xref: /petsc/src/tao/quadratic/impls/bqpip/bqpip.c (revision bd89dbf26d8a5efecb980364933175da61864cd7)

/*
    This file implements a Mehrotra predictor-corrector method for
    bound-constrained quadratic programs.

 */

#include <../src/tao/quadratic/impls/bqpip/bqpipimpl.h>
#include <petscksp.h>

static PetscErrorCode QPIPComputeResidual(TAO_BQPIP *qp, Tao tao)
{
  PetscReal dtmp = 1.0 - qp->psteplength;

  PetscFunctionBegin;
  /* Compute R3 and R5 */

  PetscCall(VecScale(qp->R3, dtmp));
  PetscCall(VecScale(qp->R5, dtmp));
  qp->pinfeas = dtmp * qp->pinfeas;

  PetscCall(VecCopy(qp->S, tao->gradient));
  PetscCall(VecAXPY(tao->gradient, -1.0, qp->Z));

  PetscCall(MatMult(tao->hessian, tao->solution, qp->RHS));
  PetscCall(VecScale(qp->RHS, -1.0));
  PetscCall(VecAXPY(qp->RHS, -1.0, qp->C));
  PetscCall(VecAXPY(tao->gradient, -1.0, qp->RHS));

  PetscCall(VecNorm(tao->gradient, NORM_1, &qp->dinfeas));
  qp->rnorm = (qp->dinfeas + qp->pinfeas) / (qp->m + qp->n);
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode QPIPSetInitialPoint(TAO_BQPIP *qp, Tao tao)
{
  PetscReal two = 2.0, p01 = 1;
  PetscReal gap1, gap2, fff, mu;

  PetscFunctionBegin;
  /* Compute function, Gradient R=Hx+b, and Hessian */
  PetscCall(MatMult(tao->hessian, tao->solution, tao->gradient));
  PetscCall(VecCopy(qp->C, qp->Work));
  PetscCall(VecAXPY(qp->Work, 0.5, tao->gradient));
  PetscCall(VecAXPY(tao->gradient, 1.0, qp->C));
  PetscCall(VecDot(tao->solution, qp->Work, &fff));
  qp->pobj = fff + qp->d;

  PetscCheck(!PetscIsInfOrNanReal(qp->pobj), PETSC_COMM_SELF, PETSC_ERR_USER, "User provided data contains infinity or NaN");

  /* Initialize slack vectors */
  /* T = XU - X; G = X - XL */
  PetscCall(VecCopy(qp->XU, qp->T));
  PetscCall(VecAXPY(qp->T, -1.0, tao->solution));
  PetscCall(VecCopy(tao->solution, qp->G));
  PetscCall(VecAXPY(qp->G, -1.0, qp->XL));

  PetscCall(VecSet(qp->GZwork, p01));
  PetscCall(VecSet(qp->TSwork, p01));

  PetscCall(VecPointwiseMax(qp->G, qp->G, qp->GZwork));
  PetscCall(VecPointwiseMax(qp->T, qp->T, qp->TSwork));

  /* Initialize Dual Variable Vectors */
  PetscCall(VecCopy(qp->G, qp->Z));
  PetscCall(VecReciprocal(qp->Z));

  PetscCall(VecCopy(qp->T, qp->S));
  PetscCall(VecReciprocal(qp->S));

  PetscCall(MatMult(tao->hessian, qp->Work, qp->RHS));
  PetscCall(VecAbs(qp->RHS));
  PetscCall(VecSet(qp->Work, p01));
  PetscCall(VecPointwiseMax(qp->RHS, qp->RHS, qp->Work));

  PetscCall(VecPointwiseDivide(qp->RHS, tao->gradient, qp->RHS));
  PetscCall(VecNorm(qp->RHS, NORM_1, &gap1));
  mu = PetscMin(10.0, (gap1 + 10.0) / qp->m);

  PetscCall(VecScale(qp->S, mu));
  PetscCall(VecScale(qp->Z, mu));

  PetscCall(VecSet(qp->TSwork, p01));
  PetscCall(VecSet(qp->GZwork, p01));
  PetscCall(VecPointwiseMax(qp->S, qp->S, qp->TSwork));
  PetscCall(VecPointwiseMax(qp->Z, qp->Z, qp->GZwork));

  qp->mu      = 0;
  qp->dinfeas = 1.0;
  qp->pinfeas = 1.0;
  while ((qp->dinfeas + qp->pinfeas) / (qp->m + qp->n) >= qp->mu) {
    PetscCall(VecScale(qp->G, two));
    PetscCall(VecScale(qp->Z, two));
    PetscCall(VecScale(qp->S, two));
    PetscCall(VecScale(qp->T, two));

    PetscCall(QPIPComputeResidual(qp, tao));

    PetscCall(VecCopy(tao->solution, qp->R3));
    PetscCall(VecAXPY(qp->R3, -1.0, qp->G));
    PetscCall(VecAXPY(qp->R3, -1.0, qp->XL));

    PetscCall(VecCopy(tao->solution, qp->R5));
    PetscCall(VecAXPY(qp->R5, 1.0, qp->T));
    PetscCall(VecAXPY(qp->R5, -1.0, qp->XU));

    PetscCall(VecNorm(qp->R3, NORM_INFINITY, &gap1));
    PetscCall(VecNorm(qp->R5, NORM_INFINITY, &gap2));
    qp->pinfeas = PetscMax(gap1, gap2);

    /* Compute the duality gap */
    PetscCall(VecDot(qp->G, qp->Z, &gap1));
    PetscCall(VecDot(qp->T, qp->S, &gap2));

    qp->gap  = gap1 + gap2;
    qp->dobj = qp->pobj - qp->gap;
    if (qp->m > 0) {
      qp->mu = qp->gap / (qp->m);
    } else {
      qp->mu = 0.0;
    }
    qp->rgap = qp->gap / (PetscAbsReal(qp->dobj) + PetscAbsReal(qp->pobj) + 1.0);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode QPIPStepLength(TAO_BQPIP *qp)
{
  PetscReal tstep1, tstep2, tstep3, tstep4, tstep;

  PetscFunctionBegin;
  /* Compute stepsize to the boundary */
  PetscCall(VecStepMax(qp->G, qp->DG, &tstep1));
  PetscCall(VecStepMax(qp->T, qp->DT, &tstep2));
  PetscCall(VecStepMax(qp->S, qp->DS, &tstep3));
  PetscCall(VecStepMax(qp->Z, qp->DZ, &tstep4));

  tstep           = PetscMin(tstep1, tstep2);
  qp->psteplength = PetscMin(0.95 * tstep, 1.0);

  tstep           = PetscMin(tstep3, tstep4);
  qp->dsteplength = PetscMin(0.95 * tstep, 1.0);

  qp->psteplength = PetscMin(qp->psteplength, qp->dsteplength);
  qp->dsteplength = qp->psteplength;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode QPIPComputeNormFromCentralPath(TAO_BQPIP *qp, PetscReal *norm)
{
  PetscReal gap[2], mu[2], nmu;

  PetscFunctionBegin;
  PetscCall(VecPointwiseMult(qp->GZwork, qp->G, qp->Z));
  PetscCall(VecPointwiseMult(qp->TSwork, qp->T, qp->S));
  PetscCall(VecNorm(qp->TSwork, NORM_1, &mu[0]));
  PetscCall(VecNorm(qp->GZwork, NORM_1, &mu[1]));

  nmu = -(mu[0] + mu[1]) / qp->m;

  PetscCall(VecShift(qp->GZwork, nmu));
  PetscCall(VecShift(qp->TSwork, nmu));

  PetscCall(VecNorm(qp->GZwork, NORM_2, &gap[0]));
  PetscCall(VecNorm(qp->TSwork, NORM_2, &gap[1]));
  gap[0] *= gap[0];
  gap[1] *= gap[1];

  qp->pathnorm = PetscSqrtScalar(gap[0] + gap[1]);
  *norm        = qp->pathnorm;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode QPIPComputeStepDirection(TAO_BQPIP *qp, Tao tao)
{
  PetscFunctionBegin;
  /* Calculate DG */
  PetscCall(VecCopy(tao->stepdirection, qp->DG));
  PetscCall(VecAXPY(qp->DG, 1.0, qp->R3));

  /* Calculate DT */
  PetscCall(VecCopy(tao->stepdirection, qp->DT));
  PetscCall(VecScale(qp->DT, -1.0));
  PetscCall(VecAXPY(qp->DT, -1.0, qp->R5));

  /* Calculate DZ */
  PetscCall(VecAXPY(qp->DZ, -1.0, qp->Z));
  PetscCall(VecPointwiseDivide(qp->GZwork, qp->DG, qp->G));
  PetscCall(VecPointwiseMult(qp->GZwork, qp->GZwork, qp->Z));
  PetscCall(VecAXPY(qp->DZ, -1.0, qp->GZwork));

  /* Calculate DS */
  PetscCall(VecAXPY(qp->DS, -1.0, qp->S));
  PetscCall(VecPointwiseDivide(qp->TSwork, qp->DT, qp->T));
  PetscCall(VecPointwiseMult(qp->TSwork, qp->TSwork, qp->S));
  PetscCall(VecAXPY(qp->DS, -1.0, qp->TSwork));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoSetup_BQPIP(Tao tao)
{
  TAO_BQPIP *qp = (TAO_BQPIP *)tao->data;

  PetscFunctionBegin;
  /* Set pointers to Data */
  PetscCall(VecGetSize(tao->solution, &qp->n));

  /* Allocate some arrays */
  if (!tao->gradient) PetscCall(VecDuplicate(tao->solution, &tao->gradient));
  if (!tao->stepdirection) PetscCall(VecDuplicate(tao->solution, &tao->stepdirection));

  PetscCall(VecDuplicate(tao->solution, &qp->Work));
  PetscCall(VecDuplicate(tao->solution, &qp->XU));
  PetscCall(VecDuplicate(tao->solution, &qp->XL));
  PetscCall(VecDuplicate(tao->solution, &qp->HDiag));
  PetscCall(VecDuplicate(tao->solution, &qp->DiagAxpy));
  PetscCall(VecDuplicate(tao->solution, &qp->RHS));
  PetscCall(VecDuplicate(tao->solution, &qp->RHS2));
  PetscCall(VecDuplicate(tao->solution, &qp->C));

  PetscCall(VecDuplicate(tao->solution, &qp->G));
  PetscCall(VecDuplicate(tao->solution, &qp->DG));
  PetscCall(VecDuplicate(tao->solution, &qp->S));
  PetscCall(VecDuplicate(tao->solution, &qp->Z));
  PetscCall(VecDuplicate(tao->solution, &qp->DZ));
  PetscCall(VecDuplicate(tao->solution, &qp->GZwork));
  PetscCall(VecDuplicate(tao->solution, &qp->R3));

  PetscCall(VecDuplicate(tao->solution, &qp->T));
  PetscCall(VecDuplicate(tao->solution, &qp->DT));
  PetscCall(VecDuplicate(tao->solution, &qp->DS));
  PetscCall(VecDuplicate(tao->solution, &qp->TSwork));
  PetscCall(VecDuplicate(tao->solution, &qp->R5));
  qp->m = 2 * qp->n;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoSolve_BQPIP(Tao tao)
{
  TAO_BQPIP *qp = (TAO_BQPIP *)tao->data;
  PetscInt   its;
  PetscReal  d1, d2, ksptol, sigmamu;
  PetscReal  gnorm, dstep, pstep, step = 0;
  PetscReal  gap[4];
  PetscBool  getdiagop;

  PetscFunctionBegin;
  qp->dobj        = 0.0;
  qp->pobj        = 1.0;
  qp->gap         = 10.0;
  qp->rgap        = 1.0;
  qp->mu          = 1.0;
  qp->dinfeas     = 1.0;
  qp->psteplength = 0.0;
  qp->dsteplength = 0.0;

  /* TODO
     - Remove fixed variables and treat them correctly
     - Use index sets for the infinite versus finite bounds
     - Update remaining code for fixed and free variables
     - Fix inexact solves for predictor and corrector
  */

  /* Tighten infinite bounds, things break when we don't do this
    -- see test_bqpip.c
  */
  PetscCall(TaoComputeVariableBounds(tao));
  PetscCall(VecSet(qp->XU, 1.0e20));
  PetscCall(VecSet(qp->XL, -1.0e20));
  if (tao->XL) PetscCall(VecPointwiseMax(qp->XL, qp->XL, tao->XL));
  if (tao->XU) PetscCall(VecPointwiseMin(qp->XU, qp->XU, tao->XU));
  PetscCall(VecMedian(qp->XL, tao->solution, qp->XU, tao->solution));

  /* Evaluate gradient and Hessian at zero to get the correct values
     without contaminating them with numerical artifacts.
  */
  PetscCall(VecSet(qp->Work, 0));
  PetscCall(TaoComputeObjectiveAndGradient(tao, qp->Work, &qp->d, qp->C));
  PetscCall(TaoComputeHessian(tao, qp->Work, tao->hessian, tao->hessian_pre));
  PetscCall(MatHasOperation(tao->hessian, MATOP_GET_DIAGONAL, &getdiagop));
  if (getdiagop) PetscCall(MatGetDiagonal(tao->hessian, qp->HDiag));

  /* Initialize starting point and residuals */
  PetscCall(QPIPSetInitialPoint(qp, tao));
  PetscCall(QPIPComputeResidual(qp, tao));

  /* Enter main loop */
  tao->reason = TAO_CONTINUE_ITERATING;
  while (1) {
    /* Check Stopping Condition      */
    gnorm = PetscSqrtScalar(qp->gap + qp->dinfeas);
    PetscCall(TaoLogConvergenceHistory(tao, qp->pobj, gnorm, qp->pinfeas, tao->ksp_its));
    PetscCall(TaoMonitor(tao, tao->niter, qp->pobj, gnorm, qp->pinfeas, step));
    PetscUseTypeMethod(tao, convergencetest, tao->cnvP);
    if (tao->reason != TAO_CONTINUE_ITERATING) break;
    /* Call general purpose update function */
    PetscTryTypeMethod(tao, update, tao->niter, tao->user_update);
    tao->niter++;
    tao->ksp_its = 0;

    /*
       Dual Infeasibility Direction should already be in the right
       hand side from computing the residuals
    */

    PetscCall(QPIPComputeNormFromCentralPath(qp, &d1));

    PetscCall(VecSet(qp->DZ, 0.0));
    PetscCall(VecSet(qp->DS, 0.0));

    /*
       Compute the Primal Infeasiblitiy RHS and the
       Diagonal Matrix to be added to H and store in Work
    */
    PetscCall(VecPointwiseDivide(qp->DiagAxpy, qp->Z, qp->G));
    PetscCall(VecPointwiseMult(qp->GZwork, qp->DiagAxpy, qp->R3));
    PetscCall(VecAXPY(qp->RHS, -1.0, qp->GZwork));

    PetscCall(VecPointwiseDivide(qp->TSwork, qp->S, qp->T));
    PetscCall(VecAXPY(qp->DiagAxpy, 1.0, qp->TSwork));
    PetscCall(VecPointwiseMult(qp->TSwork, qp->TSwork, qp->R5));
    PetscCall(VecAXPY(qp->RHS, -1.0, qp->TSwork));

    /*  Determine the solving tolerance */
    ksptol = qp->mu / 10.0;
    ksptol = PetscMin(ksptol, 0.001);
    PetscCall(KSPSetTolerances(tao->ksp, ksptol, 1e-30, 1e30, PetscMax(10, qp->n)));

    /* Shift the diagonals of the Hessian matrix */
    PetscCall(MatDiagonalSet(tao->hessian, qp->DiagAxpy, ADD_VALUES));
    if (!getdiagop) {
      PetscCall(VecCopy(qp->DiagAxpy, qp->HDiag));
      PetscCall(VecScale(qp->HDiag, -1.0));
    }
    PetscCall(MatAssemblyBegin(tao->hessian, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(tao->hessian, MAT_FINAL_ASSEMBLY));

    PetscCall(KSPSetOperators(tao->ksp, tao->hessian, tao->hessian_pre));
    PetscCall(KSPSolve(tao->ksp, qp->RHS, tao->stepdirection));
    PetscCall(KSPGetIterationNumber(tao->ksp, &its));
    tao->ksp_its += its;
    tao->ksp_tot_its += its;

    /* Restore the true diagonal of the Hessian matrix */
    if (getdiagop) {
      PetscCall(MatDiagonalSet(tao->hessian, qp->HDiag, INSERT_VALUES));
    } else {
      PetscCall(MatDiagonalSet(tao->hessian, qp->HDiag, ADD_VALUES));
    }
    PetscCall(MatAssemblyBegin(tao->hessian, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(tao->hessian, MAT_FINAL_ASSEMBLY));
    PetscCall(QPIPComputeStepDirection(qp, tao));
    PetscCall(QPIPStepLength(qp));

    /* Calculate New Residual R1 in Work vector */
    PetscCall(MatMult(tao->hessian, tao->stepdirection, qp->RHS2));
    PetscCall(VecAXPY(qp->RHS2, 1.0, qp->DS));
    PetscCall(VecAXPY(qp->RHS2, -1.0, qp->DZ));
    PetscCall(VecAYPX(qp->RHS2, qp->dsteplength, tao->gradient));

    PetscCall(VecNorm(qp->RHS2, NORM_2, &qp->dinfeas));
    PetscCall(VecDot(qp->DZ, qp->DG, gap));
    PetscCall(VecDot(qp->DS, qp->DT, gap + 1));

    qp->rnorm = (qp->dinfeas + qp->psteplength * qp->pinfeas) / (qp->m + qp->n);
    pstep     = qp->psteplength;
    step      = PetscMin(qp->psteplength, qp->dsteplength);
    sigmamu   = (pstep * pstep * (gap[0] + gap[1]) + (1 - pstep) * qp->gap) / qp->m;

    if (qp->predcorr && step < 0.9) {
      if (sigmamu < qp->mu) {
        sigmamu = sigmamu / qp->mu;
        sigmamu = sigmamu * sigmamu * sigmamu;
      } else {
        sigmamu = 1.0;
      }
      sigmamu = sigmamu * qp->mu;

      /* Compute Corrector Step */
      PetscCall(VecPointwiseMult(qp->DZ, qp->DG, qp->DZ));
      PetscCall(VecScale(qp->DZ, -1.0));
      PetscCall(VecShift(qp->DZ, sigmamu));
      PetscCall(VecPointwiseDivide(qp->DZ, qp->DZ, qp->G));

      PetscCall(VecPointwiseMult(qp->DS, qp->DS, qp->DT));
      PetscCall(VecScale(qp->DS, -1.0));
      PetscCall(VecShift(qp->DS, sigmamu));
      PetscCall(VecPointwiseDivide(qp->DS, qp->DS, qp->T));

      PetscCall(VecCopy(qp->DZ, qp->RHS2));
      PetscCall(VecAXPY(qp->RHS2, -1.0, qp->DS));
      PetscCall(VecAXPY(qp->RHS2, 1.0, qp->RHS));

      /* Approximately solve the linear system */
      PetscCall(MatDiagonalSet(tao->hessian, qp->DiagAxpy, ADD_VALUES));
      if (!getdiagop) {
        PetscCall(VecCopy(qp->DiagAxpy, qp->HDiag));
        PetscCall(VecScale(qp->HDiag, -1.0));
      }
      PetscCall(MatAssemblyBegin(tao->hessian, MAT_FINAL_ASSEMBLY));
      PetscCall(MatAssemblyEnd(tao->hessian, MAT_FINAL_ASSEMBLY));

      /* Solve using the previous tolerances that were set */
      PetscCall(KSPSolve(tao->ksp, qp->RHS2, tao->stepdirection));
      PetscCall(KSPGetIterationNumber(tao->ksp, &its));
      tao->ksp_its += its;
      tao->ksp_tot_its += its;

      if (getdiagop) {
        PetscCall(MatDiagonalSet(tao->hessian, qp->HDiag, INSERT_VALUES));
      } else {
        PetscCall(MatDiagonalSet(tao->hessian, qp->HDiag, ADD_VALUES));
      }
      PetscCall(MatAssemblyBegin(tao->hessian, MAT_FINAL_ASSEMBLY));
      PetscCall(MatAssemblyEnd(tao->hessian, MAT_FINAL_ASSEMBLY));
      PetscCall(QPIPComputeStepDirection(qp, tao));
      PetscCall(QPIPStepLength(qp));
    } /* End Corrector step */

    /* Take the step */
    dstep = qp->dsteplength;

    PetscCall(VecAXPY(qp->Z, dstep, qp->DZ));
    PetscCall(VecAXPY(qp->S, dstep, qp->DS));
    PetscCall(VecAXPY(tao->solution, dstep, tao->stepdirection));
    PetscCall(VecAXPY(qp->G, dstep, qp->DG));
    PetscCall(VecAXPY(qp->T, dstep, qp->DT));

    /* Compute Residuals */
    PetscCall(QPIPComputeResidual(qp, tao));

    /* Evaluate quadratic function */
    PetscCall(MatMult(tao->hessian, tao->solution, qp->Work));

    PetscCall(VecDot(tao->solution, qp->Work, &d1));
    PetscCall(VecDot(tao->solution, qp->C, &d2));
    PetscCall(VecDot(qp->G, qp->Z, gap));
    PetscCall(VecDot(qp->T, qp->S, gap + 1));

    /* Compute the duality gap */
    qp->pobj = d1 / 2.0 + d2 + qp->d;
    qp->gap  = gap[0] + gap[1];
    qp->dobj = qp->pobj - qp->gap;
    if (qp->m > 0) qp->mu = qp->gap / (qp->m);
    qp->rgap = qp->gap / (PetscAbsReal(qp->dobj) + PetscAbsReal(qp->pobj) + 1.0);
  } /* END MAIN LOOP  */
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoView_BQPIP(Tao tao, PetscViewer viewer)
{
  PetscFunctionBegin;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoSetFromOptions_BQPIP(Tao tao, PetscOptionItems PetscOptionsObject)
{
  TAO_BQPIP *qp = (TAO_BQPIP *)tao->data;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "Interior point method for bound constrained quadratic optimization");
  PetscCall(PetscOptionsInt("-tao_bqpip_predcorr", "Use a predictor-corrector method", "", qp->predcorr, &qp->predcorr, NULL));
  PetscOptionsHeadEnd();
  PetscCall(KSPSetFromOptions(tao->ksp));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoDestroy_BQPIP(Tao tao)
{
  TAO_BQPIP *qp = (TAO_BQPIP *)tao->data;

  PetscFunctionBegin;
  if (tao->setupcalled) {
    PetscCall(VecDestroy(&qp->G));
    PetscCall(VecDestroy(&qp->DG));
    PetscCall(VecDestroy(&qp->Z));
    PetscCall(VecDestroy(&qp->DZ));
    PetscCall(VecDestroy(&qp->GZwork));
    PetscCall(VecDestroy(&qp->R3));
    PetscCall(VecDestroy(&qp->S));
    PetscCall(VecDestroy(&qp->DS));
    PetscCall(VecDestroy(&qp->T));

    PetscCall(VecDestroy(&qp->DT));
    PetscCall(VecDestroy(&qp->TSwork));
    PetscCall(VecDestroy(&qp->R5));
    PetscCall(VecDestroy(&qp->HDiag));
    PetscCall(VecDestroy(&qp->Work));
    PetscCall(VecDestroy(&qp->XL));
    PetscCall(VecDestroy(&qp->XU));
    PetscCall(VecDestroy(&qp->DiagAxpy));
    PetscCall(VecDestroy(&qp->RHS));
    PetscCall(VecDestroy(&qp->RHS2));
    PetscCall(VecDestroy(&qp->C));
  }
  PetscCall(KSPDestroy(&tao->ksp));
  PetscCall(PetscFree(tao->data));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TaoComputeDual_BQPIP(Tao tao, Vec DXL, Vec DXU)
{
  TAO_BQPIP *qp = (TAO_BQPIP *)tao->data;

  PetscFunctionBegin;
  PetscCall(VecCopy(qp->Z, DXL));
  PetscCall(VecCopy(qp->S, DXU));
  PetscCall(VecScale(DXU, -1.0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
 TAOBQPIP - interior-point method for quadratic programs with
    box constraints.

 Notes:
    This algorithms solves quadratic problems only, the Hessian will
        only be computed once.

 Options Database Keys:
. -tao_bqpip_predcorr - use a predictor/corrector method

  Level: beginner
M*/

PETSC_EXTERN PetscErrorCode TaoCreate_BQPIP(Tao tao)
{
  TAO_BQPIP *qp;

  PetscFunctionBegin;
  PetscCall(PetscNew(&qp));

  tao->ops->setup          = TaoSetup_BQPIP;
  tao->ops->solve          = TaoSolve_BQPIP;
  tao->ops->view           = TaoView_BQPIP;
  tao->ops->setfromoptions = TaoSetFromOptions_BQPIP;
  tao->ops->destroy        = TaoDestroy_BQPIP;
  tao->ops->computedual    = TaoComputeDual_BQPIP;

  /* Override default settings (unless already changed) */
  PetscCall(TaoParametersInitialize(tao));
  PetscObjectParameterSetDefault(tao, max_it, 100);
  PetscObjectParameterSetDefault(tao, max_funcs, 500);
  PetscObjectParameterSetDefault(tao, catol, PetscDefined(USE_REAL_SINGLE) ? 1e-6 : 1e-12);

  /* Initialize pointers and variables */
  qp->n = 0;
  qp->m = 0;

  qp->predcorr = 1;
  tao->data    = (void *)qp;

  PetscCall(KSPCreate(((PetscObject)tao)->comm, &tao->ksp));
  PetscCall(PetscObjectIncrementTabLevel((PetscObject)tao->ksp, (PetscObject)tao, 1));
  PetscCall(KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix));
  PetscCall(KSPSetType(tao->ksp, KSPCG));
  PetscCall(KSPSetTolerances(tao->ksp, 1e-14, 1e-30, 1e30, PetscMax(10, qp->n)));
  PetscFunctionReturn(PETSC_SUCCESS);
}