Ensure constraints are satisfied

In the past we found that VMCON was reporting that it had converged but the constraints were not accurately satisfied, although we never understood why. To fix this we added code to ensure that the constraints were satisfied before VMCON exited.

    !  Check convergence of constraint residuals
    summ = 0.0D0
    !do i = 1,m
    ! This only includes the equality constraints Issue #505
    do i = 1,meq
      summ = summ + conf(i)*conf(i)
    end do
    sqsumsq = sqrt(summ)

    etc

    if (verbose == 1) then
      write(*,'(a,es13.5,a,es13.5)') &
        'Constraint residuals (sqsumsq) = ',sqsumsq, &
        ' Convergence parameter = ',sum
    end if

    ! Writting the step results in OPT.DAT file
    do i = 1, n
      delta_var(i) = delta(i)
    end do

    ! Comment in to write optional optimisation information output file
    !  write(opt_file, '(I5,E28.10,*(E18.10))') niter+1, abs(objf), sum, sqsumsq, conf, x, delta_var

    !  Exit if both convergence criteria are satisfied
    !  (the original criterion, plus constraint residuals below the tolerance level)
    !  Temporarily set the two tolerances equal (should perhaps be an input parameter)
    sqsumsq_tol = tol

    ! Store the lowest valid FoM (ie where constraints are satisfied)
    if (sqsumsq < sqsumsq_tol)  lowest_valid_fom = min(lowest_valid_fom, objf)

The line that actually checks for convergence:

    if ((sum <= tol).and.(sqsumsq < sqsumsq_tol)) then
      if (verbose == 1) then
        write(*,*) 'Convergence parameter < convergence criterion (epsvmc)'
        write(*,*) 'Root of sum of squares of residuals < tolerance (sqsumsq_tol)'
      end if
      exit_code = 1
      return
    end if

(original branch)

Proposed solution

It might help to add this additional convergence test to pyvmcon. One could also add a new line to the input code to allow sqsumsq_tol and tol to be input separately.
@jonmaddock @timothy-nunn