Improved Subgradient Extragradient Algorithm And Inertial Relaxed Projection Algorithm For Variational Inequalities Problems

In this thesis,the improved subgradient extragradient algorithm and inertial relaxed projection algorithm of variational inequality are mainly studied in Hilbert space.Firstly,an improved subgradient extragradient algorithm for solving pseudomonotonic variational inequality problems is proposed.The algorithm only needs to project the feasible set once.Under the condition that Lipschitz continuity does not need to map ,the strong convergence theorem of the algorithm is established.Numerical experiments of the algorithm are given,and the results show the effectiveness of the algorithm.Secondly,when the feasible set is the lower level set of a smooth convex function,an inertial relaxed projection algorithm for solving variational inequality problems is proposed.In each iteration of the algorithm,only two projections are required to the half space of the special structure.In addition,the algorithm utilizes linear search to determine the step size of the algorithm,so it is not necessary to know the Lipschitz constant mapping .Under appropriate assumptions,it is proved that the sequence produced by the algorithm is strongly convergent in the Hilbert space.Finally,numerical experiments are given,and the results show the effectiveness of the algorithm.