Optimality conditions using sum-convex approximations

The purpose of this paper is to give necessary and sufficient conditions of optimality for a general mathematical programming problem, using not a linear approximation to the constraint function but an approximation possessing certain convexity properties. Such approximations are called sum-convex. Theorems of the alternative involving sum-convex functions are also presented as part of the proof.This work is part of the author's PhD Thesis under the supervision of Professor S. Zlobec at McGill University.