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A new inexact alternating directions method for monotone variational inequalities

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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.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, P.R. China, e-mail: hebma@nju.edu.cn, , , , , , CN

    Bingsheng He

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong, P.R. China, e-mail: liliao@hkbu.edu.hk, , , , , , CN

    Li-Zhi Liao

  3. Department of Mathematics, Nanjing University, Nanjing, 210093, P.R. China, e-mail: handr@263.net, , , , , , CN

    Deren Han

  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.hk, , , , , , CN

    Hai Yang

Authors
  1. Bingsheng He
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  2. Li-Zhi Liao
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  3. Deren Han
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  4. Hai Yang
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Additional information

Received: January 4, 2000 / Accepted: October 2001¶Published online February 14, 2002

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He, B., Liao, LZ., Han, D. et al. A new inexact alternating directions method for monotone variational inequalities. Math. Program. 92, 103–118 (2002). https://doi.org/10.1007/s101070100280

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  • DOI: https://doi.org/10.1007/s101070100280