ON CHARACTERIZATIONS OF CONVEX VECTOR FUNSTIONS AND OPTIMIZATION

Abstract

 In this paper, we present characterizations of convex vector func
tions 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 con
strained 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.