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Stochastic Accelerated Alternating Direction Method of Multipliers with Importance Sampling

Author

Listed:
  • Chenxi Chen

    (University of Florida)

  • Yunmei Chen

    (University of Florida)

  • Yuyuan Ouyang

    (Clemson University)

  • Eduardo Pasiliao

    (AFB)

Abstract

In this paper, we incorporate importance sampling strategy into accelerated framework of stochastic alternating direction method of multipliers for solving a class of stochastic composite problems with linear equality constraint. The rates of convergence for primal residual and feasibility violation are established. Moreover, the estimation of variance of stochastic gradient is improved due to the use of important sampling. The proposed algorithm is capable of dealing with the situation, where the feasible set is unbounded. The experimental results indicate the effectiveness of the proposed method.

Suggested Citation

  • Chenxi Chen & Yunmei Chen & Yuyuan Ouyang & Eduardo Pasiliao, 2018. "Stochastic Accelerated Alternating Direction Method of Multipliers with Importance Sampling," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 676-695, November.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:2:d:10.1007_s10957-018-1270-0
    DOI: 10.1007/s10957-018-1270-0
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    References listed on IDEAS

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    1. NESTEROV, Yurii, 2012. "Efficiency of coordinate descent methods on huge-scale optimization problems," LIDAM Reprints CORE 2511, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Kai Tu & Haibin Zhang & Huan Gao & Junkai Feng, 2020. "A hybrid Bregman alternating direction method of multipliers for the linearly constrained difference-of-convex problems," Journal of Global Optimization, Springer, vol. 76(4), pages 665-693, April.
    2. Chih-Sheng Chuang & Hongjin He & Zhiyuan Zhang, 2022. "A unified Douglas–Rachford algorithm for generalized DC programming," Journal of Global Optimization, Springer, vol. 82(2), pages 331-349, February.
    3. Kuan Li & Chun Huang & Ziyang Yuan, 2021. "Error Estimations for Total Variation Type Regularization," Mathematics, MDPI, vol. 9(12), pages 1-14, June.

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