Global convergence of an inexact operatorsplitting method  for monotone variational inequalities

Zhili Ge; Gang Qian; Deren Han

doi:10.3934/jimo.2011.7.1013

Article Contents

2011, Volume 7, Issue 4: 1013-1026. Doi: 10.3934/jimo.2011.7.1013

This issue Previous Article Duality in linear programming: From trichotomy to quadrichotomy Next Article Nonconvex quadratic reformulations and solvable conditions for mixed integer quadratic programming problems

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

1.
School of Mathematical Sciences, Key Laboratory for NSLSCS of Jiangsu Province, Nanjing Normal University, Nanjing 210046
2.
School of Computer Sciences, Nanjing Normal University, Nanjing 210097

Received: October 2010

Revised: July 2011

Published: October 2011

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Abstract

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.

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Mathematics Subject Classification: Primary: 90B20, 49J20, 90B50, 90C33.

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