Multi Objective Optimization Nature Of Efficient Solution

This paper made some research about properties of proper efficient solutions for multi-objective optimization problem.In the first chapter, we investigate the existence of Ge-proper efficient solution map under weaker convexity condition in Euclidean space. Then we give a necessary and sufficient condition of upper semi-continuity of Ge-proper efficient solution maps.In the second chapter, firstly, we study the existence of stronger essential point of cone efficient solution under order cone perturbations, then discussed the relations between the effective cone points under the binding domain of a local minor perturbations and the proper effective Borwein points.Finally we introduce all kinds of proper effective solution concept, then in the general sense partial order, we compared and discussed the relationship in Euclidean space and general topological space in certain specific conditions,including the equivalent among them. Borwein, Benson and Heing have discussed vector optimization problems under the more general case which is closed convex cone, and get variety of corresponding proper effective solution. In this chapter, we discuss the further relationship between the solutions.In the third chapter, we discussed the connectivity of space-efficient point set when the objective function is almost like convex set-valued mapping by use the scalarization approach in set-valued optimization problem in normed space. Recently Borwein and Zhuang defined super effective solution on the general problem of vector optimization in normed spaces in the literature [11]. It has many good properties, and this has aroused the attention of people, which is considered to be one of the important research directions of multi-objective optimization theory.