Global convergence of an inexact operator splitting method for monotone variational inequalities
Zhili Ge Gang Qian Deren Han
Journal of Industrial & Management Optimization 2011, 7(4): 1013-1026 doi: 10.3934/jimo.2011.7.1013
Recently, Han (Han D, Inexact operator splitting methods with self-adaptive strategy for variational inequality problems, Journal of Optimization 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 flexible approximate rule in solving the subproblem 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 fields of applications of the method relatively. Some numerical results are also presented to illustrate the method.
keywords: self-adaptive strategy. Monotone variational inequalities operator splitting methods approximate rules

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