E-Henig Proper Efficient Solution For Set-valued Optimization Problems

Set-valued optimization problem is the hotspot in the optimization theory and ap-plication.It is widely used in economic equilibrium and transportation,optimal control,game theory,military descision-making systems and so on.Because there are a number of different forms of proper efficient solution and approximate proper efficient solutions in the research of set-valued optimization.It is meaningful to put forward the concept of proper efficient solution and to study some characterizations of proper efficient solution.Such as scalarization,Lagrange multiplier,saddle point,the duality and so on.In this paper,we study the E-Henig proper efficient solution of set-valued optimization problem.And we study some characteristics of it.The major contents are summarized as follows:In chapter 1,we give simple describes of the background and current situation of the research on the efficient solution of set-valued problems and present some definitions and lemmas which are related with this paper.In chapter 2,firstly,we introduce the concept of E-Henig proper efficient point in a real Hausdorff locally convex space and study the equivalent characterizations of E-Henig proper efficient point.Then the relationships with E-Benson proper point and E-super point are discussed.At last the existence theorem of E-Henig proper efficient solution in Bananch space is established.In chapter 3,we study some characteristics of E-Henig proper efficient solution.Un-der the assumption of nearly subconvexlikeness,scalarization theorems of E-Henig proper efficient solution and Lagrange multiplier theorem are established.Lastly,E-Henig saddle point theorem and E-Henig duality theorem are studied.