Characterization of optimality for the abstract convex program with finite dimensional range

This paper presents characterizations of optimality for the abstract convex program when S is an arbitrary convex cone in a finite dimensional space, Ω is a convex set and p and g are respectively convex and S-convex (on Ω). These characterizations, which include a Lagrange multiplier theorem and do not presume any a priori constraint qualification, subsume those presently in the literature.