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Distributed dual consensus algorithm for time-varying optimization with coupled equality constraint

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  • Yue, Yuanyuan
  • Liu, Qingshan

Abstract

This paper introduces a distributed continuous-time algorithm that utilizes dual consensus to tackle the optimization problem involving time-varying (TV) local objective functions and TV coupled equality constraint. Here, the local objective functions can be any strongly convex functions. The optimum solution is represented by a trajectory rather than a fixed point, owing to the dynamic nature of the objective functions and the constraint. The initial step involves converting the studied problem into an equivalent saddle-point problem. Subsequently, we provide the optimal conditions for this transformed problem. Then a distributed continuous-time algorithm based on dual consensus is provided, guaranteeing that all agents possess the capability to discover and follow the optimal TV trajectories. It is noticeable that there are no limitations imposed on the information regarding local objective functions and the coupled equality constraint except for the strongly convexity of local objective functions. In addition, two simulation instances and the comparisons with state-of-the-art methods are performed in order to validate the proposed algorithm.

Suggested Citation

  • Yue, Yuanyuan & Liu, Qingshan, 2024. "Distributed dual consensus algorithm for time-varying optimization with coupled equality constraint," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    • Handle: RePEc:eee:apmaco:v:474:y:2024:i:c:s009630032400184x
    DOI: 10.1016/j.amc.2024.128712
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    References listed on IDEAS

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    1. Yu, Yongchao & Peng, Jigen, 2018. "A modified primal-dual method with applications to some sparse recovery problems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 76-94.
    2. Che, Haitao & Liu, Kaiping & Chen, Haibin & Yan, Hong, 2023. "Second order self-adaptive dynamical system for sparse signal reconstruction and applications to image recovery," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    3. Liu, Chunxia & Lu, Kaihong & Chen, Xiaojie & Szolnoki, Attila, 2023. "Game-theoretical approach for task allocation problems with constraints," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    4. Golmisheh, Fatemeh Mahdavi & Shamaghdari, Saeed, 2024. "Heterogeneous optimal formation control of nonlinear multi-agent systems with unknown dynamics by safe reinforcement learning," Applied Mathematics and Computation, Elsevier, vol. 460(C).
    5. Peng, Bo & Xu, Hong-Kun, 2020. "Proximal methods for reweighted lQ-regularization of sparse signal recovery," Applied Mathematics and Computation, Elsevier, vol. 386(C).
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