Higher order efficiency, saddle point optimality, and duality for vector optimization problems

In this paper, we intend to characterize the strict local efficient solution of order m for a vector minimization. problem in terms of the vector saddle point. A new notion of strict local saddle point of higher order of the vector-valued Lagrangian function is introduced. The relationship between strict local saddle point and strict local efficient solution is derived. Lagrange duality is formulated, and duality results are presented.