On second-order Karush--Kuhn--Tucker optimality conditions for $C^{1,1}$ vector optimization problems

Abstract

This paper focuses on optimality conditions for $C^{1,1}$ vector optimization problems with inequality constraints. By employing the limiting second-order subdifferential and the second-order tangent set, we introduce a new type of second-order constraint qualification in the sense of Abadie. Then we establish some second-order necessary optimality conditions of Karush--Kuhn--Tucker-type for local (weak) efficient solutions of the considered problem. In addition, we provide some sufficient conditions for a local efficient solution of the such problem. The obtained results improve existing ones in the literature.