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

Abstract

Recently, Han (Han D, Inexact operator splitting methods with self-adaptive strategy for variational inequality problems, Journal of Optimization Theory and Applications132, 227-243 (2007))proposed an inexact operator splitting method for solvingvariational inequality problems. It has advantage over the classicaloperator splitting method of Douglas-Peaceman-Rachford-Vargaoperator splitting methods (DPRV methods) and some of theirvariants, since it adopts a very flexible approximate rule insolving the subproblem in each iteration.However, its convergence is established under somewhat stringent condition that the underlyingmapping $F$ is strongly monotone. In this paper, we mainly establish the globalconvergence of the method under weaker condition that the underlying mapping$F$ is monotone, which extends the fields of applications of the method relatively.Some numerical results are also presented to illustrate the method.