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

Abstract

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