Sufficiency and duality for e-differentiable multiobjective programming problems involving generalized v -e-invex functions

Abstract

In this paper, a class of E-differentiable multiobjective programming problems with both inequality and equality constraints is considered. For E-differentiable functions, the concepts of V-E-pseudo-invexity, strictly V -E-pseudo-invexity and V -E-quasi-invexity are introduced. Based upon these notions of generalized V -E-invex functions, the sufficiency of the so-called E-Karush-Kuhn-Tucker optimality conditions are established for the considered E-differentiable vector optimization problems with both inequality and equality constraints. Furthermore, the so-called vector Mond-Weir E-dual problem is defined for the considered E-differentiable multiobjective programming problem and several E-duality theorems in the sense of Mond-Weir are derived also under appropriate generalized V-E-invexity assumptions.