Subdifferentials for Set-valued Maps and Optimality Conditions for Set-valued Vector Optimization

Abstract

Based on the concept of the weak subdifferential for set-valued maps introduced by Sawaragi and Tanino we give the definition of Henig global subdifferentials for set-valued maps.We investigate the existence condition for this kind of subdifferential,and discuss its operational property. Using this concepts,we present the necessary condition and sufficient condition for Henig globally proper efficient solution pair for constrained set-valued vector optimization problem,respectively.