ε-Conjugate maps and ε-conjugate duality in vector optimization with set-valued maps

The aim of this article is to develop an approximate (epsilon)-conjugate duality theory for a general vector optimization problem with set-valued maps on the basis of epsilon-weak efficiency. We first introduce the concepts of epsilon-conjugate maps and epsilon-weak subgradients for set-valued maps and establish several properties of them. Then we introduce an epsilon-conjugate dual problem for the vector set-valued optimization problem. Finally, we establish a weak duality theorem and a strong duality theorem for the relationship between the primal and the dual problems.