  The optimized effective potential method is formulated as a convex
minimization problem. This formulation does not require assumptions about
$v$-representability nor functional differentiability. The formulation provides
a natural framework for fully self-consistent calculations where both a
Kohn--Sham system with a non-local potential and an additional system with a
local potential are jointly optimized. The formulation is also well suited for
extensions to other flavors of density-functional theory, e.g. current-density
functional theory, where there are additional potentials besides the ordinary
electrostatic potential.
