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Distributed Dual Subgradient Methods with Averaging and Applications to Grid Optimization

Author

Listed:
  • Haitian Liu

    (Tsinghua University)

  • Subhonmesh Bose

    (University of Illinois Urbana Champaign)

  • Hoa Dinh Nguyen

    (Kyushu University)

  • Ye Guo

    (Tsinghua University)

  • Thinh T. Doan

    (Virginia Tech)

  • Carolyn L. Beck

    (University of Illinois Urbana Champaign)

Abstract

We study finite-time performance of a recently proposed distributed dual subgradient (DDSG) method for convex-constrained multi-agent optimization problems. The algorithm enjoys performance guarantees on the last primal iterate, as opposed to those derived for ergodic means for standard DDSG algorithms. Our work improves the recently published convergence rate of $${{\mathcal {O}}}(\log T/\sqrt{T})$$ O ( log T / T ) with decaying step-sizes to $${{\mathcal {O}}}(1/\sqrt{T})$$ O ( 1 / T ) with constant step-size on a metric that combines sub-optimality and constraint violation. We then numerically evaluate the algorithm on three grid optimization problems. Namely, these are tie-line scheduling in multi-area power systems, coordination of distributed energy resources in radial distribution networks, and joint dispatch of transmission and distribution assets. The DDSG algorithm applies to each problem with various relaxations and linearizations of the power flow equations. The numerical experiments illustrate various properties of the DDSG algorithm–comparison with standard DDSG, impact of the number of agents, and why Nesterov-style acceleration can fail in DDSG settings.

Suggested Citation

  • Haitian Liu & Subhonmesh Bose & Hoa Dinh Nguyen & Ye Guo & Thinh T. Doan & Carolyn L. Beck, 2024. "Distributed Dual Subgradient Methods with Averaging and Applications to Grid Optimization," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1991-2024, November.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:2:d:10.1007_s10957-024-02385-7
    DOI: 10.1007/s10957-024-02385-7
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    References listed on IDEAS

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    1. 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.
    2. Nesterov, Yu. & Shikhman, V., 2018. "Dual subgradient method with averaging for optimal resource allocation," European Journal of Operational Research, Elsevier, vol. 270(3), pages 907-916.
    3. Yurii Nesterov & Vladimir Shikhman, 2018. "Dual subgradient method with averaging for optimal resource allocation," LIDAM Reprints CORE 2973, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Wang, Jianxiao & Zhong, Haiwang & Lai, Xiaowen & Xia, Qing & Shu, Chang & Kang, Chongqing, 2017. "Distributed real-time demand response based on Lagrangian multiplier optimal selection approach," Applied Energy, Elsevier, vol. 190(C), pages 949-959.
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