Second-order optimality conditions for strict local Pareto minima of cosntrained nonsmooth multiobjective optimization problems

Abstract

This paper presents primal and dual Fritz John secondorder necessary conditions for strict local Pareto minima of order two of nonsmooth vector optimization problems in terms of the P´ales–Zeidan second-order directional derivatives without constraint qualifications. Dual second-order Karush–Kuhn–Tucker necessary and sufficient conditions for strict local Pareto minima of order two are established under a suitable constraint qualification.