Some Relevant Research For A Class Of Quasi Variational Inequality

Variational inequality theory has emerged as an important branch of modern mathematics.It has been widely applied to many fields such as industrial,financial,economic,management and sociality.With the development of technology and the research of theory,many scholars begin to pay close attention to quasi variational inequality problems.Inspired and motivated by those new research,this paper will analyze the exsistence and uniquence of the solution for a class of quasi variational inequality.Then we use the Wiener-Hopf equation and Auxiliary principle technique to construct algorithms.We will also analyze the error bounds by merit functions.Our paper is devided into five parts.In the first chapter,we give the introduction of the research situation,the recent work in domestic and abroad and the chapters arrangement.In chapter two,we establish the equivalence between a class of the quasi variational inequality and the fixed-point problem by projection lemma in Hilbert space.Then we prove the existence and uniquence of solution under weaker conditions.we also construct the algorithms and give convergence analysis.In chapter three,we establish the equivalence between a class of the Quasi-variational inequality and the Wiener-Hopf equations in Hilbert space.Then we use the equivalence to construct the algorithms for this quasi variational inequality and give convergence analysis.In chapter four,we suggest and analysis a new Three-step predictor-corrector projection algorithm for solving a class of quasi variational inequality by using the auxiliary principle technique.Then we give convergence analysis.In chapter five,we consider merit function for quasi variational inequality.Using merit function,we obtain error bounds for the solution of quasi variational inequality.This paper extend and improve the relevant results in,such as [4],[9],[17].