On G-invex multiobjective programming. Part I. Optimality

In this paper, a generalization of convexity, namely G–invexity, is considered in the case of nonlinear multiobjective programming problems where the functions constituting vector optimization problems are differentiable. The modified Karush–Kuhn–Tucker necessary optimality conditions for a certain class of multiobjective programming problems are established. To prove this result, the Kuhn–Tucker constraint qualification and the definition of the Bouligand tangent cone for a set are used. The assumptions on (weak) Pareto optimal solutions are relaxed by means of vector–valued G–invex functions.