IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v203y2024i2d10.1007_s10957-024-02385-7.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-024-02385-7
    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/s10957-024-02385-7?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. 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. Yuan, Zhao & Hesamzadeh, Mohammad Reza, 2017. "Hierarchical coordination of TSO-DSO economic dispatch considering large-scale integration of distributed energy resources," Applied Energy, Elsevier, vol. 195(C), pages 600-615.
    3. 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.
    4. 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).
    5. 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.
    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. Vitaly G. Il’ichev & Dmitry B. Rokhlin, 2022. "Internal Prices and Optimal Exploitation of Natural Resources," Mathematics, MDPI, vol. 10(11), pages 1-14, May.
    2. Yaohua Hu & Jiawen Li & Carisa Kwok Wai Yu, 2020. "Convergence rates of subgradient methods for quasi-convex optimization problems," Computational Optimization and Applications, Springer, vol. 77(1), pages 183-212, September.
    3. Lu, Renzhi & Bai, Ruichang & Ding, Yuemin & Wei, Min & Jiang, Junhui & Sun, Mingyang & Xiao, Feng & Zhang, Hai-Tao, 2021. "A hybrid deep learning-based online energy management scheme for industrial microgrid," Applied Energy, Elsevier, vol. 304(C).
    4. Stennikov, Valery & Barakhtenko, Evgeny & Mayorov, Gleb & Sokolov, Dmitry & Zhou, Bin, 2022. "Coordinated management of centralized and distributed generation in an integrated energy system using a multi-agent approach," Applied Energy, Elsevier, vol. 309(C).
    5. Fernando E. Postigo Marcos & Carlos Mateo Domingo & Tomás Gómez San Román & Bryan Palmintier & Bri-Mathias Hodge & Venkat Krishnan & Fernando De Cuadra García & Barry Mather, 2017. "A Review of Power Distribution Test Feeders in the United States and the Need for Synthetic Representative Networks," Energies, MDPI, vol. 10(11), pages 1-14, November.
    6. 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.
    7. Zhang, Xizheng & Wang, Zeyu & Lu, Zhangyu, 2022. "Multi-objective load dispatch for microgrid with electric vehicles using modified gravitational search and particle swarm optimization algorithm," Applied Energy, Elsevier, vol. 306(PA).
    8. Biggar, Darryl, 2022. "Seven outstanding issues in energy network regulation," Energy Economics, Elsevier, vol. 115(C).
    9. Dagoumas, Athanasios S. & Polemis, Michael L., 2017. "An integrated model for assessing electricity retailer’s profitability with demand response," Applied Energy, Elsevier, vol. 198(C), pages 49-64.
    10. Rafal Dzikowski, 2020. "DSO–TSO Coordination of Day-Ahead Operation Planning with the Use of Distributed Energy Resources," Energies, MDPI, vol. 13(14), pages 1-25, July.
    11. Wang, Jun & Xu, Jian & Ke, Deping & Liao, Siyang & Sun, Yuanzhang & Wang, Jingjing & Yao, Liangzhong & Mao, Beiling & Wei, Congying, 2023. "A tri-level framework for distribution-level market clearing considering strategic participation of electrical vehicles and interactions with wholesale market," Applied Energy, Elsevier, vol. 329(C).
    12. 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.
    13. Gerard, Helena & Rivero Puente, Enrique Israel & Six, Daan, 2018. "Coordination between transmission and distribution system operators in the electricity sector: A conceptual framework," Utilities Policy, Elsevier, vol. 50(C), pages 40-48.
    14. Jiang, Tao & Wu, Chenghao & Zhang, Rufeng & Li, Xue & Li, Fangxing, 2022. "Risk-averse TSO-DSOs coordinated distributed dispatching considering renewable energy and demand response uncertainties," Applied Energy, Elsevier, vol. 327(C).
    15. Hou, Lingxi & Li, Weiqi & Zhou, Kui & Jiang, Qirong, 2019. "Integrating flexible demand response toward available transfer capability enhancement," Applied Energy, Elsevier, vol. 251(C), pages 1-1.
    16. Aryandoust, Arsam & Lilliestam, Johan, 2017. "The potential and usefulness of demand response to provide electricity system services," Applied Energy, Elsevier, vol. 204(C), pages 749-766.
    17. Oskouei, Morteza Zare & Mohammadi-Ivatloo, Behnam & Abapour, Mehdi & Shafiee, Mahmood & Anvari-Moghaddam, Amjad, 2021. "Privacy-preserving mechanism for collaborative operation of high-renewable power systems and industrial energy hubs," Applied Energy, Elsevier, vol. 283(C).
    18. Talal Alazemi & Mohamed Darwish & Mohammed Radi, 2022. "TSO/DSO Coordination for RES Integration: A Systematic Literature Review," Energies, MDPI, vol. 15(19), pages 1-26, October.
    19. Gan, Wei & Yan, Mingyu & Yao, Wei & Guo, Jianbo & Ai, Xiaomeng & Fang, Jiakun & Wen, Jinyu, 2021. "Decentralized computation method for robust operation of multi-area joint regional-district integrated energy systems with uncertain wind power," Applied Energy, Elsevier, vol. 298(C).
    20. 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.

    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:203:y:2024:i:2:d:10.1007_s10957-024-02385-7. 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.