impls/ipm/ipm.c

#include "taolinesearch.h"
#include "ipm.h" /*I "ipm.h" I*/
/*
#define DEBUG_IPM
#define DEBUG_K
#define DEBUG_SCATTER
#define DEBUG_KKT
*/
/*
   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)
   lamdai in R^nb (ipmP->lamdai)
   lamdae in R^me (ipmP->lamdae)
   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(TaoSolver tao);
static PetscErrorCode IPMPushInitialPoint(TaoSolver tao);
static PetscErrorCode IPMEvaluate(TaoSolver tao);
static PetscErrorCode IPMUpdateK(TaoSolver tao);
static PetscErrorCode IPMUpdateAi(TaoSolver tao);
static PetscErrorCode IPMGatherRHS(TaoSolver tao,Vec,Vec,Vec,Vec,Vec);
static PetscErrorCode IPMScatterStep(TaoSolver tao,Vec,Vec,Vec,Vec,Vec);
static PetscErrorCode IPMInitializeBounds(TaoSolver tao);

#undef __FUNCT__
#define __FUNCT__ "TaoSolve_IPM"
static PetscErrorCode TaoSolve_IPM(TaoSolver tao)
{
  PetscErrorCode ierr;
  TAO_IPM* ipmP = (TAO_IPM*)tao->data;


  TaoSolverTerminationReason reason = TAO_CONTINUE_ITERATING;
  PetscInt iter = 0,its,i;
  PetscScalar stepsize=1.0;
  PetscScalar step_s,step_l,alpha,tau,sigma,phi_target;
  PetscFunctionBegin;

  /* Push initial point away from bounds */
#if defined(DEBUG_IPM)
  ierr = VecNorm(tao->solution,NORM_2,&tau); CHKERRQ(ierr);
  VecView(tao->solution,0);
#endif
  ierr = IPMInitializeBounds(tao); CHKERRQ(ierr);
  ierr = IPMPushInitialPoint(tao); CHKERRQ(ierr);
#if defined(DEBUG_IPM)
  ierr = VecNorm(tao->solution,NORM_2,&tau); CHKERRQ(ierr);
  VecView(tao->solution,0);
  /*  PetscPrintf(PETSC_COMM_WORLD,"||x0|| = %g\n",tau); */
#endif
  ierr = VecCopy(tao->solution,ipmP->rhs_x); CHKERRQ(ierr);
  ierr = IPMEvaluate(tao); CHKERRQ(ierr);
  ierr = IPMComputeKKT(tao); CHKERRQ(ierr);
  ierr = TaoMonitor(tao,iter++,ipmP->kkt_f,ipmP->phi,0.0,1.0,&reason);


  while (reason == TAO_CONTINUE_ITERATING) {
    ierr = IPMUpdateK(tao); CHKERRQ(ierr);
    /*
       rhs.x    = -rd
       rhs.lame = -rpe
       rhs.lami = -rpi
       rhs.com  = -com
    */

    ierr = VecCopy(ipmP->rd,ipmP->rhs_x); CHKERRQ(ierr);
    if (ipmP->me > 0) {
      ierr = VecCopy(ipmP->rpe,ipmP->rhs_lamdae); CHKERRQ(ierr);
    }
    if (ipmP->nb > 0) {
	ierr = VecCopy(ipmP->rpi,ipmP->rhs_lamdai); CHKERRQ(ierr);
	ierr = VecCopy(ipmP->complementarity,ipmP->rhs_s); CHKERRQ(ierr);
    }
    ierr = IPMGatherRHS(tao,ipmP->bigrhs,ipmP->rhs_x,ipmP->rhs_lamdae,
			ipmP->rhs_lamdai,ipmP->rhs_s); CHKERRQ(ierr);
    ierr = VecScale(ipmP->bigrhs,-1.0); CHKERRQ(ierr);

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

    ierr = IPMScatterStep(tao,ipmP->bigstep,tao->stepdirection,ipmP->ds,
			  ipmP->dlamdae,ipmP->dlamdai); CHKERRQ(ierr);
    ierr = KSPGetIterationNumber(tao->ksp,&its); CHKERRQ(ierr);
    tao->ksp_its += its;
#if defined DEBUG_KKT
    PetscPrintf(PETSC_COMM_WORLD,"first solve.\n");
    PetscPrintf(PETSC_COMM_WORLD,"rhs_lamdai\n");
    /* VecView(ipmP->rhs_lamdai,0);
    ierr = VecView(ipmP->bigrhs,0);
    ierr = VecView(ipmP->bigstep,0); */
    PetscScalar norm1,norm2;
    ierr = VecNorm(ipmP->bigrhs,NORM_2,&norm1);
    ierr = VecNorm(ipmP->bigstep,NORM_2,&norm2);
    PetscPrintf(PETSC_COMM_WORLD,"||rhs|| = %g\t ||step|| = %g\n",norm1,norm2);
#endif
     /* Find distance along step direction to closest bound */
    if (ipmP->nb > 0) {
      ierr = VecStepBoundInfo(ipmP->s,ipmP->Zero_nb,ipmP->Inf_nb,ipmP->ds,&step_s,PETSC_NULL,PETSC_NULL); CHKERRQ(ierr);
      ierr = VecStepBoundInfo(ipmP->lamdai,ipmP->Zero_nb,ipmP->Inf_nb,ipmP->dlamdai,&step_l,PETSC_NULL,PETSC_NULL); CHKERRQ(ierr);
      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 */
    ierr = VecCopy(tao->solution,ipmP->save_x); CHKERRQ(ierr);
    if (ipmP->me > 0) {
      ierr = VecCopy(ipmP->lamdae,ipmP->save_lamdae); CHKERRQ(ierr);
    }
    if (ipmP->nb > 0) {
      ierr = VecCopy(ipmP->lamdai,ipmP->save_lamdai); CHKERRQ(ierr);
      ierr = VecCopy(ipmP->s,ipmP->save_s); CHKERRQ(ierr);
    }

    ierr = VecAXPY(tao->solution,alpha,tao->stepdirection); CHKERRQ(ierr);
    if (ipmP->me > 0) {
      ierr = VecAXPY(ipmP->lamdae,alpha,ipmP->dlamdae); CHKERRQ(ierr);
    }
    if (ipmP->nb > 0) {
      ierr = VecAXPY(ipmP->lamdai,alpha,ipmP->dlamdai); CHKERRQ(ierr);
      ierr = VecAXPY(ipmP->s,alpha,ipmP->ds); CHKERRQ(ierr);
    }


    /* 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;
    }
    ierr = IPMComputeKKT(tao); CHKERRQ(ierr);
    sigma *= ipmP->mu;
    sigma*=sigma*sigma;

    /* revert kkt info */
    ierr = VecCopy(ipmP->save_x,tao->solution); CHKERRQ(ierr);
    if (ipmP->me > 0) {
      ierr = VecCopy(ipmP->save_lamdae,ipmP->lamdae); CHKERRQ(ierr);
    }
    if (ipmP->nb > 0) {
      ierr = VecCopy(ipmP->save_lamdai,ipmP->lamdai); CHKERRQ(ierr);
      ierr = VecCopy(ipmP->save_s,ipmP->s); CHKERRQ(ierr);
    }
    ierr = IPMComputeKKT(tao); CHKERRQ(ierr);

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

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

    ierr = IPMScatterStep(tao,ipmP->bigstep,tao->stepdirection,ipmP->ds,
			  ipmP->dlamdae,ipmP->dlamdai); CHKERRQ(ierr);
    ierr = KSPGetIterationNumber(tao->ksp,&its); CHKERRQ(ierr);
#if defined DEBUG_KKT2
    PetscPrintf(PETSC_COMM_WORLD,"rhs_lamdai\n");
    VecView(ipmP->rhs_lamdai,0);
    ierr = VecView(ipmP->bigrhs,0);
    ierr = VecView(ipmP->bigstep,0);
#endif
    tao->ksp_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) {
	ierr = VecScale(ipmP->s,tau); CHKERRQ(ierr);
	ierr = VecScale(ipmP->lamdai,tau); CHKERRQ(ierr);
      }
      ierr = VecStepBoundInfo(ipmP->s,ipmP->Zero_nb,ipmP->Inf_nb,ipmP->ds,&step_s,PETSC_NULL,PETSC_NULL); CHKERRQ(ierr);
      ierr = VecStepBoundInfo(ipmP->lamdai,ipmP->Zero_nb,ipmP->Inf_nb,ipmP->dlamdai,&step_l,PETSC_NULL,PETSC_NULL); CHKERRQ(ierr);
      if (tau != 1.0) {
	ierr = VecCopy(ipmP->save_s,ipmP->s); CHKERRQ(ierr);
	ierr = VecCopy(ipmP->save_lamdai,ipmP->lamdai); CHKERRQ(ierr);
      }
      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++) {
#if defined DEBUG_KKT2
    PetscPrintf(PETSC_COMM_WORLD,"alpha2=%g\n",alpha);
      PetscPrintf(PETSC_COMM_WORLD,"old point:\n");
      VecView(tao->solution,0);
      VecView(ipmP->lamdae,0);
      VecView(ipmP->s,0);
      VecView(ipmP->lamdai,0);
#endif
      ierr = VecAXPY(tao->solution,alpha,tao->stepdirection); CHKERRQ(ierr);
      if (ipmP->nb > 0) {
	ierr = VecAXPY(ipmP->s,alpha,ipmP->ds); CHKERRQ(ierr);
	ierr = VecAXPY(ipmP->lamdai,alpha,ipmP->dlamdai); CHKERRQ(ierr);
      }
      if (ipmP->me > 0) {
	ierr = VecAXPY(ipmP->lamdae,alpha,ipmP->dlamdae); CHKERRQ(ierr);
      }
#if defined DEBUG_KKT
      PetscPrintf(PETSC_COMM_WORLD,"step direction:\n");
      VecView(tao->stepdirection,0);
      /* VecView(ipmP->dlamdae,0);
      VecView(ipmP->ds,0);
      VecView(ipmP->dlamdai,0);

      PetscPrintf(PETSC_COMM_WORLD,"New iterate:\n");
      VecView(tao->solution,0);
      VecView(ipmP->lamdae,0);
      VecView(ipmP->s,0);
      VecView(ipmP->lamdai,0); */
#endif
      /* update dual variables */
      if (ipmP->me > 0) {
	ierr = VecCopy(ipmP->lamdae,tao->DE); CHKERRQ(ierr);
      }
      /* TODO: fix
      if (ipmP->nb > 0) {
	ierr = VecScatterBegin
	PetscInt lstart,lend;

	ierr = VecGetOwnershipRange(ipmP->lamdai,&lstart,&lend);
	ierr = VecGetArray(ipmP->lamdai,&li); CHKERRQ(ierr);
	ierr = VecGetArray(tao->DI,&di); CHKERRQ(ierr);
	for (j=lstart;j<lend;j++) {
	  if (j < ipmP->nilb) {
	    di[j] = li[j];
	  }
	}
	ierr = VecRestoreArray(ipmP->lamdai,&li); CHKERRQ(ierr);
	ierr = VecRestoreArray(tao->DI,&di); CHKERRQ(ierr);
      }
      */


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

    ierr = TaoMonitor(tao,iter,ipmP->kkt_f,ipmP->phi,0.0,stepsize,&reason);
    iter++;
    CHKERRQ(ierr);

  }

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TaoSetup_IPM"
static PetscErrorCode TaoSetup_IPM(TaoSolver tao)
{
  TAO_IPM *ipmP = (TAO_IPM*)tao->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ipmP->nb = ipmP->mi = ipmP->me = 0;
  ipmP->K=0;
  ierr = VecGetSize(tao->solution,&ipmP->n); CHKERRQ(ierr);
  if (!tao->gradient) {
    ierr = VecDuplicate(tao->solution, &tao->gradient); CHKERRQ(ierr);
    ierr = VecDuplicate(tao->solution, &tao->stepdirection); CHKERRQ(ierr);
    ierr = VecDuplicate(tao->solution, &ipmP->rd); CHKERRQ(ierr);
    ierr = VecDuplicate(tao->solution, &ipmP->rhs_x); CHKERRQ(ierr);
    ierr = VecDuplicate(tao->solution, &ipmP->work); CHKERRQ(ierr);
    ierr = VecDuplicate(tao->solution, &ipmP->save_x); CHKERRQ(ierr);
  }

  if (tao->constraints_equality) {
    ierr = VecGetSize(tao->constraints_equality,&ipmP->me); CHKERRQ(ierr);
    ierr = VecDuplicate(tao->constraints_equality,&ipmP->lamdae); CHKERRQ(ierr);
    ierr = VecDuplicate(tao->constraints_equality,&ipmP->dlamdae); CHKERRQ(ierr);
    ierr = VecDuplicate(tao->constraints_equality,&ipmP->rhs_lamdae); CHKERRQ(ierr);
    ierr = VecDuplicate(tao->constraints_equality,&ipmP->save_lamdae); CHKERRQ(ierr);
    ierr = VecDuplicate(tao->constraints_equality,&ipmP->rpe); CHKERRQ(ierr);
    ierr = VecDuplicate(tao->constraints_equality,&tao->DE); CHKERRQ(ierr);
  }
  if (tao->constraints_inequality) {
    ierr = VecDuplicate(tao->constraints_inequality,&tao->DI); CHKERRQ(ierr);
  }

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "IPMInitializeBounds"
static PetscErrorCode IPMInitializeBounds(TaoSolver tao)
{
  TAO_IPM *ipmP = (TAO_IPM*)tao->data;
  Vec xtmp;
  /* PetscInt cstart,cend; */ /* ci (userci + lb + ub) */
  PetscInt xstart,xend;
  PetscInt ucstart,ucend; /* user ci */
  PetscInt ucestart,uceend; /* user ce */
  PetscInt sstart,send;
  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;
  PetscErrorCode ierr;

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

  ierr = VecDuplicate(tao->solution,&xtmp); CHKERRQ(ierr);
  if (!tao->XL && !tao->XU && tao->ops->computebounds) {
    ierr = TaoComputeVariableBounds(tao); CHKERRQ(ierr);
  }
  if (tao->XL) {
    ierr = VecSet(xtmp,TAO_NINFINITY); CHKERRQ(ierr);
    ierr = VecWhichGreaterThan(tao->XL,xtmp,&ipmP->isxl); CHKERRQ(ierr);
    ierr = ISGetSize(ipmP->isxl,&ipmP->nxlb); CHKERRQ(ierr);
  } else {
    ipmP->nxlb=0;
  }
  if (tao->XU) {
    ierr = VecSet(xtmp,TAO_INFINITY); CHKERRQ(ierr);
    ierr = VecWhichLessThan(tao->XU,xtmp,&ipmP->isxu); CHKERRQ(ierr);
    ierr = ISGetSize(ipmP->isxu,&ipmP->nxub); CHKERRQ(ierr);
  } else {
    ipmP->nxub=0;
  }
  ierr = VecDestroy(&xtmp); CHKERRQ(ierr);
  if (tao->constraints_inequality) {
    ierr = VecGetSize(tao->constraints_inequality,&ipmP->mi); CHKERRQ(ierr);
  } else {
    ipmP->mi = 0;
  }
#if defined DEBUG_K
  PetscPrintf(PETSC_COMM_WORLD,"isxl:\n");
  if (ipmP->nxlb) {
    ISView(ipmP->isxl,0);
  }
  PetscPrintf(PETSC_COMM_WORLD,"isxu:\n");
  if (ipmP->nxub) {
    ISView(ipmP->isxu,0);
  }

#endif
  ipmP->nb = ipmP->nxlb + ipmP->nxub + ipmP->mi;

  comm = ((PetscObject)(tao->solution))->comm;

  bigsize = ipmP->n+2*ipmP->nb+ipmP->me;
  ierr = PetscMalloc(bigsize*sizeof(PetscInt),&stepind); CHKERRQ(ierr);
  ierr = PetscMalloc(ipmP->n*sizeof(PetscInt),&xind); CHKERRQ(ierr);
  ierr = PetscMalloc(ipmP->me*sizeof(PetscInt),&uceind); CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(tao->solution,&xstart,&xend);CHKERRQ(ierr);

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

    ierr = VecDuplicate(ipmP->s,&ipmP->lamdai); CHKERRQ(ierr);
    ierr = VecDuplicate(ipmP->s,&ipmP->dlamdai); CHKERRQ(ierr);
    ierr = VecDuplicate(ipmP->s,&ipmP->rhs_lamdai); CHKERRQ(ierr);
    ierr = VecDuplicate(ipmP->s,&ipmP->save_lamdai); CHKERRQ(ierr);


    ierr = VecDuplicate(ipmP->s,&ipmP->save_s); CHKERRQ(ierr);
    ierr = VecDuplicate(ipmP->s,&ipmP->rpi); CHKERRQ(ierr);
    ierr = VecDuplicate(ipmP->s,&ipmP->Zero_nb); CHKERRQ(ierr);
    ierr = VecSet(ipmP->Zero_nb,0.0); CHKERRQ(ierr);
    ierr = VecDuplicate(ipmP->s,&ipmP->One_nb); CHKERRQ(ierr);
    ierr = VecSet(ipmP->One_nb,1.0); CHKERRQ(ierr);
    ierr = VecDuplicate(ipmP->s,&ipmP->Inf_nb); CHKERRQ(ierr);
    ierr = VecSet(ipmP->Inf_nb,TAO_INFINITY); CHKERRQ(ierr);

    ierr = PetscMalloc(ipmP->nb*sizeof(PetscInt),&cind); CHKERRQ(ierr);
    ierr = PetscMalloc(ipmP->mi*sizeof(PetscInt),&ucind); CHKERRQ(ierr);
    ierr = VecGetOwnershipRange(ipmP->s,&sstart,&send);CHKERRQ(ierr);


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

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

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

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


    if (ipmP->nxub) {
      ierr = ISAllGather(ipmP->isxu,&bigxu);CHKERRQ(ierr);
      ierr = ISGetIndices(bigxu,&xui);CHKERRQ(ierr);
      /* 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;
      }
      ierr = ISRestoreIndices(bigxu,&xui);CHKERRQ(ierr);

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

      ierr = ISCreateGeneral(comm,nloc,xind,PETSC_COPY_VALUES,&isx); CHKERRQ(ierr);
      ierr = ISCreateGeneral(comm,nloc,cind,PETSC_COPY_VALUES,&isc);CHKERRQ(ierr);
      ierr = VecScatterCreate(tao->XU,isx,ipmP->ci,isc,&ipmP->xu_scat); CHKERRQ(ierr);
      ierr = ISDestroy(&isx);CHKERRQ(ierr);
      ierr = ISDestroy(&isc);CHKERRQ(ierr);
      ierr = ISDestroy(&bigxu);CHKERRQ(ierr);
    }
  }


  ierr = VecCreate(comm,&ipmP->bigrhs); CHKERRQ(ierr);
  ierr = VecGetType(tao->solution,&vtype); CHKERRQ(ierr);
  ierr = VecSetType(ipmP->bigrhs,vtype); CHKERRQ(ierr);
  ierr = VecSetSizes(ipmP->bigrhs,PETSC_DECIDE,bigsize); CHKERRQ(ierr);
  ierr = VecSetFromOptions(ipmP->bigrhs); CHKERRQ(ierr);
  ierr = VecDuplicate(ipmP->bigrhs,&ipmP->bigstep); CHKERRQ(ierr);

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

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

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


  }

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

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


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

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

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

  ierr = PetscFree(stepind); CHKERRQ(ierr);
  ierr = PetscFree(cind); CHKERRQ(ierr);
  ierr = PetscFree(ucind); CHKERRQ(ierr);
  ierr = PetscFree(uceind); CHKERRQ(ierr);
  ierr = PetscFree(xind); CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TaoDestroy_IPM"
static PetscErrorCode TaoDestroy_IPM(TaoSolver tao)
{
  TAO_IPM *ipmP = (TAO_IPM*)tao->data;
  PetscErrorCode ierr;
  PetscFunctionBegin;
  ierr = VecDestroy(&ipmP->rd); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->rpe); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->rpi); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->work); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->lamdae); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->lamdai); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->s); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->ds); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->ci); CHKERRQ(ierr);

  ierr = VecDestroy(&ipmP->rhs_x); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->rhs_lamdae); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->rhs_lamdai); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->rhs_s); CHKERRQ(ierr);

  ierr = VecDestroy(&ipmP->save_x); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->save_lamdae); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->save_lamdai); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->save_s); CHKERRQ(ierr);

  ierr = VecScatterDestroy(&ipmP->step1); CHKERRQ(ierr);
  ierr = VecScatterDestroy(&ipmP->step2); CHKERRQ(ierr);
  ierr = VecScatterDestroy(&ipmP->step3); CHKERRQ(ierr);
  ierr = VecScatterDestroy(&ipmP->step4); CHKERRQ(ierr);

  ierr = VecScatterDestroy(&ipmP->rhs1); CHKERRQ(ierr);
  ierr = VecScatterDestroy(&ipmP->rhs2); CHKERRQ(ierr);
  ierr = VecScatterDestroy(&ipmP->rhs3); CHKERRQ(ierr);
  ierr = VecScatterDestroy(&ipmP->rhs4); CHKERRQ(ierr);

  ierr = VecScatterDestroy(&ipmP->ci_scat); CHKERRQ(ierr);
  ierr = VecScatterDestroy(&ipmP->xl_scat); CHKERRQ(ierr);
  ierr = VecScatterDestroy(&ipmP->xu_scat); CHKERRQ(ierr);

  ierr = VecDestroy(&ipmP->dlamdai); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->dlamdae); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->Zero_nb); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->One_nb); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->Inf_nb); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->complementarity); CHKERRQ(ierr);


  ierr = VecDestroy(&ipmP->bigrhs); CHKERRQ(ierr);
  ierr = VecDestroy(&ipmP->bigstep); CHKERRQ(ierr);
  ierr = MatDestroy(&ipmP->Ai); CHKERRQ(ierr);
  ierr = MatDestroy(&ipmP->K); CHKERRQ(ierr);
  ierr = ISDestroy(&ipmP->isxu); CHKERRQ(ierr);
  ierr = ISDestroy(&ipmP->isxl); CHKERRQ(ierr);
  ierr = PetscFree(tao->data); CHKERRQ(ierr);
  tao->data = PETSC_NULL;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TaoSetFromOptions_IPM"
static PetscErrorCode TaoSetFromOptions_IPM(TaoSolver tao)
{
  TAO_IPM *ipmP = (TAO_IPM*)tao->data;
  PetscErrorCode ierr;
  PetscBool flg;
  PetscFunctionBegin;
  ierr = PetscOptionsHead("IPM method for constrained optimization"); CHKERRQ(ierr);
  ierr = PetscOptionsBool("-ipm_monitorkkt","monitor kkt status",PETSC_NULL,ipmP->monitorkkt,&ipmP->monitorkkt,&flg); CHKERRQ(ierr);
  ierr = PetscOptionsReal("-ipm_pushs","parameter to push initial slack variables away from bounds",PETSC_NULL,ipmP->pushs,&ipmP->pushs,&flg);
  ierr = PetscOptionsReal("-ipm_pushnu","parameter to push initial (inequality) dual variables away from bounds",PETSC_NULL,ipmP->pushnu,&ipmP->pushnu,&flg);
  ierr = PetscOptionsTail(); CHKERRQ(ierr);
  ierr =KSPSetFromOptions(tao->ksp); CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TaoView_IPM"
static PetscErrorCode TaoView_IPM(TaoSolver tao, PetscViewer viewer)
{
  return 0;
}

/* 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||
*/
/*
#undef __FUNCT__
#define __FUNCT__ "IPMObjective"
static PetscErrorCode IPMObjective(TaoLineSearch ls, Vec X, PetscReal *f, void *tptr)
{
  TaoSolver tao = (TaoSolver)tptr;
  TAO_IPM *ipmP = (TAO_IPM*)tao->data;
  PetscErrorCode ierr;
  PetscFunctionBegin;
  ierr = IPMComputeKKT(tao); CHKERRQ(ierr);
  *f = ipmP->phi;
  PetscFunctionReturn(0);
}
*/

/*
   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||
*/
#undef __FUNCT__
#define __FUNCT__ "IPMComputeKKT"
static PetscErrorCode IPMComputeKKT(TaoSolver tao)
{
  TAO_IPM *ipmP = (TAO_IPM *)tao->data;
  PetscScalar norm;
  PetscErrorCode ierr;
  ierr = VecCopy(tao->gradient,ipmP->rd); CHKERRQ(ierr);

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

#if defined DEBUG_KKT
    PetscPrintf(PETSC_COMM_WORLD,"\nAe.lamdae\n");
    ierr = VecView(ipmP->work,0);
#endif
    /* rpe = ce(x) */
    ierr = VecCopy(tao->constraints_equality,ipmP->rpe); CHKERRQ(ierr);

  }
  if (ipmP->nb > 0) {
    /* rd = rd - Ai'*lamdai */
    ierr = MatMultTranspose(ipmP->Ai,ipmP->lamdai,ipmP->work); CHKERRQ(ierr);
    ierr = VecAXPY(ipmP->rd, -1.0, ipmP->work); CHKERRQ(ierr);
#if defined DEBUG_KKT
    PetscPrintf(PETSC_COMM_WORLD,"\nAi\n");
    ierr = MatView(ipmP->Ai,0);
    PetscPrintf(PETSC_COMM_WORLD,"\nAi.lamdai\n");
    ierr = VecView(ipmP->work,0);
#endif
    /* rpi = cin - s */
    ierr = VecCopy(ipmP->ci,ipmP->rpi); CHKERRQ(ierr);
    ierr = VecAXPY(ipmP->rpi, -1.0, ipmP->s); CHKERRQ(ierr);

    /* com = s .* lami */
    ierr = VecPointwiseMult(ipmP->complementarity, ipmP->s,ipmP->lamdai); CHKERRQ(ierr);

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

  ipmP->phi = PetscSqrtScalar(ipmP->phi);
#if defined DEBUG_KKT
  if (ipmP->monitorkkt) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"obj=%G,\tphi = %G,\tmu=%G\talpha1=%G\talpha2=%G\n",ipmP->kkt_f,ipmP->phi,ipmP->mu,ipmP->alpha1,ipmP->alpha2);
  }
  CHKMEMQ;
  PetscPrintf(PETSC_COMM_WORLD,"\ngradient\n");
  ierr = VecView(tao->gradient,0);
  PetscPrintf(PETSC_COMM_WORLD,"\nrd\n");
  ierr = VecView(ipmP->rd,0);
  PetscPrintf(PETSC_COMM_WORLD,"\nrpe\n");
  ierr = VecView(ipmP->rpe,0);
  PetscPrintf(PETSC_COMM_WORLD,"\nrpi\n");
  ierr = VecView(ipmP->rpi,0);
  PetscPrintf(PETSC_COMM_WORLD,"\ncomplementarity\n");
  ierr = VecView(ipmP->complementarity,0);
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "IPMEvaluate"
/* evaluate user info at current point */
PetscErrorCode IPMEvaluate(TaoSolver tao)
{
  TAO_IPM *ipmP = (TAO_IPM *)tao->data;
  PetscErrorCode ierr;
  PetscFunctionBegin;
  ierr = TaoComputeObjectiveAndGradient(tao,tao->solution,&ipmP->kkt_f,tao->gradient); CHKERRQ(ierr);
  ierr = TaoComputeHessian(tao,tao->solution,&tao->hessian,&tao->hessian_pre,&ipmP->Hflag); CHKERRQ(ierr);

  if (ipmP->me > 0) {
    ierr = TaoComputeEqualityConstraints(tao,tao->solution,tao->constraints_equality);
    ierr = TaoComputeJacobianEquality(tao,tao->solution,&tao->jacobian_equality,&tao->jacobian_equality_pre,&ipmP->Aiflag); CHKERRQ(ierr);
  }
  if (ipmP->mi > 0) {
    ierr = TaoComputeInequalityConstraints(tao,tao->solution,tao->constraints_inequality);
    ierr = TaoComputeJacobianInequality(tao,tao->solution,&tao->jacobian_inequality,&tao->jacobian_inequality_pre,&ipmP->Aeflag); CHKERRQ(ierr);

  }
  if (ipmP->nb > 0) {
    /* Ai' =   jac_ineq | I (w/lb) | -I (w/ub)  */
    ierr = IPMUpdateAi(tao); CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "IPMPushInitialPoint"
/* Push initial point away from bounds */
PetscErrorCode IPMPushInitialPoint(TaoSolver tao)
{
  TAO_IPM *ipmP = (TAO_IPM *)tao->data;
  PetscErrorCode ierr;
  PetscFunctionBegin;

  ierr = TaoComputeVariableBounds(tao); CHKERRQ(ierr);
  if (tao->XL && tao->XU) {
    ierr = VecMedian(tao->XL, tao->solution, tao->XU, tao->solution); CHKERRQ(ierr);
  }
  if (ipmP->nb > 0) {
    ierr = VecSet(ipmP->s,ipmP->pushs); CHKERRQ(ierr);
    ierr = VecSet(ipmP->lamdai,ipmP->pushnu); CHKERRQ(ierr);
    if (ipmP->mi > 0) {
      ierr = VecSet(tao->DI,ipmP->pushnu); CHKERRQ(ierr);
    }
  }
  if (ipmP->me > 0) {
    ierr = VecSet(tao->DE,1.0); CHKERRQ(ierr);
    ierr = VecSet(ipmP->lamdae,1.0); CHKERRQ(ierr);
  }


  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "IPMUpdateAi"
PetscErrorCode IPMUpdateAi(TaoSolver 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 mpisize;
  PetscErrorCode ierr;

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

  if (!ipmP->nb) {
    PetscFunctionReturn(0);
  }
  CHKMEMQ;

  /* Create Ai matrix if it doesn't exist yet */
  if (!ipmP->Ai) {
    comm = ((PetscObject)(tao->solution))->comm;
    ierr = PetscMalloc(ipmP->nb*sizeof(PetscInt),&nonzeros); CHKERRQ(ierr);
    ierr = MPI_Comm_size(comm,&mpisize);
    if (mpisize == 1) {
      for (i=0;i<ipmP->mi;i++) {
	ierr = MatGetRow(tao->jacobian_inequality,i,&ncols,PETSC_NULL,PETSC_NULL); CHKERRQ(ierr);
	nonzeros[i] = ncols;
	ierr = MatRestoreRow(tao->jacobian_inequality,i,&ncols,PETSC_NULL,PETSC_NULL); CHKERRQ(ierr);
      }
      for (i=r2;i<r4;i++) {
	nonzeros[i] = 1;
      }
    }
    ierr = MatCreate(comm,&ipmP->Ai); CHKERRQ(ierr);
    ierr = MatSetType(ipmP->Ai,MATAIJ); CHKERRQ(ierr);
    ierr = MatSetSizes(ipmP->Ai,PETSC_DECIDE,PETSC_DECIDE,ipmP->nb,ipmP->n);CHKERRQ(ierr);
    ierr = MatSetFromOptions(ipmP->Ai); CHKERRQ(ierr);
    ierr = MatMPIAIJSetPreallocation(ipmP->Ai,ipmP->nb,PETSC_NULL,ipmP->nb,PETSC_NULL);
    ierr = MatSeqAIJSetPreallocation(ipmP->Ai,PETSC_DEFAULT,nonzeros);CHKERRQ(ierr);
    if (mpisize ==1) {
      ierr = PetscFree(nonzeros);CHKERRQ(ierr);
    }
  }


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

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


  /* 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;
	ierr = MatSetValues(ipmP->Ai,1,&newrow,1,&newcol,&newval,INSERT_VALUES); CHKERRQ(ierr);
      }
    }
  }
  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;
      ierr = MatSetValues(ipmP->Ai,1,&newrow,1,&newcol,&newval,INSERT_VALUES); CHKERRQ(ierr);
      }
    }
  }


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

  ierr = VecSet(ipmP->ci,0.0); CHKERRQ(ierr);

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

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

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "IPMUpdateK"
/* create K = [ Hlag , 0 , Ae', -Ai'];
              [Ae , 0,   0  , 0];
              [Ai ,-I,   0 ,  0];
              [ 0 , S ,  0,   Y ];  */
PetscErrorCode IPMUpdateK(TaoSolver tao)
{
  TAO_IPM *ipmP = (TAO_IPM *)tao->data;
  MPI_Comm comm;
  PetscMPIInt mpisize;
  PetscErrorCode ierr;
  PetscInt i,j,row;
  PetscInt ncols,newcol,newcols[2],newrow;
  const PetscInt *cols;
  const PetscReal *vals;
  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;
  ierr = MPI_Comm_size(comm,&mpisize);
  ierr = IPMUpdateAi(tao); CHKERRQ(ierr);
#if defined DEBUG_K
  PetscPrintf(PETSC_COMM_WORLD,"H\n");  MatView(tao->hessian,0);
  if (ipmP->nb) {
    PetscPrintf(PETSC_COMM_WORLD,"Ai\n"); MatView(ipmP->Ai,0);
  }
  if (ipmP->me) {
    PetscPrintf(PETSC_COMM_WORLD,"Ae\n"); MatView(tao->jacobian_equality,0);
  }

#endif
  /* allocate workspace */
  subsize = PetscMax(ipmP->n,ipmP->nb);
  subsize = PetscMax(ipmP->me,subsize);
  subsize = PetscMax(2,subsize);
  ierr = PetscMalloc(sizeof(PetscInt)*subsize,&indices); CHKERRQ(ierr);
  ierr = PetscMalloc(sizeof(PetscReal)*subsize,&newvals); CHKERRQ(ierr);

  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;
  ierr = VecGetOwnershipRange(ipmP->bigrhs,&kstart,&kend); CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(tao->hessian,&hstart,&hend); CHKERRQ(ierr);
  klocalsize = kend-kstart;
  if (!ipmP->K) {
    if (mpisize == 1) {
      ierr = PetscMalloc((kend-kstart)*sizeof(PetscInt),&nonzeros);CHKERRQ(ierr);
      for (i=0;i<bigsize;i++) {
	if (i<r1) {
	  ierr = MatGetRow(tao->hessian,i,&ncols,PETSC_NULL,PETSC_NULL); CHKERRQ(ierr);
	  nonzeros[i] = ncols;
	  ierr = MatRestoreRow(tao->hessian,i,&ncols,PETSC_NULL,PETSC_NULL); CHKERRQ(ierr);
	  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;
	}
      }
      ierr = MatCreate(comm,&ipmP->K); CHKERRQ(ierr);
      ierr = MatSetType(ipmP->K,MATSEQAIJ); CHKERRQ(ierr);
      ierr = MatSetSizes(ipmP->K,klocalsize,klocalsize,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
      ierr = MatSeqAIJSetPreallocation(ipmP->K,0,nonzeros); CHKERRQ(ierr);
      ierr = MatSetFromOptions(ipmP->K); CHKERRQ(ierr);
      ierr = PetscFree(nonzeros); CHKERRQ(ierr);
    } else {
      ierr = PetscMalloc((kend-kstart)*sizeof(PetscInt),&d_nonzeros); CHKERRQ(ierr);
      ierr = PetscMalloc((kend-kstart)*sizeof(PetscInt),&o_nonzeros); CHKERRQ(ierr);
      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));
	}
      }
      ierr = MatCreate(comm,&ipmP->K); CHKERRQ(ierr);
      ierr = MatSetType(ipmP->K,MATMPIAIJ); CHKERRQ(ierr);
      ierr = MatSetSizes(ipmP->K,klocalsize,klocalsize,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
      ierr = MatMPIAIJSetPreallocation(ipmP->K,0,d_nonzeros,0,o_nonzeros); CHKERRQ(ierr);
      ierr = PetscFree(d_nonzeros); CHKERRQ(ierr);
      ierr = PetscFree(o_nonzeros); CHKERRQ(ierr);
      ierr = MatSetFromOptions(ipmP->K); CHKERRQ(ierr);

    }
  }


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

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

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


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

    /* Copy L,Y */
    ierr = VecGetOwnershipRange(ipmP->s,&sstart,&send);CHKERRQ(ierr);
    ierr = VecGetArray(ipmP->lamdai,&l); CHKERRQ(ierr);
    ierr = VecGetArray(ipmP->s,&y); CHKERRQ(ierr);

    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;
      ierr = MatSetValues(ipmP->K,1,&newrow,2,newcols,newvals,INSERT_VALUES); CHKERRQ(ierr);
    }

    ierr = VecRestoreArray(ipmP->lamdai,&l); CHKERRQ(ierr);
    ierr = VecRestoreArray(ipmP->s,&y); CHKERRQ(ierr);
  }

  ierr = PetscFree(indices); CHKERRQ(ierr);
  ierr = PetscFree(newvals); CHKERRQ(ierr);
  ierr = MatAssemblyBegin(ipmP->K,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
  ierr = MatAssemblyEnd(ipmP->K,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
#if defined DEBUG_K
  PetscPrintf(PETSC_COMM_WORLD,"K\n");  MatView(ipmP->K,0);
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "IPMGatherRHS"
PetscErrorCode IPMGatherRHS(TaoSolver tao,Vec RHS,Vec X1,Vec X2,Vec X3,Vec X4)
{
  TAO_IPM *ipmP = (TAO_IPM *)tao->data;
  PetscErrorCode ierr;
  PetscFunctionBegin;

  /* rhs = [x1      (n)
            x2     (me)
	    x3     (nb)
	    x4     (nb)] */
  if (X1) {
    ierr = VecScatterBegin(ipmP->rhs1,X1,RHS,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(ipmP->rhs1,X1,RHS,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  }
  if (ipmP->me > 0 && X2) {
    ierr = VecScatterBegin(ipmP->rhs2,X2,RHS,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(ipmP->rhs2,X2,RHS,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  }
  if (ipmP->nb > 0) {
    if (X3) {
      ierr = VecScatterBegin(ipmP->rhs3,X3,RHS,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(ipmP->rhs3,X3,RHS,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    }
    if (X4) {
      ierr = VecScatterBegin(ipmP->rhs4,X4,RHS,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(ipmP->rhs4,X4,RHS,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    }
  }
#if defined(DEBUG_SCATTER)
  PetscPrintf(PETSC_COMM_WORLD,"X1-X4\n");
  if (X1) {VecView(X1,0);}
  if (X2) {VecView(X2,0);}
  if (X3) {VecView(X3,0);}
  if (X4) {VecView(X4,0);}
  PetscPrintf(PETSC_COMM_WORLD,"RHS\n");
  VecView(RHS,0);
#endif
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "IPMScatterStep"
PetscErrorCode IPMScatterStep(TaoSolver tao, Vec STEP, Vec X1, Vec X2, Vec X3, Vec X4)
{
  TAO_IPM *ipmP = (TAO_IPM *)tao->data;
  PetscErrorCode ierr;
  PetscFunctionBegin;
  CHKMEMQ;
  /*        [x1    (n)
	     x2    (nb) may be 0
 	     x3    (me) may be 0
	     x4    (nb) may be 0 */
  if (X1) {
    ierr = VecScatterBegin(ipmP->step1,STEP,X1,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(ipmP->step1,STEP,X1,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  }
  if (X2 && ipmP->nb > 0) {
    ierr = VecScatterBegin(ipmP->step2,STEP,X2,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(ipmP->step2,STEP,X2,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  }
  if (X3 && ipmP->me > 0) {
    ierr = VecScatterBegin(ipmP->step3,STEP,X3,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(ipmP->step3,STEP,X3,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  }
  if (X4 && ipmP->nb > 0) {
    ierr = VecScatterBegin(ipmP->step4,STEP,X4,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(ipmP->step4,STEP,X4,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  }
  CHKMEMQ;
#if defined(DEBUG_SCATTER)
  PetscPrintf(PETSC_COMM_WORLD,"Step\n");
  VecView(STEP,0);
  PetscPrintf(PETSC_COMM_WORLD,"X1-X4\n");
  if (X1) {VecView(X1,0);}
  if (X2) {VecView(X2,0);}
  if (X3) {VecView(X3,0);}
  if (X4) {VecView(X4,0);}
#endif
  PetscFunctionReturn(0);
}


EXTERN_C_BEGIN

#undef __FUNCT__
#define __FUNCT__ "TaoCreate_IPM"
PetscErrorCode TaoCreate_IPM(TaoSolver tao)
{
  TAO_IPM *ipmP;
  /*  const char *ipmls_type = TAOLINESEARCH_IPM; */
  PetscErrorCode ierr;

  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; */

  ierr = PetscNewLog(tao,&ipmP); CHKERRQ(ierr);
  tao->data = (void*)ipmP;
  tao->max_it = 200;
  tao->max_funcs = 500;
  tao->fatol = 1e-4;
  tao->frtol = 1e-4;
  ipmP->dec = 10000; /* line search critera */
  ipmP->taumin = 0.995;
  ipmP->monitorkkt = PETSC_FALSE;
  ipmP->pushs = 100;
  ipmP->pushnu = 100;
  ierr = KSPCreate(((PetscObject)tao)->comm, &tao->ksp); CHKERRQ(ierr);
  PetscFunctionReturn(0);


}
EXTERN_C_END