Global convergence of an inexact operator splitting method for monotone variational inequalities

Recently, Han (Han D, Inexact operator splitting methods with self-adaptive strategy for variational inequality problems, Journal of Opti-mization Theory and Applications 132, 227-243 (2007)) proposed an inexact operator splitting method for solving variational inequality problems. It has advantage over the classical operator splitting method of Douglas-Peaceman-Rachford-Varga operator splitting methods (DPRV methods) and some of their variants, since it adopts a very exible approximate rule in solving the subprob-lem in each iteration. However, its convergence is established under somewhat stringent condition that the underlying mapping F is strongly monotone. In this paper, we mainly establish the global convergence of the method under weaker condition that the underlying mapping F is monotone, which extends the elds of applications of the method relatively. Some numerical results are also presented to illustrate the method.