A Double Projection Algorithm for Solving Non-Monotone Variational Inequalities

Abstract

The projection algorithm is one of the main methods to solve variational inequality problems. At present, the research on projection algorithms usually requires the assumption that the mapping is monotone and Lipschitz continuous, but in practical problems, these assumptions are often unsatisfied. In this paper, a new double projection algorithm for solving non-monotone variational inequality problems is proposed by using the line search method. Under the assumption that the mapping is uniformly continuous, it is proved that the sequence generated by the algorithm strongly converges to a solution of variational inequalities. The numerical experiments illustrate effectiveness and superiority of the proposed algorithm.