Karush-Kuhn-Tucker necessary conditions for local Pareto minima of constrained multiobjective programming problems

Abstract

Under the constraint qualification of Abadie type we establish necessary efficiency conditions described by inconsistent inequalities, Karush-Kuhn-Tucker necessary conditions and strong Karush-Kuhn-Tucker necessary conditions for local Pareto minima of nonsmooth multiobjective programming problems involving inequality, equality and set constraints in Banach spaces in terms of convexificators. Note that all the constraint functions involving in the considering problem are not necessarily continuous, except inactive constraints.