Stability Of Solutions To Inverse Quasi-variational Inequality Problem

This thesis mainly studies the properties of solutions inverse quasi-variational inequality problems.First,we investigate the existence and Hadamard well-posedness of solutions to inverse quasi-variational inequality problems.Then,we study an approximation theorem and generic convergence of solutions of inverse quasi-variational inequality problems under the perspective of bounded rationality.Finally,the structural stability and robustness of solutions to inverse quasi-variational inequality problems are studied under bounded rationality.This thesis is divided six chapters as follows:In chapter 1,the research background and current situation of variational inequality,quasivariational inequality,inverse variational inequality and inverse quasi-variational inequality problems are introduced,and the main research work and the innovation of this thesis are clarified.In chapter 2,the continuity of the set-valued mappings and the other related properties are introduced.In chapter 3,we first give the existence theorem for solutions to inverse quasi-variational inequality problems.Then,the definitions of convergence of the sequence for inverse quasivariational inequality problems and the upper semi-continuity of the solution set mapping are given under certain conditions.Finally,the Hadamard well-posedness of inverse quasivariational inequality problems is explored,and a sufficient condition for the Hadamard wellposedness of inverse quasi-variational inequality problems to hold is obtained.In chapter 4,we first define the concept of the -approximation solution for the inverse quasi-variational inequality problems.Then,we investigate the approximation theorem that satisfies fairly mild assumptions.Finally,we establish a function space and prove that the solutions of inverse quasi-variational inequality problems have generic convergence results on the meaning of Baire category with perturbation of the objective function by means of Fort’s theorem and set-valued analysis.In chapter 5,under bounded rationality,the stability of solutions for inverse quasi-variational inequality problems is discussed by structuring a rationality function and establishing bounded rationality model for the inverse quasi-variational inequality problems.we prove that most of inverse quasi-variational inequality problems are structurally stable and robust to-approximation solution on the meaning of Baire category.In chapter 6,we summarize and look forward to the contents of chapters 3,4 and 5.