The Gap Functions, Error Bound And Algorithm Of Some Variational Inequalities

Abstract: In this dissertation, we mainly study the gap functions and the error bound of set-valued quasi-variational inequalities, and the projection algo-rithm for set-valued variational inequality problems. The thesis is divided into three chapters:In chapter 1, we introduce the research status, present situation and the main contents of this thesis.In chapter 2, we consider the gap functions for set-valued quasi-variational inequalities. Using these functions, we show the equivalence between optimiza-tion problem and the set-valued quasi-variational inequalities. We also use this equivalence to study error bounds for the solutions of set-valued quasi-variational inequalities.In chapter 3, we present a new projection algorithm for solving the set-valued mixed variational inequalities. At each step of the iteration, the current point xi is first utilized, and the zi is obtained by calculating the resolvent operator, and the iteration step size is satisfied with an kind of Armijo linesearch. Then, we use zi to construct a superplane to separate the current point xi and solution set of set-valued mixed variational inequalities, and then the current point is projected into the superplane to get the next iteration point. Under certain conditions, the infinite sequence generated by the algorithm is globally convergent. At the same time, the numerical results show that the algorithm is effective.