Stability Of Solutions For Vector Equilibrium Problems Via Variational Analysis Method

Vector equilibrium problem is a kind of mathematical model of universal significance.Many of the problems can be transformed into the equilibrium problem,such as optimiza-tion problems,Nash equilibrium problems,complementarity problems,fixed point problems,saddle point problems and it has wide applications in the fields of economy,finance,trans-portation,resource allocation and project management.In this article,we are going to study stability of solutions for vector equilibrium problems via variational analysis method.It is organized as follows:In Chapter 1,we introduce the background and significance of vector equilibrium prob-lems.Then,we give an outline of present situation about variational analysis methods,including its applications to study of existence,stability,nonemptiness and boundedness for vector equilibrium problems.At last,we list some basic conceptions and lemmas which are used is this dissertation.In Chapter 2,we study the variational convergence properties of vector-valued functions in the reflexive Banach space by means of variational analysis method.Firstly,we define many notions in the reflexive Banach space,such as lop convergence,epi convergence,hypo convergence,which extend the notion of variational convergence in finite-dimensional space already.Secondly,we characterize the variational convergence in the reflexive Banach space.Finally,we use the result to get some other equivalent condition of solution sets for vector equilibrium problems.In Chapter 3,we study the stability of the vector equilibrium problem when(Ck,Fk)?lop,(C,F).We first employ the asymptotic function and asymptotic cone to define three impor-tant notions of R0(C,F),R1(C,F),R(C,F)and we also study their stability to establish the corresponding variational convergence properties.At the last,we obtain the stability of solutions for vector equilibrium problems by using the properties of variational convergence for Ro(C,F),R1(C,F),R(C,F).Moreover,we also get a variety of sequential properties of vector equilibrium problems solution set maps.