 0; i < ipmP->nxlb; i++) {
        if (xli[i] < xstart) {
          xl_offset++;
        } else break;
      }
      PetscCall(ISRestoreIndices(bigxl, &xli));

      PetscCall(ISGetIndices(ipmP->isxl, &xli));
      PetscCall(ISGetLocalSize(ipmP->isxl, &nloc));
      for (i = 0; i < nloc; i++) {
        xind[i] = xli[i];
        cind[i] = xl_offset + i;
      }

      PetscCall(ISCreateGeneral(comm, nloc, xind, PETSC_COPY_VALUES, &isx));
      PetscCall(ISCreateGeneral(comm, nloc, cind, PETSC_COPY_VALUES, &isc));
      PetscCall(VecScatterCreate(tao->XL, isx, ipmP->ci, isc, &ipmP->xl_scat));
      PetscCall(ISDestroy(&isx));
      PetscCall(ISDestroy(&isc));
      PetscCall(ISDestroy(&bigxl));
    }

    if (ipmP->nxub) {
      PetscCall(ISAllGather(ipmP->isxu, &bigxu));
      PetscCall(ISGetIndices(bigxu, &xui));
      /* find offsets for this processor */
      xu_offset = ipmP->mi + ipmP->nxlb;
      for (i = 0; i < ipmP->nxub; i++) {
        if (xui[i] < xstart) {
          xu_offset++;
        } else break;
      }
      PetscCall(ISRestoreIndices(bigxu, &xui));

      PetscCall(ISGetIndices(ipmP->isxu, &xui));
      PetscCall(ISGetLocalSize(ipmP->isxu, &nloc));
      for (i = 0; i < nloc; i++) {
        xind[i] = xui[i];
        cind[i] = xu_offset + i;
      }

      PetscCall(ISCreateGeneral(comm, nloc, xind, PETSC_COPY_VALUES, &isx));
      PetscCall(ISCreateGeneral(comm, nloc, cind, PETSC_COPY_VALUES, &isc));
      PetscCall(VecScatterCreate(tao->XU, isx, ipmP->ci, isc, &ipmP->xu_scat));
      PetscCall(ISDestroy(&isx));
      PetscCall(ISDestroy(&isc));
      PetscCall(ISDestroy(&bigxu));
    }
  }
  PetscCall(VecCreate(comm, &ipmP->bigrhs));
  PetscCall(VecGetType(tao->solution, &vtype));
  PetscCall(VecSetType(ipmP->bigrhs, vtype));
  PetscCall(VecSetSizes(ipmP->bigrhs, PETSC_DECIDE, bigsize));
  PetscCall(VecSetFromOptions(ipmP->bigrhs));
  PetscCall(VecDuplicate(ipmP->bigrhs, &ipmP->bigstep));

  /* create scatters for step->x and x->rhs */
  for (i = xstart; i < xend; i++) {
    stepind[i - xstart] = i;
    xind[i - xstart]    = i;
  }
  PetscCall(ISCreateGeneral(comm, xend - xstart, stepind, PETSC_COPY_VALUES, &sis));
  PetscCall(ISCreateGeneral(comm, xend - xstart, xind, PETSC_COPY_VALUES, &is1));
  PetscCall(VecScatterCreate(ipmP->bigstep, sis, tao->solution, is1, &ipmP->step1));
  PetscCall(VecScatterCreate(tao->solution, is1, ipmP->bigrhs, sis, &ipmP->rhs1));
  PetscCall(ISDestroy(&sis));
  PetscCall(ISDestroy(&is1));

  if (ipmP->nb > 0) {
    for (i = sstart; i < send; i++) {
      stepind[i - sstart] = i + ipmP->n;
      cind[i - sstart]    = i;
    }
    PetscCall(ISCreateGeneral(comm, send - sstart, stepind, PETSC_COPY_VALUES, &sis));
    PetscCall(ISCreateGeneral(comm, send - sstart, cind, PETSC_COPY_VALUES, &is1));
    PetscCall(VecScatterCreate(ipmP->bigstep, sis, ipmP->s, is1, &ipmP->step2));
    PetscCall(ISDestroy(&sis));

    for (i = sstart; i < send; i++) {
      stepind[i - sstart] = i + ipmP->n + ipmP->me;
      cind[i - sstart]    = i;
    }
    PetscCall(ISCreateGeneral(comm, send - sstart, stepind, PETSC_COPY_VALUES, &sis));
    PetscCall(VecScatterCreate(ipmP->s, is1, ipmP->bigrhs, sis, &ipmP->rhs3));
    PetscCall(ISDestroy(&sis));
    PetscCall(ISDestroy(&is1));
  }

  if (ipmP->me > 0) {
    PetscCall(VecGetOwnershipRange(tao->constraints_equality, &ucestart, &uceend));
    for (i = ucestart; i < uceend; i++) {
      stepind[i - ucestart] = i + ipmP->n + ipmP->nb;
      uceind[i - ucestart]  = i;
    }

    PetscCall(ISCreateGeneral(comm, uceend - ucestart, stepind, PETSC_COPY_VALUES, &sis));
    PetscCall(ISCreateGeneral(comm, uceend - ucestart, uceind, PETSC_COPY_VALUES, &is1));
    PetscCall(VecScatterCreate(ipmP->bigstep, sis, tao->constraints_equality, is1, &ipmP->step3));
    PetscCall(ISDestroy(&sis));

    for (i = ucestart; i < uceend; i++) stepind[i - ucestart] = i + ipmP->n;

    PetscCall(ISCreateGeneral(comm, uceend - ucestart, stepind, PETSC_COPY_VALUES, &sis));
    PetscCall(VecScatterCreate(tao->constraints_equality, is1, ipmP->bigrhs, sis, &ipmP->rhs2));
    PetscCall(ISDestroy(&sis));
    PetscCall(ISDestroy(&is1));
  }

  if (ipmP->nb > 0) {
    for (i = sstart; i < send; i++) {
      stepind[i - sstart] = i + ipmP->n + ipmP->nb + ipmP->me;
      cind[i - sstart]    = i;
    }
    PetscCall(ISCreateGeneral(comm, send - sstart, cind, PETSC_COPY_VALUES, &is1));
    PetscCall(ISCreateGeneral(comm, send - sstart, stepind, PETSC_COPY_VALUES, &sis));
    PetscCall(VecScatterCreate(ipmP->bigstep, sis, ipmP->s, is1, &ipmP->step4));
    PetscCall(VecScatterCreate(ipmP->s, is1, ipmP->bigrhs, sis, &ipmP->rhs4));
    PetscCall(ISDestroy(&sis));
    PetscCall(ISDestroy(&is1));
  }

  PetscCall(PetscFree(stepind));
  PetscCall(PetscFree(cind));
  PetscCall(PetscFree(ucind));
  PetscCall(PetscFree(uceind));
  PetscCall(PetscFree(xind));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoDestroy_IPM(Tao tao)
{
  TAO_IPM *ipmP = (TAO_IPM *)tao->data;

  PetscFunctionBegin;
  PetscCall(VecDestroy(&ipmP->rd));
  PetscCall(VecDestroy(&ipmP->rpe));
  PetscCall(VecDestroy(&ipmP->rpi));
  PetscCall(VecDestroy(&ipmP->work));
  PetscCall(VecDestroy(&ipmP->lambdae));
  PetscCall(VecDestroy(&ipmP->lambdai));
  PetscCall(VecDestroy(&ipmP->s));
  PetscCall(VecDestroy(&ipmP->ds));
  PetscCall(VecDestroy(&ipmP->ci));

  PetscCall(VecDestroy(&ipmP->rhs_x));
  PetscCall(VecDestroy(&ipmP->rhs_lambdae));
  PetscCall(VecDestroy(&ipmP->rhs_lambdai));
  PetscCall(VecDestroy(&ipmP->rhs_s));

  PetscCall(VecDestroy(&ipmP->save_x));
  PetscCall(VecDestroy(&ipmP->save_lambdae));
  PetscCall(VecDestroy(&ipmP->save_lambdai));
  PetscCall(VecDestroy(&ipmP->save_s));

  PetscCall(VecScatterDestroy(&ipmP->step1));
  PetscCall(VecScatterDestroy(&ipmP->step2));
  PetscCall(VecScatterDestroy(&ipmP->step3));
  PetscCall(VecScatterDestroy(&ipmP->step4));

  PetscCall(VecScatterDestroy(&ipmP->rhs1));
  PetscCall(VecScatterDestroy(&ipmP->rhs2));
  PetscCall(VecScatterDestroy(&ipmP->rhs3));
  PetscCall(VecScatterDestroy(&ipmP->rhs4));

  PetscCall(VecScatterDestroy(&ipmP->ci_scat));
  PetscCall(VecScatterDestroy(&ipmP->xl_scat));
  PetscCall(VecScatterDestroy(&ipmP->xu_scat));

  PetscCall(VecDestroy(&ipmP->dlambdai));
  PetscCall(VecDestroy(&ipmP->dlambdae));
  PetscCall(VecDestroy(&ipmP->Zero_nb));
  PetscCall(VecDestroy(&ipmP->One_nb));
  PetscCall(VecDestroy(&ipmP->Inf_nb));
  PetscCall(VecDestroy(&ipmP->complementarity));

  PetscCall(VecDestroy(&ipmP->bigrhs));
  PetscCall(VecDestroy(&ipmP->bigstep));
  PetscCall(MatDestroy(&ipmP->Ai));
  PetscCall(MatDestroy(&ipmP->K));
  PetscCall(ISDestroy(&ipmP->isxu));
  PetscCall(ISDestroy(&ipmP->isxl));
  PetscCall(KSPDestroy(&tao->ksp));
  PetscCall(PetscFree(tao->data));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoSetFromOptions_IPM(Tao tao, PetscOptionItems *PetscOptionsObject)
{
  TAO_IPM *ipmP = (TAO_IPM *)tao->data;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "IPM method for constrained optimization");
  PetscCall(PetscOptionsBool("-tao_ipm_monitorkkt", "monitor kkt status", NULL, ipmP->monitorkkt, &ipmP->monitorkkt, NULL));
  PetscCall(PetscOptionsReal("-tao_ipm_pushs", "parameter to push initial slack variables away from bounds", NULL, ipmP->pushs, &ipmP->pushs, NULL));
  PetscCall(PetscOptionsReal("-tao_ipm_pushnu", "parameter to push initial (inequality) dual variables away from bounds", NULL, ipmP->pushnu, &ipmP->pushnu, NULL));
  PetscOptionsHeadEnd();
  PetscCall(KSPSetFromOptions(tao->ksp));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoView_IPM(Tao tao, PetscViewer viewer)
{
  return PETSC_SUCCESS;
}

/* IPMObjectiveAndGradient()
   f = d'x + 0.5 * x' * H * x
   rd = H*x + d + Ae'*lame - Ai'*lami
   rpe = Ae*x - be
   rpi = Ai*x - yi - bi
   mu = yi' * lami/mi;
   com = yi.*lami

   phi = ||rd|| + ||rpe|| + ||rpi|| + ||com||
*/
/*
static PetscErrorCode IPMObjective(TaoLineSearch ls, Vec X, PetscReal *f, void *tptr)
{
  Tao tao = (Tao)tptr;
  TAO_IPM *ipmP = (TAO_IPM*)tao->data;
  PetscFunctionBegin;
  PetscCall(IPMComputeKKT(tao));
  *f = ipmP->phi;
  PetscFunctionReturn(PETSC_SUCCESS);
}
*/

/*
   f = d'x + 0.5 * x' * H * x
   rd = H*x + d + Ae'*lame - Ai'*lami
       Ai =   jac_ineq
               I (w/lb)
              -I (w/ub)

   rpe = ce
   rpi = ci - s;
   com = s.*lami
   mu = yi' * lami/mi;

   phi = ||rd|| + ||rpe|| + ||rpi|| + ||com||
*/
static PetscErrorCode IPMComputeKKT(Tao tao)
{
  TAO_IPM    *ipmP = (TAO_IPM *)tao->data;
  PetscScalar norm;

  PetscFunctionBegin;
  PetscCall(VecCopy(tao->gradient, ipmP->rd));

  if (ipmP->me > 0) {
    /* rd = gradient + Ae'*lambdae */
    PetscCall(MatMultTranspose(tao->jacobian_equality, ipmP->lambdae, ipmP->work));
    PetscCall(VecAXPY(ipmP->rd, 1.0, ipmP->work));

    /* rpe = ce(x) */
    PetscCall(VecCopy(tao->constraints_equality, ipmP->rpe));
  }
  if (ipmP->nb > 0) {
    /* rd = rd - Ai'*lambdai */
    PetscCall(MatMultTranspose(ipmP->Ai, ipmP->lambdai, ipmP->work));
    PetscCall(VecAXPY(ipmP->rd, -1.0, ipmP->work));

    /* rpi = cin - s */
    PetscCall(VecCopy(ipmP->ci, ipmP->rpi));
    PetscCall(VecAXPY(ipmP->rpi, -1.0, ipmP->s));

    /* com = s .* lami */
    PetscCall(VecPointwiseMult(ipmP->complementarity, ipmP->s, ipmP->lambdai));
  }
  /* phi = ||rd; rpe; rpi; com|| */
  PetscCall(VecDot(ipmP->rd, ipmP->rd, &norm));
  ipmP->phi = norm;
  if (ipmP->me > 0) {
    PetscCall(VecDot(ipmP->rpe, ipmP->rpe, &norm));
    ipmP->phi += norm;
  }
  if (ipmP->nb > 0) {
    PetscCall(VecDot(ipmP->rpi, ipmP->rpi, &norm));
    ipmP->phi += norm;
    PetscCall(VecDot(ipmP->complementarity, ipmP->complementarity, &norm));
    ipmP->phi += norm;
    /* mu = s'*lami/nb */
    PetscCall(VecDot(ipmP->s, ipmP->lambdai, &ipmP->mu));
    ipmP->mu /= ipmP->nb;
  } else {
    ipmP->mu = 1.0;
  }

  ipmP->phi = PetscSqrtScalar(ipmP->phi);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* evaluate user info at current point */
PetscErrorCode IPMEvaluate(Tao tao)
{
  TAO_IPM *ipmP = (TAO_IPM *)tao->data;

  PetscFunctionBegin;
  PetscCall(TaoComputeObjectiveAndGradient(tao, tao->solution, &ipmP->kkt_f, tao->gradient));
  PetscCall(TaoComputeHessian(tao, tao->solution, tao->hessian, tao->hessian_pre));
  if (ipmP->me > 0) {
    PetscCall(TaoComputeEqualityConstraints(tao, tao->solution, tao->constraints_equality));
    PetscCall(TaoComputeJacobianEquality(tao, tao->solution, tao->jacobian_equality, tao->jacobian_equality_pre));
  }
  if (ipmP->mi > 0) {
    PetscCall(TaoComputeInequalityConstraints(tao, tao->solution, tao->constraints_inequality));
    PetscCall(TaoComputeJacobianInequality(tao, tao->solution, tao->jacobian_inequality, tao->jacobian_inequality_pre));
  }
  if (ipmP->nb > 0) {
    /* Ai' =   jac_ineq | I (w/lb) | -I (w/ub)  */
    PetscCall(IPMUpdateAi(tao));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Push initial point away from bounds */
PetscErrorCode IPMPushInitialPoint(Tao tao)
{
  TAO_IPM *ipmP = (TAO_IPM *)tao->data;

  PetscFunctionBegin;
  PetscCall(TaoComputeVariableBounds(tao));
  PetscCall(VecMedian(tao->XL, tao->solution, tao->XU, tao->solution));
  if (ipmP->nb > 0) {
    PetscCall(VecSet(ipmP->s, ipmP->pushs));
    PetscCall(VecSet(ipmP->lambdai, ipmP->pushnu));
    if (ipmP->mi > 0) PetscCall(VecSet(tao->DI, ipmP->pushnu));
  }
  if (ipmP->me > 0) {
    PetscCall(VecSet(tao->DE, 1.0));
    PetscCall(VecSet(ipmP->lambdae, 1.0));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode IPMUpdateAi(Tao tao)
{
  /* Ai =     Ji
              I (w/lb)
             -I (w/ub) */

  /* Ci =    user->ci
             Xi - lb (w/lb)
             -Xi + ub (w/ub)  */

  TAO_IPM           *ipmP = (TAO_IPM *)tao->data;
  MPI_Comm           comm;
  PetscInt           i;
  PetscScalar        newval;
  PetscInt           newrow, newcol, ncols;
  const PetscScalar *vals;
  const PetscInt    *cols;
  PetscInt           astart, aend, jstart, jend;
  PetscInt          *nonzeros;
  PetscInt           r2, r3, r4;
  PetscMPIInt        size;
  Vec                solu;
  PetscInt           nloc;

  PetscFunctionBegin;
  r2 = ipmP->mi;
  r3 = r2 + ipmP->nxlb;
  r4 = r3 + ipmP->nxub;

  if (!ipmP->nb) PetscFunctionReturn(PETSC_SUCCESS);

  /* Create Ai matrix if it doesn't exist yet */
  if (!ipmP->Ai) {
    comm = ((PetscObject)(tao->solution))->comm;
    PetscCallMPI(MPI_Comm_size(comm, &size));
    if (size == 1) {
      PetscCall(PetscMalloc1(ipmP->nb, &nonzeros));
      for (i = 0; i < ipmP->mi; i++) {
        PetscCall(MatGetRow(tao->jacobian_inequality, i, &ncols, NULL, NULL));
        nonzeros[i] = ncols;
        PetscCall(MatRestoreRow(tao->jacobian_inequality, i, &ncols, NULL, NULL));
      }
      for (i = r2; i < r4; i++) nonzeros[i] = 1;
    }
    PetscCall(MatCreate(comm, &ipmP->Ai));
    PetscCall(MatSetType(ipmP->Ai, MATAIJ));

    PetscCall(TaoGetSolution(tao, &solu));
    PetscCall(VecGetLocalSize(solu, &nloc));
    PetscCall(MatSetSizes(ipmP->Ai, PETSC_DECIDE, nloc, ipmP->nb, PETSC_DECIDE));
    PetscCall(MatSetFromOptions(ipmP->Ai));
    PetscCall(MatMPIAIJSetPreallocation(ipmP->Ai, ipmP->nb, NULL, ipmP->nb, NULL));
    PetscCall(MatSeqAIJSetPreallocation(ipmP->Ai, PETSC_DEFAULT, nonzeros));
    if (size == 1) PetscCall(PetscFree(nonzeros));
  }

  /* Copy values from user jacobian to Ai */
  PetscCall(MatGetOwnershipRange(ipmP->Ai, &astart, &aend));

  /* Ai w/lb */
  if (ipmP->mi) {
    PetscCall(MatZeroEntries(ipmP->Ai));
    PetscCall(MatGetOwnershipRange(tao->jacobian_inequality, &jstart, &jend));
    for (i = jstart; i < jend; i++) {
      PetscCall(MatGetRow(tao->jacobian_inequality, i, &ncols, &cols, &vals));
      newrow = i;
      PetscCall(MatSetValues(ipmP->Ai, 1, &newrow, ncols, cols, vals, INSERT_VALUES));
      PetscCall(MatRestoreRow(tao->jacobian_inequality, i, &ncols, &cols, &vals));
    }
  }

  /* I w/ xlb */
  if (ipmP->nxlb) {
    for (i = 0; i < ipmP->nxlb; i++) {
      if (i >= astart && i < aend) {
        newrow = i + r2;
        newcol = i;
        newval = 1.0;
        PetscCall(MatSetValues(ipmP->Ai, 1, &newrow, 1, &newcol, &newval, INSERT_VALUES));
      }
    }
  }
  if (ipmP->nxub) {
    /* I w/ xub */
    for (i = 0; i < ipmP->nxub; i++) {
      if (i >= astart && i < aend) {
        newrow = i + r3;
        newcol = i;
        newval = -1.0;
        PetscCall(MatSetValues(ipmP->Ai, 1, &newrow, 1, &newcol, &newval, INSERT_VALUES));
      }
    }
  }

  PetscCall(MatAssemblyBegin(ipmP->Ai, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(ipmP->Ai, MAT_FINAL_ASSEMBLY));
  CHKMEMQ;

  PetscCall(VecSet(ipmP->ci, 0.0));

  /* user ci */
  if (ipmP->mi > 0) {
    PetscCall(VecScatterBegin(ipmP->ci_scat, tao->constraints_inequality, ipmP->ci, INSERT_VALUES, SCATTER_FORWARD));
    PetscCall(VecScatterEnd(ipmP->ci_scat, tao->constraints_inequality, ipmP->ci, INSERT_VALUES, SCATTER_FORWARD));
  }
  if (!ipmP->work) PetscCall(VecDuplicate(tao->solution, &ipmP->work));
  PetscCall(VecCopy(tao->solution, ipmP->work));
  if (tao->XL) {
    PetscCall(VecAXPY(ipmP->work, -1.0, tao->XL));

    /* lower bounds on variables */
    if (ipmP->nxlb > 0) {
      PetscCall(VecScatterBegin(ipmP->xl_scat, ipmP->work, ipmP->ci, INSERT_VALUES, SCATTER_FORWARD));
      PetscCall(VecScatterEnd(ipmP->xl_scat, ipmP->work, ipmP->ci, INSERT_VALUES, SCATTER_FORWARD));
    }
  }
  if (tao->XU) {
    /* upper bounds on variables */
    PetscCall(VecCopy(tao->solution, ipmP->work));
    PetscCall(VecScale(ipmP->work, -1.0));
    PetscCall(VecAXPY(ipmP->work, 1.0, tao->XU));
    if (ipmP->nxub > 0) {
      PetscCall(VecScatterBegin(ipmP->xu_scat, ipmP->work, ipmP->ci, INSERT_VALUES, SCATTER_FORWARD));
      PetscCall(VecScatterEnd(ipmP->xu_scat, ipmP->work, ipmP->ci, INSERT_VALUES, SCATTER_FORWARD));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* create K = [ Hlag , 0 , Ae', -Ai'];
              [Ae , 0,   0  , 0];
              [Ai ,-I,   0 ,  0];
              [ 0 , S ,  0,   Y ];  */
PetscErrorCode IPMUpdateK(Tao tao)
{
  TAO_IPM         *ipmP = (TAO_IPM *)tao->data;
  MPI_Comm         comm;
  PetscMPIInt      size;
  PetscInt         i, j, row;
  PetscInt         ncols, newcol, newcols[2], newrow;
  const PetscInt  *cols;
  const PetscReal *vals;
  const PetscReal *l, *y;
  PetscReal       *newvals;
  PetscReal        newval;
  PetscInt         subsize;
  const PetscInt  *indices;
  PetscInt        *nonzeros, *d_nonzeros, *o_nonzeros;
  PetscInt         bigsize;
  PetscInt         r1, r2, r3;
  PetscInt         c1, c2, c3;
  PetscInt         klocalsize;
  PetscInt         hstart, hend, kstart, kend;
  PetscInt         aistart, aiend, aestart, aeend;
  PetscInt         sstart, send;

  PetscFunctionBegin;
  comm = ((PetscObject)(tao->solution))->comm;
  PetscCallMPI(MPI_Comm_size(comm, &size));
  PetscCall(IPMUpdateAi(tao));

  /* allocate workspace */
  subsize = PetscMax(ipmP->n, ipmP->nb);
  subsize = PetscMax(ipmP->me, subsize);
  subsize = PetscMax(2, subsize);
  PetscCall(PetscMalloc1(subsize, (PetscInt **)&indices));
  PetscCall(PetscMalloc1(subsize, &newvals));

  r1 = c1 = ipmP->n;
  r2      = r1 + ipmP->me;
  c2      = c1 + ipmP->nb;
  r3 = c3 = r2 + ipmP->nb;

  bigsize = ipmP->n + 2 * ipmP->nb + ipmP->me;
  PetscCall(VecGetOwnershipRange(ipmP->bigrhs, &kstart, &kend));
  PetscCall(MatGetOwnershipRange(tao->hessian, &hstart, &hend));
  klocalsize = kend - kstart;
  if (!ipmP->K) {
    if (size == 1) {
      PetscCall(PetscMalloc1(kend - kstart, &nonzeros));
      for (i = 0; i < bigsize; i++) {
        if (i < r1) {
          PetscCall(MatGetRow(tao->hessian, i, &ncols, NULL, NULL));
          nonzeros[i] = ncols;
          PetscCall(MatRestoreRow(tao->hessian, i, &ncols, NULL, NULL));
          nonzeros[i] += ipmP->me + ipmP->nb;
        } else if (i < r2) {
          nonzeros[i - kstart] = ipmP->n;
        } else if (i < r3) {
          nonzeros[i - kstart] = ipmP->n + 1;
        } else if (i < bigsize) {
          nonzeros[i - kstart] = 2;
        }
      }
      PetscCall(MatCreate(comm, &ipmP->K));
      PetscCall(MatSetType(ipmP->K, MATSEQAIJ));
      PetscCall(MatSetSizes(ipmP->K, klocalsize, klocalsize, PETSC_DETERMINE, PETSC_DETERMINE));
      PetscCall(MatSeqAIJSetPreallocation(ipmP->K, 0, nonzeros));
      PetscCall(MatSetFromOptions(ipmP->K));
      PetscCall(PetscFree(nonzeros));
    } else {
      PetscCall(PetscMalloc1(kend - kstart, &d_nonzeros));
      PetscCall(PetscMalloc1(kend - kstart, &o_nonzeros));
      for (i = kstart; i < kend; i++) {
        if (i < r1) {
          /* TODO fix preallocation for mpi mats */
          d_nonzeros[i - kstart] = PetscMin(ipmP->n + ipmP->me + ipmP->nb, kend - kstart);
          o_nonzeros[i - kstart] = PetscMin(ipmP->n + ipmP->me + ipmP->nb, bigsize - (kend - kstart));
        } else if (i < r2) {
          d_nonzeros[i - kstart] = PetscMin(ipmP->n, kend - kstart);
          o_nonzeros[i - kstart] = PetscMin(ipmP->n, bigsize - (kend - kstart));
        } else if (i < r3) {
          d_nonzeros[i - kstart] = PetscMin(ipmP->n + 2, kend - kstart);
          o_nonzeros[i - kstart] = PetscMin(ipmP->n + 2, bigsize - (kend - kstart));
        } else {
          d_nonzeros[i - kstart] = PetscMin(2, kend - kstart);
          o_nonzeros[i - kstart] = PetscMin(2, bigsize - (kend - kstart));
        }
      }
      PetscCall(MatCreate(comm, &ipmP->K));
      PetscCall(MatSetType(ipmP->K, MATMPIAIJ));
      PetscCall(MatSetSizes(ipmP->K, klocalsize, klocalsize, PETSC_DETERMINE, PETSC_DETERMINE));
      PetscCall(MatMPIAIJSetPreallocation(ipmP->K, 0, d_nonzeros, 0, o_nonzeros));
      PetscCall(PetscFree(d_nonzeros));
      PetscCall(PetscFree(o_nonzeros));
      PetscCall(MatSetFromOptions(ipmP->K));
    }
  }

  PetscCall(MatZeroEntries(ipmP->K));
  /* Copy H */
  for (i = hstart; i < hend; i++) {
    PetscCall(MatGetRow(tao->hessian, i, &ncols, &cols, &vals));
    if (ncols > 0) PetscCall(MatSetValues(ipmP->K, 1, &i, ncols, cols, vals, INSERT_VALUES));
    PetscCall(MatRestoreRow(tao->hessian, i, &ncols, &cols, &vals));
  }

  /* Copy Ae and Ae' */
  if (ipmP->me > 0) {
    PetscCall(MatGetOwnershipRange(tao->jacobian_equality, &aestart, &aeend));
    for (i = aestart; i < aeend; i++) {
      PetscCall(MatGetRow(tao->jacobian_equality, i, &ncols, &cols, &vals));
      if (ncols > 0) {
        /*Ae*/
        row = i + r1;
        PetscCall(MatSetValues(ipmP->K, 1, &row, ncols, cols, vals, INSERT_VALUES));
        /*Ae'*/
        for (j = 0; j < ncols; j++) {
          newcol = i + c2;
          newrow = cols[j];
          newval = vals[j];
          PetscCall(MatSetValues(ipmP->K, 1, &newrow, 1, &newcol, &newval, INSERT_VALUES));
        }
      }
      PetscCall(MatRestoreRow(tao->jacobian_equality, i, &ncols, &cols, &vals));
    }
  }

  if (ipmP->nb > 0) {
    PetscCall(MatGetOwnershipRange(ipmP->Ai, &aistart, &aiend));
    /* Copy Ai,and Ai' */
    for (i = aistart; i < aiend; i++) {
      row = i + r2;
      PetscCall(MatGetRow(ipmP->Ai, i, &ncols, &cols, &vals));
      if (ncols > 0) {
        /*Ai*/
        PetscCall(MatSetValues(ipmP->K, 1, &row, ncols, cols, vals, INSERT_VALUES));
        /*-Ai'*/
        for (j = 0; j < ncols; j++) {
          newcol = i + c3;
          newrow = cols[j];
          newval = -vals[j];
          PetscCall(MatSetValues(ipmP->K, 1, &newrow, 1, &newcol, &newval, INSERT_VALUES));
        }
      }
      PetscCall(MatRestoreRow(ipmP->Ai, i, &ncols, &cols, &vals));
    }

    /* -I */
    for (i = kstart; i < kend; i++) {
      if (i >= r2 && i < r3) {
        newrow = i;
        newcol = i - r2 + c1;
        newval = -1.0;
        PetscCall(MatSetValues(ipmP->K, 1, &newrow, 1, &newcol, &newval, INSERT_VALUES));
      }
    }

    /* Copy L,Y */
    PetscCall(VecGetOwnershipRange(ipmP->s, &sstart, &send));
    PetscCall(VecGetArrayRead(ipmP->lambdai, &l));
    PetscCall(VecGetArrayRead(ipmP->s, &y));

    for (i = sstart; i < send; i++) {
      newcols[0] = c1 + i;
      newcols[1] = c3 + i;
      newvals[0] = l[i - sstart];
      newvals[1] = y[i - sstart];
      newrow     = r3 + i;
      PetscCall(MatSetValues(ipmP->K, 1, &newrow, 2, newcols, newvals, INSERT_VALUES));
    }

    PetscCall(VecRestoreArrayRead(ipmP->lambdai, &l));
    PetscCall(VecRestoreArrayRead(ipmP->s, &y));
  }

  PetscCall(PetscFree(indices));
  PetscCall(PetscFree(newvals));
  PetscCall(MatAssemblyBegin(ipmP->K, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(ipmP->K, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode IPMGatherRHS(Tao tao, Vec RHS, Vec X1, Vec X2, Vec X3, Vec X4)
{
  TAO_IPM *ipmP = (TAO_IPM *)tao->data;

  PetscFunctionBegin;
  /* rhs = [x1      (n)
            x2     (me)
            x3     (nb)
            x4     (nb)] */
  if (X1) {
    PetscCall(VecScatterBegin(ipmP->rhs1, X1, RHS, INSERT_VALUES, SCATTER_FORWARD));
    PetscCall(VecScatterEnd(ipmP->rhs1, X1, RHS, INSERT_VALUES, SCATTER_FORWARD));
  }
  if (ipmP->me > 0 && X2) {
    PetscCall(VecScatterBegin(ipmP->rhs2, X2, RHS, INSERT_VALUES, SCATTER_FORWARD));
    PetscCall(VecScatterEnd(ipmP->rhs2, X2, RHS, INSERT_VALUES, SCATTER_FORWARD));
  }
  if (ipmP->nb > 0) {
    if (X3) {
      PetscCall(VecScatterBegin(ipmP->rhs3, X3, RHS, INSERT_VALUES, SCATTER_FORWARD));
      PetscCall(VecScatterEnd(ipmP->rhs3, X3, RHS, INSERT_VALUES, SCATTER_FORWARD));
    }
    if (X4) {
      PetscCall(VecScatterBegin(ipmP->rhs4, X4, RHS, INSERT_VALUES, SCATTER_FORWARD));
      PetscCall(VecScatterEnd(ipmP->rhs4, X4, RHS, INSERT_VALUES, SCATTER_FORWARD));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode IPMScatterStep(Tao tao, Vec STEP, Vec X1, Vec X2, Vec X3, Vec X4)
{
  TAO_IPM *ipmP = (TAO_IPM *)tao->data;

  PetscFunctionBegin;
  CHKMEMQ;
  /*        [x1    (n)
             x2    (nb) may be 0
             x3    (me) may be 0
             x4    (nb) may be 0 */
  if (X1) {
    PetscCall(VecScatterBegin(ipmP->step1, STEP, X1, INSERT_VALUES, SCATTER_FORWARD));
    PetscCall(VecScatterEnd(ipmP->step1, STEP, X1, INSERT_VALUES, SCATTER_FORWARD));
  }
  if (X2 && ipmP->nb > 0) {
    PetscCall(VecScatterBegin(ipmP->step2, STEP, X2, INSERT_VALUES, SCATTER_FORWARD));
    PetscCall(VecScatterEnd(ipmP->step2, STEP, X2, INSERT_VALUES, SCATTER_FORWARD));
  }
  if (X3 && ipmP->me > 0) {
    PetscCall(VecScatterBegin(ipmP->step3, STEP, X3, INSERT_VALUES, SCATTER_FORWARD));
    PetscCall(VecScatterEnd(ipmP->step3, STEP, X3, INSERT_VALUES, SCATTER_FORWARD));
  }
  if (X4 && ipmP->nb > 0) {
    PetscCall(VecScatterBegin(ipmP->step4, STEP, X4, INSERT_VALUES, SCATTER_FORWARD));
    PetscCall(VecScatterEnd(ipmP->step4, STEP, X4, INSERT_VALUES, SCATTER_FORWARD));
  }
  CHKMEMQ;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
  TAOIPM - Interior point algorithm for generally constrained optimization.

  Options Database Keys:
+   -tao_ipm_pushnu - parameter to push initial dual variables away from bounds
-   -tao_ipm_pushs - parameter to push initial slack variables away from bounds

  Notes:
    This algorithm is more of a place-holder for future constrained optimization algorithms and should not yet be used for large problems or production code.
  Level: beginner

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

PETSC_EXTERN PetscErrorCode TaoCreate_IPM(Tao tao)
{
  TAO_IPM *ipmP;

  PetscFunctionBegin;
  tao->ops->setup          = TaoSetup_IPM;
  tao->ops->solve          = TaoSolve_IPM;
  tao->ops->view           = TaoView_IPM;
  tao->ops->setfromoptions = TaoSetFromOptions_IPM;
  tao->ops->destroy        = TaoDestroy_IPM;
  /* tao->ops->computedual = TaoComputeDual_IPM; */

  PetscCall(PetscNew(&ipmP));
  tao->data = (void *)ipmP;

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

  ipmP->dec        = 10000; /* line search criteria */
  ipmP->taumin     = 0.995;
  ipmP->monitorkkt = PETSC_FALSE;
  ipmP->pushs      = 100;
  ipmP->pushnu     = 100;
  PetscCall(KSPCreate(((PetscObject)tao)->comm, &tao->ksp));
  PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1));
  PetscCall(KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix));
  PetscFunctionReturn(PETSC_SUCCESS);
}