The Scalarization Of Generalized Mixed Vector Variational Inequalities And A Class Of Equilibrium Problems And Their Applications

Konnov has put forward the scalarization method to the vector variational inequalities(VVI).The strongly variational inequalities(SVI)and the weakly variational inequalities(WVI)are further discussed and generalized by this method.The strongly generalized mixed vector variational inequalities(SGMVVI)and weakly generalized mixed vector variational inequalities(WGMVVI)are introduced.Specically,considering their gap functions,we obtain the relationship between the strongly generalized mixed variational inequalities(SGMVI)gap function and SGMVVI gap function and also between the WGMVVI gap function and SGMVI gap function under the weak conditions.By using their gap function,we apply to the global error bound.Then,basing on the characteristics of the dual cone,generalized equilibrium problem can be reached the purpose of scalarization.Therefore,we also provide a scalarization for generalized vector equilibrium problem.The main contents are as follows:In the first chapter,we introduce the background of vector variational inequality and the situation of the abroad and the work will do what we intend to.In the second chapter,we give necessary preliminary knowledge.For generalized mixed vector variational inequalities,we give the generalized mixed variational inequality and its gap function,which makes it to achieve the purpose of scalarization under the certain conditions.Then,using the generalized mixed variational inequality and its gap function,we discuss relationship of solution of variational inequalities.In the third chapter,we use the characteristics of dual cone to scalar the generalized vector equilibrium problem.In the fourth chapter,we consider gap function of the new generalized vector variational inequality,which apply to the global error bounds.And we apply the conclusion of generalized vector equilibrium problem scalarization to vector variational inequality problems in the Euclidean space.In the fifth chapter,we give the summary and the work of the future.