Stability properties of KKT points in vector optimization

Abstract

In this article we introduce the notion of approximate Karush–Kuhn–Tucker (KKT) points for smooth, convex and nonsmooth, nonconvex vector optimization problems. We study a kind of stability of these points and KKT points of vector optimization problems. In the convex case we also introduce and study the notion of modified approximate KKT points motivated by Ekeland's variational principle. We prove stability properties of these points for several optimization problems.