SET APPROACH DUALITY ASSERTIONS FOR SET-VALUED PROBLEMS WITH THE NONSOLID ORDERING CONE

In this paper, we establish a new duality theorem for set-valued optimization problems, where the solution concept is based on the set approach. The ordering cone in the image space might have an empty interior. A new concept of set less order relation with respect to the quasi-interior of the ordering cone is introduced and related primal/dual problems are studied. The main tool for the proof of the new duality assertions is the relationship between optimal solutions based on the set approach and optimal solutions based on the vector approach. Finally, we establish a saddle points theorem with mild conditions.