  In this article we consider a convex feasible set described by inequality
constraints that are continuous and not necessarily Lipschitz or convex. We
show that if the Slater constraint qualification and a non-degeneracy condition
are satisfied, then the Karush-Kuhn-Tucker type optimality condition is both
necessary and sufficient. In this way we extend previous results which are
proved for Lipschitz and differentiable inequalities.
