CONVEX VECTOR FUNCTIONS AND THEIR SUBDIFFERENTIAL

Abstract

The continuity of a convex vector function on relative interior points of its domain is studied. As a corollary of this we can see that a convex vector function is Lipschitz near any relative interior point of its do- main. A new concept of subdifierential of a convex function is introduced and some its properties similar to those in the scalar case are shown. The inclusive relations between generalized Jacobian and subdifierential, the convexcity of a vector function and the monotonicity of its subdifierential are also established. Further, some neccessary and su-cient conditions for the existence of e-cient solutions of vector optimization problems are also proved.