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Distributed Optimization Algorithm for Composite Optimization Problems with Non-Smooth Function

Author

Listed:
  • Yawei Shi

    (Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China)

  • Liang Ran

    (Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China)

  • Jialong Tang

    (Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China)

  • Xiangzhao Wu

    (Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China)

Abstract

This paper mainly studies the distributed optimization problems in a class of undirected networks. The objective function of the problem consists of a smooth convex function and a non-smooth convex function. Each agent in the network needs to optimize the sum of the two objective functions. For this kind of problem, based on the operator splitting method, this paper uses the proximal operator to deal with the non-smooth term and further designs a distributed algorithm that allows the use of uncoordinated step-sizes. At the same time, by introducing the random-block coordinate mechanism, this paper develops an asynchronous iterative version of the synchronous algorithm. Finally, the convergence of the algorithms is proven, and the effectiveness is verified through numerical simulations.

Suggested Citation

  • Yawei Shi & Liang Ran & Jialong Tang & Xiangzhao Wu, 2022. "Distributed Optimization Algorithm for Composite Optimization Problems with Non-Smooth Function," Mathematics, MDPI, vol. 10(17), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3135-:d:903784
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    References listed on IDEAS

    as
    1. Laurent Condat, 2013. "A Primal–Dual Splitting Method for Convex Optimization Involving Lipschitzian, Proximable and Linear Composite Terms," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 460-479, August.
    2. Puya Latafat & Panagiotis Patrinos, 2017. "Asymmetric forward–backward–adjoint splitting for solving monotone inclusions involving three operators," Computational Optimization and Applications, Springer, vol. 68(1), pages 57-93, September.
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