ε-Strict Effeciency And ε-Strong Efficiency In Vector Optimization With Set-Valued Maps

In this paper, we introduce and research systematically ε- strict efficiency and ε- strong efficiency of vector optimization with set-valued maps in locally convex topological spaces. At first, when set A is convex, we get scalarazation, convexity and density of the sets of ε- strict efficient points and ε- strong efficient points of set A. And then, under the assumption that the objective function is cone-convexlike, we get the results off - Lagrange multiplier,ε - Lagrange duality of the set of ε- proper strict efficient solutions of (SVP). We also introduce the concept of ε- (proper) strict saddle points and obtain the saddle point theorem. At last, we discuss the relationships between ε- strong efficiency, ε- proper strict efficiency, ε- strict efficiency, ε- super efficiency and ε - Benson proper efficiency.