Double Projection Algorithm And Subgradient Extragradient Algorithm For Variational Inequalities

Projection algorithm is a class of important algorithms for studying variational inequalities.In this paper,we study the double projection algorithm and subgradient extragradient projection algorithm for variational inequalities.First,we propose a new double projection algorithm for solving variational inequalities,by constructing a new hyperplane which is different from the known methods.Under the condition that the solution set of variational inequality is nonempty and the mapping is pseudomonotone continuous,we prove the global convergence of the algorithm.If the local error bound condition holds and the mapping is Lipschitz continuous,the convergence rate analysis of the algorithm is established.Numerical experiments show that our algorithm is effective.Then,we construct a new search direction and use a convex combination to establish a new iteration point,and propose a new subgradient extragradient algorithm for solving variational inequalities.Under the assumption that the mapping is continuous and pseudomonotone,we get the global convergence of the algorithm.Finally,the numerical results are presented.