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A Class of Distributed Online Aggregative Optimization in Unknown Dynamic Environment

Author

Listed:
  • Chengqian Yang

    (School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Shuang Wang

    (School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Shuang Zhang

    (College of Computer Engineering, Jimei University, Xiamen 361021, China)

  • Shiwei Lin

    (College of Computer Engineering, Jimei University, Xiamen 361021, China)

  • Bomin Huang

    (College of Computer Engineering, Jimei University, Xiamen 361021, China)

Abstract

This paper considers a class of distributed online aggregative optimization problems over an undirected and connected network. It takes into account an unknown dynamic environment and some aggregation functions, which is different from the problem formulation of the existing approach, making the aggregative optimization problem more challenging. A distributed online optimization algorithm is designed for the considered problem via the mirror descent algorithm and the distributed average tracking method. In particular, the dynamic environment and the gradient are estimated by the averaged tracking methods, and then an online optimization algorithm is designed via a dynamic mirror descent method. It is shown that the dynamic regret is bounded in the order of O ( T ) . Finally, the effectiveness of the designed algorithm is verified by some simulations of cooperative control of a multi-robot system.

Suggested Citation

  • Chengqian Yang & Shuang Wang & Shuang Zhang & Shiwei Lin & Bomin Huang, 2024. "A Class of Distributed Online Aggregative Optimization in Unknown Dynamic Environment," Mathematics, MDPI, vol. 12(16), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2460-:d:1452734
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    References listed on IDEAS

    as
    1. 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.
    2. Shuang Wang & Bomin Huang, 2024. "Distributed online optimisation in unknown dynamic environment," International Journal of Systems Science, Taylor & Francis Journals, vol. 55(6), pages 1167-1176, April.
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