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Proximal nested primal-dual gradient algorithms for distributed constraint-coupled composite optimization

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  • Li, Jingwang
  • An, Qing
  • Su, Housheng

Abstract

In this paper, we study a class of distributed constraint-coupled optimization problems, where each local function is composed of a smooth and strongly convex function and a convex but possibly non-smooth function. We design a novel proximal nested primal-dual gradient algorithm (Prox-NPGA), which is a generalized version of the exiting algorithm–NPGA. The convergence of Prox-NPGA is proved and the upper bounds of the step-sizes are given. Finally, numerical experiments are employed to verify the theoretical results and compare the convergence rates of different versions of Prox-NPGA.

Suggested Citation

  • Li, Jingwang & An, Qing & Su, Housheng, 2023. "Proximal nested primal-dual gradient algorithms for distributed constraint-coupled composite optimization," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    • Handle: RePEc:eee:apmaco:v:444:y:2023:i:c:s0096300322008694
    DOI: 10.1016/j.amc.2022.127801
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    References listed on IDEAS

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    1. Wei Ni & Xiaoli Wang, 2022. "A Multi-Scale Method for Distributed Convex Optimization with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 379-400, January.
    2. Yurii Nesterov, 2018. "Lectures on Convex Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-91578-4, March.
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    4. Sakurama, Kazunori & Miura, Masashi, 2017. "Distributed constraint optimization on networked multi-agent systems," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 272-281.
    5. Li, Jun & Ji, Lianghao & Li, Huaqing, 2021. "Optimal consensus control for unknown second-order multi-agent systems: Using model-free reinforcement learning method," Applied Mathematics and Computation, Elsevier, vol. 410(C).
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