New Forward Backward Splitting Methods for Solving Pseudomonotone Variational Inequalities

In this paper, we propose the new forward backward splitting method for solving variational inequality problem. The proposed method can be viewed as an extension of the extragradient method by additional projection step at each iteration under the relaxed condition that the mapping is pseudomonotone. The convergence of the proposed method has been proved. Moreover, to show the effectiveness of the proposed method the numerical experiments are performed.