Dual Kuhn-Tucker necessary conditions for strict minima of order two for nonsmooth vector optimization problems with inequality and equality constraints

Abstract

In this paper, we give primal and dual Kuhn-Tucker necessary conditions for the existence of a strict local minimum of order two for vector optimization problems with equality and inequality constraints under some new regularity conditions. First, we improve the existing primal necessary conditions for such minima. Then, we apply an alternative theorem to derive dual Kuhn-Tucker necessary conditions of second and higher-order. To compare our results to the ones in the literature, we provide some examples.