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.

 ------------------------------------------------------------

 initialize trust radius (default: BNK_INIT_INTERPOLATION)
 x_0 = VecMedian(x_0)
 f_0, g_0 = TaoComputeObjectiveAndGradient(x_0)
 pg_0 = VecBoundGradientProjection(g_0)
 check convergence at pg_0
 niter = 0
 step_accepted = true

 while niter <= max_it
    niter += 1
    H_k = TaoComputeHessian(x_k)
    if pc_type == BNK_PC_BFGS
      add correction to BFGS approx
      if scale_type == BNK_SCALE_AHESS
        D = VecMedian(1e-6, abs(diag(H_k)), 1e6)
        scale BFGS with VecReciprocal(D)
      end
    end

    if pc_type = BNK_PC_BFGS
      B_k = BFGS
    else
      B_k = VecMedian(1e-6, abs(diag(H_k)), 1e6)
      B_k = VecReciprocal(B_k)
    end
    w = x_k - VecMedian(x_k - 0.001*B_k*g_k)
    eps = min(eps, norm2(w))
    determine the active and inactive index sets such that
      L = {i : (x_k)_i <= l_i + eps && (g_k)_i > 0}
      U = {i : (x_k)_i >= u_i - eps && (g_k)_i < 0}
      F = {i : l_i = (x_k)_i = u_i}
      A = {L + U + F}
      I = {i : i not in A}

    generate the reduced system Hr_k dr_k = -gr_k for variables in I
    if pc_type == BNK_PC_BFGS && scale_type == BNK_SCALE_PHESS
      D = VecMedian(1e-6, abs(diag(Hr_k)), 1e6)
      scale BFGS with VecReciprocal(D)
    end
    solve Hr_k dr_k = -gr_k
    set d_k to (l - x) for variables in L, (u - x) for variables in U, and 0 for variables in F

    x_{k+1} = VecMedian(x_k + d_k)
    s = x_{k+1} - x_k
    prered = dot(s, 0.5*gr_k - Hr_k*s)
    f_{k+1} = TaoComputeObjective(x_{k+1})
    actred = f_k - f_{k+1}

    oldTrust = trust
    step_accepted, trust = TaoBNKUpdateTrustRadius(default: BNK_UPDATE_REDUCTION)
    if step_accepted
      g_{k+1} = TaoComputeGradient(x_{k+1})
      pg_{k+1} = VecBoundGradientProjection(g_{k+1})
      count the accepted Newton step
    else
      if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
        dr_k = -BFGS*gr_k for variables in I
        if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
          reset the BFGS preconditioner
          calculate scale delta and apply it to BFGS
          dr_k = -BFGS*gr_k for variables in I
          if dot(d_k, pg_k)) >= 0 || norm(d_k) == NaN || norm(d_k) == Inf
            dr_k = -gr_k for variables in I
          end
        end
      end

      x_{k+1}, f_{k+1}, g_{k+1}, ls_failed = TaoBNKPerformLineSearch()
      if ls_failed
        f_{k+1} = f_k
        x_{k+1} = x_k
        g_{k+1} = g_k
        pg_{k+1} = pg_k
        terminate
      else
        pg_{k+1} = VecBoundGradientProjection(g_{k+1})
        trust = oldTrust
        trust = TaoBNKUpdateTrustRadius(BNK_UPDATE_STEP)
        count the accepted step type (Newton, BFGS, scaled grad or grad)
      end
    end

    check convergence at pg_{k+1}
 end
*/

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

  PetscReal                    resnorm, oldTrust, prered, actred, stepNorm, steplen;
  PetscBool                    cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_FALSE;
  PetscInt                     stepType;

  PetscFunctionBegin;
  /* Initialize the preconditioner, KSP solver and trust radius/line search */
  tao->reason = TAO_CONTINUE_ITERATING;
  ierr = TaoBNKInitialize(tao, bnk->init_type, &needH);CHKERRQ(ierr);
  if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);

  /* Have not converged; continue with Newton method */
  while (tao->reason == TAO_CONTINUE_ITERATING) {
    tao->niter++;

    if (needH) {
      /* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
      ierr = TaoBNKTakeCGSteps(tao, &cgTerminate);CHKERRQ(ierr);
      if (cgTerminate) {
        tao->reason = bnk->bncg->reason;
        PetscFunctionReturn(0);
      }
      /* Compute the hessian and update the BFGS preconditioner at the new iterate */
      ierr = TaoBNKComputeHessian(tao);CHKERRQ(ierr);
      needH = PETSC_FALSE;
    }

    /* Use the common BNK kernel to compute the Newton step (for inactive variables only) */
    ierr = TaoBNKComputeStep(tao, shift, &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 = TaoBNKRecomputePred(tao, tao->stepdirection, &prered);CHKERRQ(ierr);
    } 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, bnk->update_type, stepType, &stepAccepted);CHKERRQ(ierr);

    if (stepAccepted) {
      /* Step is good, evaluate the gradient and the hessian */
      steplen = 1.0;
      needH = PETSC_TRUE;
      ++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 */
        stepAccepted = PETSC_FALSE;
        needH = PETSC_FALSE;
        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 {
        /* new iterate so we need to recompute the Hessian */
        needH = PETSC_TRUE;
        /* compute the projected gradient */
        ierr = VecBoundGradientProjection(bnk->unprojected_gradient,tao->solution,tao->XL,tao->XU,tao->gradient);CHKERRQ(ierr);
        ierr = VecNorm(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");
        /* Line search succeeded so we should update the trust radius based on the LS step length */
        tao->trust = oldTrust;
        ierr = TaoBNKUpdateTrustRadius(tao, prered, actred, BNK_UPDATE_STEP, stepType, &stepAccepted);CHKERRQ(ierr);
        /* count the accepted step type */
        ierr = TaoBNKAddStepCounts(tao, stepType);CHKERRQ(ierr);
      }
    }

    /*  Check for termination */
    ierr = VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->Gwork);CHKERRQ(ierr);
    ierr = VecNorm(bnk->Gwork, NORM_2, &resnorm);CHKERRQ(ierr);
    ierr = TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its);CHKERRQ(ierr);
    ierr = TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen);CHKERRQ(ierr);
    ierr = (*tao->ops->convergencetest)(tao, tao->cnvP);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

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

PETSC_INTERN PetscErrorCode TaoSetUp_BNTL(Tao tao)
{
  TAO_BNK        *bnk = (TAO_BNK *)tao->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = TaoSetUp_BNK(tao);CHKERRQ(ierr);
  if (!bnk->is_nash && !bnk->is_stcg && !bnk->is_gltr) SETERRQ(PETSC_COMM_SELF,1,"Must use a trust-region CG method for KSP (KSPNASH, KSPSTCG, KSPGLTR)");
  PetscFunctionReturn(0);
}

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

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

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

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