Research On E-Globally Proper Efficient Solution Of Set-Valued Equilibrium Problems And Its Applications

The set-valued equilibrium problems,as an important part of optimization theory,have important significance of the study and theoretical value in mathematical economy and transportation system.First,using the notion of improvement set,we introduce the notion of the E-globally proper efficient solution for set-valued equilibrium problems with constraints in locally convex spaces.Second,we study the properties of the E-globally proper efficient solutions,and discuss the relationship between the E-globally proper efficient solutions and the E-weakly efficient solutions,E-Henig proper efficient solutions.Finally,the linear scalarization theorems,the Kuhn-Tucker type optimality condition and the Lagrange type optimality conditions with respect to the E-globally proper efficient solutions have been obtained.The structure of the thesis is as follows:In Chapter 1,first,we briefly present the background and research significance of the set-valued equilibrium problem.Second,we recall the research status of the set-valued equilibrium problems.Finally,combined with the related concepts such as improvement set,we arrange the main contents of each chapter.In Chapter 2,we recall some basic concepts and lemmas related to the set-valued equilibrium problems,including the convex sets,the cones,the point convex cones,the bases,the improvement sets,the nearly E-subconvex and so on.In Chapter 3,first,based on the notion of improvement sets,we introduce the E-globally proper efficient solutions.The solutions provide a unified framework for the study of the globally proper efficient solutions and the ε-global globally proper efficient solutions.Second,we disccuss the relationships between E-globally proper efficient solutions and E-weakly efficient solutions,E-Henig proper efficient solutions.Meanwhile,some examples are given to illustrate our results.In Chapter 4,we establish the linear scalar characterizations and optimality conditions of the E-globally proper efficient solutions for the set-valued equilibrium problems with constraints.First,proposing the linear scalarization problems of the set-valued equilibrium problems with constrained,we introduce the E-optimal solution of the linear scalarization problems.At the same time,the linear scalarization theorems of E-globally proper efficient solutions are obtained.Then,the Kuhn-Tucker type optimality condition of the E-globally proper efficient solution of set-valued equilibrium problems with constraints are obtained under the hypothesis of nearly E-subconvexlikeness of set-valued maps.Finally,by establishing the unconstrained set-valued equilibrium problems and using the conclusion of the Kuhn-Tucker type optimality condition,we study the Lagrange type optimality conditions of the E-globally proper efficient solutions of set-valued equilibrium problems with constrains.In particular,the results are also analyzed and compared with others,some examples are given to prove our conclusions.