Modified self-adaptive projection method for solving pseudomonotone variational inequalities

In this paper, a self-adaptive projection method with a new search direction for solving pseudomonotone variational inequality (VI) problems is proposed, which can be viewed as an extension of the methods in B.S. He, X.M. Yuan, J.Z. Zhang, Comparison of two kinds of prediction-correction methods for monotone variational inequalities, Computational Optimization and Applications 27 (2004) 247-267] and X.H. Yan, D.R. Han, W.Y. Sun, A self-adaptive projection method with improved step-size for solving variational inequalities, Computers & Mathematics with Applications 55 (2008) 819-832]. The descent property of the new search direction is proved, which is useful to guarantee the convergence. Under the relatively relaxed condition that F is continuous and pseudomonotone, the global convergence of the proposed method is proved. Numerical experiments are provided to illustrate the efficiency of the proposed method.