Strong efficiency in vector optimization of set-valued maps

Recently a new kind of proper efficiency, namely strong efficiency, has been introduced by Cheng and Fu which generalizes Borwein's super efficiency and other proper efficiency. The purpose of this paper is to extend the concept of strong efficiency to set-valued optimization problems. This concept of strong efficiency is used to establish scalarization theorems and Lagrange multiplier theorems in association with a vector optimization problem of set-valued maps. Lagrange duality theorems are also derived in the end.