Modified projection method and strong convergence theorem for solving variational inequality problems with non-Lipschitz operators

Abstract

In this paper, we introduce a modified projection method and give a strong convergence theorem for solving variational inequality problems in real Hilbert spaces. Under mild assumptions, there exists a novel line-search rule that makes the proposed algorithm suitable for non-Lipschitz continuous and pseudo-monotone operators. Compared with other known algorithms in numerical experiments, it is shown that our algorithm has better numerical performance.