Optimality conditions for a cone-convex programming problem

Abstract

Optimality conditions without constraint qualifications are given for the convex programming problem: Maximize f(x) such that g(x) ∈ B, where f maps X into R and is concave, g maps X into R^m and is B-concave, X is a locally convex topological vector space and B is a closed convex cone containing no line. In the case when B is the nonnegative orthant, the results reduce to some of those obtained recently by Ben-Israel, Ben-Tal and Zlobec.