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Mathematical Programming

, Volume 92, Issue 1, pp 103–118 | Cite as

A new inexact alternating directions method for monotone variational inequalities

  • Bingsheng He
  • Li-Zhi Liao
  • Deren Han
  • Hai Yang

Abstract.

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.

Key words: variational inequality – alternating directions method – inexact method Mathematics Subject Classification (1991): 90C30, 90C33, 65K05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Bingsheng He
    • 1
  • Li-Zhi Liao
    • 2
  • Deren Han
    • 3
  • Hai Yang
    • 4
  1. 1.Department of Mathematics, Nanjing University, Nanjing, 210093, P.R. China, e-mail: hebma@nju.edu.cnCN
  2. 2.Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong, P.R. China, e-mail: liliao@hkbu.edu.hkCN
  3. 3.Department of Mathematics, Nanjing University, Nanjing, 210093, P.R. China, e-mail: handr@263.netCN
  4. 4.Department of Civil Engineering, The Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong, P.R. China. e-mail: cehyang@ust.hkCN

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