Strong duality with super efficiency in set-valued optimization

This paper is devoted to the study of four dual problems of a primal vector optimization problem involving nearly subconvexlike set-valued mappings. For each dual problem, a strong duality theorem with super efficiency is established. The strong duality result can be expressed as follows: starting from a super minimizer of the primal problem, a super maximizer of the dual problem can be constructed such that the corresponding objective values of both problems are equal. The results improve the corresponding ones in the literature.