Optimality conditions and duality for E-differentiable multiobjective programming involving V-E-type I functions

In this paper, we introduce a new concept of sets and a new class of functions called a-E-invex sets and V-E-preinvex functions. Furthermore, a new concept of generalized convexity is introduced for (not necessarily) differentiable vector optimization problems. Namely, the concept of V-E-type I functions is defined for E-differentiable vector opti-mization problem. A number of sufficiency results are established under various types of (generalized) V-E-type I requirements. Moreover, several E-duality theorems in the sense of Mond-Weir are proved under appropriate (generalized) V-E-type I functions.