ε-Super Efficient Solutions Of Set-valued Optimization Programs And The Subdifferential Of Benson Proper Efficiency

In locally convex linear topological spaces, theε- super efficient solution for vector optimization with set-valued maps is introduced. Under the assumption of the ic-cone-convexlikeness of set-valued maps, by applying separation theorem for convex sets, the scalarization theorems are established. By using the alternative theorem, theε- Lagrange multiplier theorems are derived.The subdifferential of Benson proper efficiency is introduced, under suitable conditions, the existence of subdifferential are proved and the properties of subdifferential are derived, by applying the convex set separation theorem; the stability of set-valued optimization with perturbed parameter of objective functions and perturbed order of constraint sets are investigated in the sense of subdifferential defined under Benson proper efficiency.