Multiobjective programming under generalized V-type I invexity

Abstract

In this paper, we are concerned with a differentiable multiob- jective programming problem with inequality constraints. We introduce new concepts of generalized V-type I invexity problems in which each component of the objective and constraint functions is considered with respect to its own function ηi or θj . In the setting of these definitions, we establish new Karush-Kuhn-Tucker type necessary and sufficient op- timality conditions for a feasible point to be efficient or properly efficient. Furthermore, we show, with examples, that the obtained results allow to prove that a feasible point is an efficient or properly efficient solution even if it is not an usual vector Karush-Kuhn-Tucker point for a multi- objective programming problem