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A Linearized Proximal ADMM for Stochastic and Large-scale Convex Optimization

Author

Listed:
  • Haiming Song

    (Jilin University, Changchun)

  • Hao Wang

    (Jilin University, Changchun)

  • Jiageng Wu

    (Jilin University, Changchun)

  • Jinda Yang

    (Lanzhou University, Lanzhou)

Abstract

The alternating direction method of multipliers (ADMM) has been widely applied in the field of data science. In this paper, we develop an ADMM-type scheme for solving separable convex problems with linear constraints in stochastic and large-scale models. To achieve a balance in computational load, we suggest a proximal linearization of the primal subproblem by the stochastic first-order oracle, while reshaping the dual subproblem for easier solvability. Inheriting the benefits of the balance methodology and first-order approximation, the proposed algorithm is applicable to a broad class of problems even with functions that have no closed-form solution to the subproblem. Convergence analyses are established for various cases of the objective function and a proper extrapolation has been also discussed with underlying weight. Numerical experiments demonstrate that our algorithm is effective and promising for solving problems with application to data science.

Suggested Citation

  • Haiming Song & Hao Wang & Jiageng Wu & Jinda Yang, 2025. "A Linearized Proximal ADMM for Stochastic and Large-scale Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 207(2), pages 1-31, November.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:2:d:10.1007_s10957-025-02773-7
    DOI: 10.1007/s10957-025-02773-7
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    References listed on IDEAS

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    1. Deren Han & Defeng Sun & Liwei Zhang, 2018. "Linear Rate Convergence of the Alternating Direction Method of Multipliers for Convex Composite Programming," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 622-637, May.
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