Inertial Projection-type Algorithms For Variational Inequalities

The solution of variational inequality problem is an important branch of the optimization method and a significant part of nonlinear functional analysis.In order to explore relevant convergent results and analyze error estimates,the research of algorithms for solving variational inequality problem has attracted many scholar’s attention.This paper focuses on the inertial projection algorithm for finding the common elements of variational inequality problems and fixed point problems.The paper is divided into five chapters.In the first chapter,the research background and significance of the variational inequality problem are summarized,the current research status of this topic at home and abroad is analyzed,and the research content and main structure of the paper are introduced.In the second chapter,the common symbols and basic definitions involved in this article are mainly introduced,as well as the basic propositions and basic theorems required for theorem proof.In the third chapter,an inertial project algorithm is proposed to solve the common elements of the solution set of the variational inequality problem and the fix point set of quasi-strict pseudo contractive mapping.Under the assumption that the mapping is monotone and continuous,the strong convergence of the algorithm is obtained.Finally,the numerical experiment is reported for the proposed algorithm.In the fourth chapter,an inertial sub-gradient extra-gradient algorithm is introduced for solving the variatianal inequality problem.Under the assumption that the mapping is pseudo-monotone and Lipschitz continuous,the strong convergence of the algorithm is proved.At the same time,numerical experiments are carried out on the established algorithm to verify the effectiveness of the algorithm.In the fifth chapter,summarizes the main results and innovation of the full text,and further research on variational inequality is expected.