IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v197y2023i1d10.1007_s10957-023-02173-9.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-023-02173-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-023-02173-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. R. Díaz Millán & M. Pentón Machado, 2019. "Inexact proximal $$\epsilon $$ϵ-subgradient methods for composite convex optimization problems," Journal of Global Optimization, Springer, vol. 75(4), pages 1029-1060, December.
    2. Jueyou Li & Chuanye Gu & Zhiyou Wu & Changzhi Wu, 2017. "Distributed Optimization Methods for Nonconvex Problems with Inequality Constraints over Time-Varying Networks," Complexity, Hindawi, vol. 2017, pages 1-10, December.
    3. Zheng, Yuchen & Xie, Yujia & Lee, Ilbin & Dehghanian, Amin & Serban, Nicoleta, 2022. "Parallel subgradient algorithm with block dual decomposition for large-scale optimization," European Journal of Operational Research, Elsevier, vol. 299(1), pages 60-74.
    4. William W. Hager & Hongchao Zhang, 2019. "Inexact alternating direction methods of multipliers for separable convex optimization," Computational Optimization and Applications, Springer, vol. 73(1), pages 201-235, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:197:y:2023:i:1:d:10.1007_s10957-023-02173-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.