ON CHARACTERIZATIONS OF CONVEX VECTOR FUNSTIONS AND OPTIMIZATION

Abstract

In this paper, we present characterizations of convex vector functions via generalized monotonicity of their directional derivatives and differentials. By applying these results to vector optimization, we have established some necessary/sufficient conditions for optimality of vector optimization problems, especially the Kuhn-Tucker condition for constrained problems. The results obtained in this paper generalize some corresponding well-known results of W. Fenchel [8], O.L. Mangasarian [9] and R.T. Rockafellar [7] in the scalar case