A new inexact alternating directions method for monotone variational inequalities

The alternating directions method (ADM) is an effective method for solving a class of variational inequalities (VI) when the proximal and penalty parameters in sub-VI problems are properly selected. In this paper, we propose a new ADM method which needs to solve two strongly monotone sub-VI problems...

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Bibliographic Details
Published inMathematical programming Vol. 92; no. 1; pp. 103 - 118
Main Authors He, Bingsheng, Liao, Li-Zhi, Han, Deren, Yang, Hai
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.03.2002
Subjects
Lagrange multiplier
Mathematics
Methods
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Summary:The alternating directions method (ADM) is an effective method for solving a class of variational inequalities (VI) when the proximal and penalty parameters in sub-VI problems are properly selected. In this paper, we propose a new ADM method which needs to solve two strongly monotone sub-VI problems in each iteration approximately and allows the parameters to vary from iteration to iteration. The convergence of the proposed ADM method is proved under quite mild assumptions and flexible parameter conditions.
ISSN:0025-5610
1436-4646
DOI:10.1007/s101070100280