A NEW ITERATIVE METHOD FOR SOLVING PSEUDOMONOTONE VARIATIONAL INEQUALITIES

Abstract

In this paper, we introduce a modified algorithm for pseudomono- tone variational inequalities. This problem has many important applications in different fields such as optimization problem, Nash equilibrium problem, game theory, traffic equilibrium problem, fixed point problem. The proposed algorithm bases on the self-adaptive method and the modified Popov extragradient method that have been applied to solve many other problems with Lipschitz continuous mapping. The advantage of the algorithm is that it only needs to compute one value of the inequality mapping as well as it does not require knowing the Lipschitz constants of the variational inequality mapping. Moreover, our algorithm does not require its step-sizes tending to zero. This feature helps to speed up our method. The convergence of the method has been proved based on the specified conditions of the parameters. A numerical experiment in Euclidean spaces is given to illustrate the convergence of the new algorithm.