A Subgradient Exgradient Proection Method For Solving Pseudomonotone Variational Inequalities Problems

In this Dissertation,on the basis of the subgradient extragradient projection algorithm proposed by Censor,Gibali and Reich,we further studies the algorithm of solving pseudomonotone variational inequality.We propose a class of subgradient extragradient projection algorithm for pseudomonotone variational inequalities.In addition,using line search to weaken the Lipschitz continuity of mappings,we present a new kind of self-adaptive subgradient extragradient projection methods.Then,we analyze and prove the convergence of the algorithm under certain assumptions,giving the numerical test of the algorithm.In the first chapter,we introduce the research background of variational inequalities,the situation at home and abroad and the content structure of the dissertation.In the second chapter,we propose a class of subgradient extragradient projection algorithm for solving pseudomonotone variational inequalities.First of all,we give a new descent direction d(x~k,?)=(1/?)(x~k-y~k)-(F(x~k)-F(y~k)) of the subgradient extragradient projection algorithm and prove the convergence of the algorithm.Subsequently,considering the nonnegative linear combination of the descent direction and the original descent direction,the general framework for solving the subgradient gradient algorithm is given.Finally,we prove the global convergence of the algorithm under the same assumption of the subgradient extragradient projection algorithm,giving the numerical results of the algorithm.The numerical results show that the new algorithm is of certain significance.In the third chapter,on the basis of the algorithm in the second chapter,we propose an adaptive subgradient projection algorithm for the nonlipschitz continuous variational inequalities.In order to weaken the condition of Lipschitz continuity,we constructed new algorithms using the techniques of adaptive step-size rules proposed by Han and Lo and He and Liao.Compared with the subgradient extragradient projection algorithm,this algorithm eliminates the Lipschitz continuity requirements for mapping and optimizes the step length of the algorithm,thus we also have obtained better numerical results.The fourth chapter,we study and give the main conclusion of this dissertation,illustrating the deficiency of the dissertation and giving an improvement direction.