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Convergence Analysis of the Generalized Alternating Direction Method of Multipliers with Logarithmic–Quadratic Proximal Regularization

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  • Min Li

    (Southeast University)

  • Xinxin Li

    (Hong Kong Baptist University)

  • Xiaoming Yuan

    (Hong Kong Baptist University)

Abstract

We consider combining the generalized alternating direction method of multipliers, proposed by Eckstein and Bertsekas, with the logarithmic–quadratic proximal method proposed by Auslender, Teboulle, and Ben-Tiba for solving a variational inequality with separable structures. For the derived algorithm, we prove its global convergence and establish its worst-case convergence rate measured by the iteration complexity in both the ergodic and nonergodic senses.

Suggested Citation

  • Min Li & Xinxin Li & Xiaoming Yuan, 2015. "Convergence Analysis of the Generalized Alternating Direction Method of Multipliers with Logarithmic–Quadratic Proximal Regularization," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 218-233, January.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:1:d:10.1007_s10957-014-0567-x
    DOI: 10.1007/s10957-014-0567-x
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    References listed on IDEAS

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    1. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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