On second-order optimality conditions in constrained multiobjective optimization

In this paper we study a multiobjective optimization problem with inequality constraints on finite dimensional spaces. A second-order necessary condition for local weak efficiency is proved under strict differentiability assumptions. We also establish a second-order sufficient condition for local firm efficiency of order 2 under ℓℓ-stability assumptions. In this way we generalize some corresponding results obtained by P.Q. Khanh and N.D. Tuan, and by the authors.