Solution Continuity And Gap Functions With Error Bounds For Generalized Vector Equilibrium Problems

The vector equilibrium problem is an important model in the field of vector optimization and nonlinear analysis.It is also famous for the generalized Ky Fan inequality,and it contains the vector variational inequality,the vector complementarity problem,and the vector optimization problem as special cases.Stability analysis occupies a central position in mathematical optimization,including solution semicontinuity,Lipschitz continuity,H(?)lder continuity,error bounds and so on.The scalarization method is a kind of practical processing method to solve the vector equilibrium problem.The application of it to the solution continuity,gap functions and error bounds for unified vector equilibrium problems based on improvement sets is the focus of this thesis.In this thesis,firstly,we discuss useful linear scalarization characterizations to solutions for unified vector equilibrium problems via improvement sets.Then,using scalarization methods and main assumptions of generalized convexity and monotonicity,the solution continuity for parametric unified vector equilibrium problems,(regularized)gap functions and error bounds,and gap functions via the minimax strategy for unified vector equilibrium problems under improvement sets are investigated,respectively.Our results generalize or improve related ones in the literature.Secondly,we extend all discussions to more general models with set-valued mappings by the above ideas.Similarly,using linear scalarization approaches,the solution continuity for parametric unified set-valued vector equilibrium problems,(regularized)gap functions and error bounds,and gap functions via the minimax strategy for unified set-valued vector equilibrium problems under improvement sets are investigated as well,respectively.Especially,the results obtained on(regularized)gap functions and error bounds are general and new.