ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces

Abstract EN

We study ϵ-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces.

Firstly, an equivalent characterization of ϵ-Henig saddle point of the Lagrangian set-valued map is obtained.

Secondly, under the assumption of the generalized cone subconvexlikeness of set-valued maps, the relationship between the ϵ-Henig saddle point of the Lagrangian set-valued map and the ϵ-Henig properly efficient element of the set-valued optimization problem is presented.

Finally, some duality theorems are given.