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Privacy-Preserving Dual Stochastic Push-Sum Algorithm for Distributed Constrained Optimization

Author

Listed:
  • Chuanye Gu

    (Guangzhou University)

  • Lin Jiang

    (Curtin University)

  • Jueyou Li

    (Chongqing Normal University)

  • Zhiyou Wu

    (Chongqing Normal University)

Abstract

This paper investigates a private distributed optimization problem over a multi-agent network, where the goal is to cooperatively minimize the sum of all locally convex cost functions subject to coupled equality constraints over time-varying unbalanced directed networks while considering privacy concerns. To solve this problem, we integrate push-sum protocols with dual subgradient methods to design a private distributed dual stochastic push-sum algorithm. Under the assumption of convexity, we first establish the convergence of the algorithm in terms of dual variables, primal variables and constraint violations. Then we show that the algorithm has a sub-linear growth with order of $$O(\ln t/\sqrt{t})$$ O ( ln t / t ) . The result reveals that there is a tradeoff between the privacy level and the accuracy of the algorithm. Finally, the efficiency of the algorithm is verified numerically over two applications to the economic dispatch problems and electric vehicles charging control problems.

Suggested Citation

  • Chuanye Gu & Lin Jiang & Jueyou Li & Zhiyou Wu, 2023. "Privacy-Preserving Dual Stochastic Push-Sum Algorithm for Distributed Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 22-50, April.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:1:d:10.1007_s10957-023-02173-9
    DOI: 10.1007/s10957-023-02173-9
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    References listed on IDEAS

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    1. Maude J. Blondin & Matthew Hale, 2021. "A Decentralized Multi-objective Optimization Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 458-485, May.
    2. Bin Du & Jiazhen Zhou & Dengfeng Sun, 2020. "Improving the Convergence of Distributed Gradient Descent via Inexact Average Consensus," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 504-521, May.
    3. Jueyou Li & Zhiyou Wu & Changzhi Wu & Qiang Long & Xiangyu Wang, 2016. "An Inexact Dual Fast Gradient-Projection Method for Separable Convex Optimization with Linear Coupled Constraints," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 153-171, January.
    4. Zhengqing Shi & Chuan Zhou, 2019. "An Improved Distributed Gradient-Push Algorithm for Bandwidth Resource Allocation over Wireless Local Area Network," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 1153-1176, December.
    5. Andrea Simonetto & Hadi Jamali-Rad, 2016. "Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 172-197, January.
    6. Shengnan Wang & Chunguang Li, 2018. "Distributed Stochastic Algorithm for Global Optimization in Networked System," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 1001-1007, December.
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