The Extragradient-type Algorithms For Solving Variational Inequalities And It's Applications

The problem of variational inequality is an essential tool in many fields of mathematics and applied science.such as systems of equations,complementarity problems,and many equilibrium problems can be expressed in terms of variational inequalities.Projection method,as an important tool to solve the approximate solution of variational inequality,has been favored by many scholars.In this thesis,through the study of extragradient projection algorithm,two extragradient-type algorithms are proposed to solve the problem of variational inequality.This thesis is divided into five chapters:In the first chapter,the research background and significance of the problem of variational inequality are summarized,the research status of this topic at home and abroad,and the research content and the main structure of this thesis are introduced.In the second chapter,the basic definitions involved in this paper,as well as the basic propositions and theorems needed for subsequent proof are introduced.In the third chapter,an inertial Tseng extragradient algorithm is proposed to solve the multi-valued variational inequality problems.Under the pseudo-monotonic condition of the algorithm,the convergence is proved,and the effectiveness of the algorithm is verified by comparing two different numerical examples with the other two documents.In the fourth chapter,an inertial subgradient extragradient algorithm is proposed to solve the bilevel variational inequality problems.Under the pseudo-monotonic condition of the algorithm,the convergence is proved,and the effectiveness of the algorithm is verified by comparing two different numerical examples with the other two documents.In the fifth chapter,the main results and innovations of the paper are summarized,and the further research on the algorithm of variational inequality problem is prospected.