Research On Approximate Solutions To Vector Equilibrium And Set-Valued Optimization Problems

In this paper,we consider approximate efficient solution to the set-valued vector equilibrium problems and set-valued optimization problems with constraints in locally convex Hausdorff linear topological space and real linear space,present the relationships among the approximate efficient solutions.Under the assumption of the near cone-subconvexlikeness,by virtue of separation theorem for convex sets,we obtain Kuhn-Tucker-like and Lagrange-like optimality conditions for set-valued vector equilibrium problems and set-valued optimization problems with constraints respectively.The paper is divided into four chapters as follows:Chapter 1 is an introduction in which the background of approximate efficient solutions to set-valued optimization problems and current research situation were presented.Moreover,some related concepts of approximate efficient solution to set-valued optimization problems were summarized.Chapter 2 is devoted to the research on approximate weakly efficient solutions to set-valued vector equilibrium problems,Under the assumption of the near cone-subconvexlikeness,by virtue of separation theorem for convex sets,we obtain Kuhn-Tucker-like and Lagrange-like optimality conditions for set-valued vector equilibrium problems with constraints respectively.Chapter 3 presents some kinds of inner properly efficient points of a set,the relationships among those kinds of inner properly efficient points are discussed.In chapter 4,we consider approximate properly efficient solutions to set-valued optimization problems via a variable improvement set in real linear space without topological structure.By virtue of diffierent linear functions,some optimality conditions for properly efficient solutions were established,and then we discussed the relationships among those properly efficient solutions.