Higher - order optimality conditions in multiobjective oftimization

Abstract

In this paper we present higher-order necessary optimality conditions for local weak and Pareto minima of multiobjective optimization problems involving a cone constraint and a set constraint with n-times Gâteaux differentiable functions in terms of higher-order Gâteaux derivatives and higher-order tangent cones in infinite dimension. Higher-order sufficient optimality conditions are presented for strict local Pareto minima of order n in finite dimension together with some illustrative examples.