Global convergence of an inexact operatorsplitting method for monotone variational inequalities
Global convergence of an inexact operatorsplitting method for monotone variational inequalities
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DOI：
10.3934/jimo.2011.7.1013
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发表时间：
2011-08
影响因子：
1.3
通讯作者：
Zhili Ge;Gang Qian;Deren Han
中科院分区：
文献类型：
--
作者：
Zhili Ge;Gang Qian;Deren Han
最近，Han D .，基于自适应策略的变分不等式问题的不精确算子分裂方法，优化理论与应用学报，132,227-243(2007))提出了一种求解变分不等式问题的不精确算子分裂方法。它比经典的算子分裂方法Douglas-Peaceman-Rachford-Varga算子分裂方法（DPRV方法）及其一些变体具有优势，因为它在每次迭代中求解子问题时采用了非常灵活的近似规则。然而，它的收敛性是在底层映射$F$是强单调的较严格条件下建立的。本文主要建立了该方法在底层映射$F$为单调的较弱条件下的全局收敛性，从而相对扩展了该方法的应用领域。给出了一些数值结果来说明该方法。
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.