  Our goal is to develop a flux limiter of the Flux-Corrected Transport method
for a nonconservative convection-diffusion equation. For this, we consider a
hybrid difference scheme that is a linear combination of a monotone scheme and
a scheme of high-order accuracy. The flux limiter is computed as an approximate
solution of a corresponding optimization problem with a linear objective
function. The constraints for this optimization problem are derived from
inequalities that are valid for the monotone scheme and apply to the hybrid
scheme. Our numerical results with the flux limiters, which are exact and
approximate solutions to the optimization problem, are in good agreement.
