Research On The Related Problems Of Generalized Mixed Variational Inequalities

Variatioal inequality has widely applications in different areas of economic,financial,control and optimization,engineering,transportation,and other fields.the research of variational inequality is mainly from three aspects: theory,algorithm and application.It is well known that the mixed variational inequality problem is a generalized form of a variational inequality problem.With the development of variational inequality theory with its applications,several classes of inverse inequalities have been introduced and studied,which has widely applications in normative flow control problems,which require the network equilibrium state to be in a linearly constrained set,and bipartite market equilibrium problems,and the split generalized mixed variational inequality problems as the split variational inequality problem extentions,has play a significant role in studying the existence of solutions.At present,many scholars pay special attention to it.In this thesis,we study a new class of generalized inverse mixed quasi-variatational inequalities and a class of split general nonlinear mixed variational inequality problem,Two types of problems associated with generalized mixed variational inequalities.The main research results of this paper can be summarized as follows:In chapter 2,we study a new class of generalized inverse mixed quasi-variatational inequalities(GIMQVI)in Hilbert Space.By making use of the properties of generalized f-projection operators,under the appropriate conditions,we obtain and study the existence and uniqueness result for GIMQVI solution.Furthermore,Moreover,the error bound theorem of GIMQVI is constructed by using the residual function.The results presented here extend some results in the related literature.In chapter 3,The purpose of this paper is to study a split general nonlinear mixed variational inequality problem in Hilbert spaces.Above all,by using the resolvent operator technique,we obtain the equivalence of the generalized nonlinear mixed variational inequality problem and the resolvent equations.Next,by using this equivalence,the iterative algorithm is proposed and the convergence criteria of the iterative algorithm are discussed.In addition,we discuss the special case of split generalized nonlinear mixed variational inequalities.