e Conjugate maps and e conjugate duality in vector optimization with set valued maps
The aim of this article is to develop an approximate (e) conjugate duality theory for a general vector optimization problem with set valued maps on the basis of e weak efficiency. We first introduce the concepts of e conjugate maps and e weak subgradients for set valued maps and establish several properties of them. Then we introduce an e 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.