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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.
In this paper we study the abstract convex program
where 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 (on Ω). We use the concept of a minimal cone for (P) to correct and strengthen a previous characterization of optimality for (P), see Theorem 3.2. The results presented here are used in a sequel to provide a Lagrange multiplier theorem for (P) which holds without any constraint qualification.
