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Inexact Alternating Direction Methods of Multipliers with Logarithmic–Quadratic Proximal Regularization

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  • Min Li

    (Southeast University)

  • Li-Zhi Liao

    (Hong Kong Baptist University)

  • Xiaoming Yuan

    (Hong Kong Baptist University)

Abstract

In the literature, it was shown recently that the Douglas–Rachford alternating direction method of multipliers can be combined with the logarithmic-quadratic proximal regularization for solving a class of variational inequalities with separable structures. This paper studies the inexact version of this combination, where the resulting subproblems are allowed to be solved approximately subject to different inexactness criteria. We prove the global convergence and establish worst-case convergence rates for the derived inexact algorithms.

Suggested Citation

  • Min Li & Li-Zhi Liao & Xiaoming Yuan, 2013. "Inexact Alternating Direction Methods of Multipliers with Logarithmic–Quadratic Proximal Regularization," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 412-436, November.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:2:d:10.1007_s10957-013-0334-4
    DOI: 10.1007/s10957-013-0334-4
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    References listed on IDEAS

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    1. NESTEROV, Yu., 2007. "Gradient methods for minimizing composite objective function," LIDAM Discussion Papers CORE 2007076, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Jiaxin Xie, 2018. "On inexact ADMMs with relative error criteria," Computational Optimization and Applications, Springer, vol. 71(3), pages 743-765, December.
    2. William W. Hager & Hongchao Zhang, 2019. "Inexact alternating direction methods of multipliers for separable convex optimization," Computational Optimization and Applications, Springer, vol. 73(1), pages 201-235, May.
    3. William W. Hager & Hongchao Zhang, 2020. "Convergence rates for an inexact ADMM applied to separable convex optimization," Computational Optimization and Applications, Springer, vol. 77(3), pages 729-754, December.
    4. Caihua Chen & Min Li & Xiaoming Yuan, 2015. "Further Study on the Convergence Rate of Alternating Direction Method of Multipliers with Logarithmic-quadratic Proximal Regularization," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 906-929, September.

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