A theorem on nonconvex functions and its application to vector optimization

A basic result of convex analysis is the Fundamental Theorem on Convex Functions. We present a counterpart of this theorem for the case the convexity assumption does not hold and we shall show that some well known necessary conditions for weak efficiency and proper efficiency in nonconvex vector optimization are implicit in our result. The significance of this result in vector optimization and in supporting decision making is briefly discussed.