A Subgradient Exgradient Projection Method For Pseudomonotone Variational Inequalities

Variational inequality problem received extensive attention of the experts and scholars.Projection algorithm is one of the important methods of solving variational inequality problems,so many scholars study projection algorithm for variational inequality of lithology,and get good results about projection algorithm research of the variational inequality.The main content of the research include the number of projection,projection plane and the nature of the map.The calculation to the orthogonal projection of non-empty closed convex set is more complex,on the basis of the Korpelevich's algorithm projection,so the Censor,Gibali and Reich has made the improvement.Then this paper studied the Censor in finite dimensional European space,Gibali and Reich sense outside the time gradient of variational inequality gradient projection algorithm,through the line search generalized the Censor,Gibali and Reich sense projection algorithm.In this dissertation,the main content is as following:The first chapter introduces the research background and the situation at home and abroad,and main contents of this dissertation.The second chapter reviews the concept and common conclusion as theoretical basis of this topic research,and analyzes the research status of variational inequality projection algorithm.The third chapter investigates a subgradient exgradient projection method for variational inequalities in the sense of Censor,Gibali and Reich in finite dimensional spaces.Compared with the assumptions by Censor,Gibali and Reich,we remove the Lipschitz continuity condition.Under pseudo monotonicity assumptions,by using the linear search condition of He and Liao we prove the convergence of this subgradient exgradient projection method.In the fourth chapter,on the basis of the previous chapter algorithm,through numerical experiments of the two classic examples of subgradient gradient projection algorithm for pseudo monotone variational inequalities,and from the time it takes to operation,the iteration number and the total number of projection respectively,we give a simple comparison with other algorithms.In the fifth chapter,we study and give the main conclusions of this dissertation,in order to illustrate the deficiency of the dissertation,we give an improvement direction.