impls/bnk/bntl.c

#include <../src/tao/bound/impls/bnk/bnk.h>
#include <petscksp.h>

/*
 Implements Newton's Method with a trust region approach for solving
 bound constrained minimization problems. This version includes a
 line search fall-back in the event of a trust region failure.

 The linear system solve has to be done with a conjugate gradient method.
*/

static PetscErrorCode TaoSolve_BNTL(Tao tao)
{
  PetscErrorCode               ierr;
  TAO_BNK                      *bnk = (TAO_BNK *)tao->data;
  KSPConvergedReason           ksp_reason;
  TaoLineSearchConvergedReason ls_reason;

  PetscReal                    oldTrust, prered, actred, stepNorm, steplen;
  PetscBool                    stepAccepted = PETSC_TRUE;
  PetscInt                     stepType, updateType;

  PetscFunctionBegin;
  /*   Project the current point onto the feasible set */
  ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
  ierr = TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);CHKERRQ(ierr);

  /* Project the initial point onto the feasible region */
  ierr = VecMedian(tao->XL,tao->solution,tao->XU,tao->solution);CHKERRQ(ierr);

  /* Check convergence criteria */
  ierr = TaoComputeObjectiveAndGradient(tao, tao->solution, &bnk->f, bnk->unprojected_gradient);CHKERRQ(ierr);
  ierr = VecBoundGradientProjection(bnk->unprojected_gradient,tao->solution,tao->XL,tao->XU,tao->gradient);CHKERRQ(ierr);
  ierr = TaoGradientNorm(tao, tao->gradient,NORM_2,&bnk->gnorm);CHKERRQ(ierr);
  if (PetscIsInfOrNanReal(bnk->f) || PetscIsInfOrNanReal(bnk->gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");

  tao->reason = TAO_CONTINUE_ITERATING;
  ierr = TaoLogConvergenceHistory(tao,bnk->f,bnk->gnorm,0.0,tao->ksp_its);CHKERRQ(ierr);
  ierr = TaoMonitor(tao,tao->niter,bnk->f,bnk->gnorm,0.0,tao->trust);CHKERRQ(ierr);
  ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr);
  if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);

  /* Initialize the preconditioner and trust radius */
  ierr = TaoBNKInitialize(tao);CHKERRQ(ierr);

  /* Have not converged; continue with Newton method */
  while (tao->reason == TAO_CONTINUE_ITERATING) {
    tao->niter++;
    tao->ksp_its=0;
    /* Compute the Hessian */
    ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
    /* Update the BFGS preconditioner */
    if (BNK_PC_BFGS == bnk->pc_type) {
      if (BFGS_SCALE_PHESS == bnk->bfgs_scale_type) {
        /* Obtain diagonal for the bfgs preconditioner  */
        ierr = MatGetDiagonal(tao->hessian, bnk->Diag);CHKERRQ(ierr);
        ierr = VecAbs(bnk->Diag);CHKERRQ(ierr);
        ierr = VecReciprocal(bnk->Diag);CHKERRQ(ierr);
        ierr = MatLMVMSetScale(bnk->M,bnk->Diag);CHKERRQ(ierr);
      }
      /* Update the limited memory preconditioner and get existing # of updates */
      ierr = MatLMVMUpdate(bnk->M, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
    }

    /* Use the common BNK kernel to compute the Newton step (for inactive variables only) */
    ierr = TaoBNKComputeStep(tao, &ksp_reason);CHKERRQ(ierr);

    /* Store current solution before it changes */
    oldTrust = tao->trust;
    bnk->fold = bnk->f;
    ierr = VecCopy(tao->solution, bnk->Xold);CHKERRQ(ierr);
    ierr = VecCopy(tao->gradient, bnk->Gold);CHKERRQ(ierr);
    ierr = VecCopy(bnk->unprojected_gradient, bnk->unprojected_gradient_old);CHKERRQ(ierr);

    /* Temporarily accept the step and project it into the bounds */
    ierr = VecAXPY(tao->solution, 1.0, tao->stepdirection);CHKERRQ(ierr);
    ierr = VecMedian(tao->XL, tao->solution, tao->XU, tao->solution);CHKERRQ(ierr);

    /* Check if the projection changed the step direction */
    ierr = VecCopy(tao->solution, tao->stepdirection);CHKERRQ(ierr);
    ierr = VecAXPY(tao->stepdirection, -1.0, bnk->Xold);CHKERRQ(ierr);
    ierr = VecNorm(tao->stepdirection, NORM_2, &stepNorm);CHKERRQ(ierr);
    if (stepNorm != bnk->dnorm) {
      /* Projection changed the step, so we have to recompute predicted reduction.
         However, we deliberately do not change the step norm and the trust radius
         in order for the safeguard to more closely mimic a piece-wise linesearch
         along the bounds. */
      ierr = MatMult(tao->hessian, tao->stepdirection, bnk->Xwork);CHKERRQ(ierr);
      ierr = VecAYPX(bnk->Xwork, -0.5, tao->gradient);CHKERRQ(ierr);
      ierr = VecDot(bnk->Xwork, tao->stepdirection, &prered);
    } else {
      /* Step did not change, so we can just recover the pre-computed prediction */
      ierr = KSPCGGetObjFcn(tao->ksp, &prered);CHKERRQ(ierr);
    }
    prered = -prered;

    /* Compute the actual reduction and update the trust radius */
    ierr = TaoComputeObjective(tao, tao->solution, &bnk->f);CHKERRQ(ierr);
    actred = bnk->fold - bnk->f;
    ierr = TaoBNKUpdateTrustRadius(tao, prered, actred, stepType, &stepAccepted);CHKERRQ(ierr);

    if (stepAccepted) {
      /* Step is good, evaluate the gradient and the hessian */
      steplen = 1.0;
      ++bnk->newt;
      ierr = TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
      ierr = VecBoundGradientProjection(bnk->unprojected_gradient,tao->solution,tao->XL,tao->XU,tao->gradient);CHKERRQ(ierr);
    } else {
      /* Trust-region rejected the step. Revert the solution. */
      bnk->f = bnk->fold;
      ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr);

      /* Trigger the line search */
      ierr = TaoBNKSafeguardStep(tao, ksp_reason, &stepType);CHKERRQ(ierr);
      ierr = TaoBNKPerformLineSearch(tao, stepType, &steplen, &ls_reason);CHKERRQ(ierr);
      if (ls_reason != TAOLINESEARCH_SUCCESS && ls_reason != TAOLINESEARCH_SUCCESS_USER) {
        /* Line search failed, revert solution and terminate */
        bnk->f = bnk->fold;
        ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr);
        ierr = VecCopy(bnk->Gold, tao->gradient);CHKERRQ(ierr);
        ierr = VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);CHKERRQ(ierr);
        tao->trust = 0.0;
        tao->reason = TAO_DIVERGED_LS_FAILURE;
      } else {
        /* Line search succeeded so we should update the trust radius based on the LS step length */
        updateType = bnk->update_type;
        bnk->update_type = BNK_UPDATE_STEP;
        tao->trust = oldTrust;
        ierr = TaoBNKUpdateTrustRadius(tao, prered, actred, stepType, &stepAccepted);CHKERRQ(ierr);
        bnk->update_type = updateType;
        /* count the accepted step types */
        switch (stepType) {
        case BNK_NEWTON:
          ++bnk->newt;
          break;
        case BNK_BFGS:
          ++bnk->bfgs;
          break;
        case BNK_SCALED_GRADIENT:
          ++bnk->sgrad;
          break;
        case BNK_GRADIENT:
          ++bnk->grad;
          break;
        default:
          break;
        }
      }
    }

    /*  Check for termination */
    ierr = TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);CHKERRQ(ierr);
    if (PetscIsInfOrNanReal(bnk->gnorm)) SETERRQ(PETSC_COMM_SELF,1,"User provided compute function generated Not-a-Number");
    ierr = TaoLogConvergenceHistory(tao,bnk->f,bnk->gnorm,0.0,tao->ksp_its);CHKERRQ(ierr);
    ierr = TaoMonitor(tao,tao->niter,bnk->f,bnk->gnorm,0.0,steplen);CHKERRQ(ierr);
    ierr = (*tao->ops->convergencetest)(tao,tao->cnvP);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*------------------------------------------------------------*/

PETSC_EXTERN PetscErrorCode TaoCreate_BNTL(Tao tao)
{
  TAO_BNK        *bnk;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = TaoCreate_BNK(tao);CHKERRQ(ierr);
  tao->ops->solve=TaoSolve_BNTL;

  bnk = (TAO_BNK *)tao->data;
  bnk->update_type = BNK_UPDATE_REDUCTION; /* trust region updates based on predicted/actual reduction */
  bnk->sval = 0.0; /* disable Hessian shifting */
  PetscFunctionReturn(0);
}