E -invexity and generalized E -invexity in E -differentiable multiobjective programming

In this paper, a new concept of generalized convexity is introduced for not necessarily differentiable vector optimization problems. For an E -differentiable function, the concept of E -invexity is introduced as a generalization of the E -differentiable E -convexity notion. In addition, some properties of E -differentiable E -invex functions are investigated. Furthermore, the so-called E -Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E -differentiable vector optimization problems with both inequality and equality constraints. Also, the sufficiency of the E -Karush-Kuhn-Tucker necessary optimality conditions are proved for such E -differentiable vector optimization problems in which the involved functions are E -invex and/or generalized E -invex.