New step lengths in projection method for variational inequality problems

摘要

In this paper, we consider projection method for variational inequality problems. First, we give a new modification of recently proposed self-adaptive step length rules, with possibly minimal parameters. Then, the resulting self-adaptive projection method is proven to converge globally at a R-linear rate provided that the underlying mapping is strongly monotone and Lipschitz continuous. Preliminary numerical results confirm its flexibility and effectiveness.