IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v168y2016i1d10.1007_s10957-015-0758-0.html
   My bibliography  Save this article

Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization

Author

Listed:
  • Andrea Simonetto

    (Delft University of Technology)

  • Hadi Jamali-Rad

    (Delft University of Technology)

Abstract

Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled, the dual decomposition scheme involves local parallel subgradient calculations and a global subgradient update performed by a master node. In this paper, we propose a consensus-based dual decomposition to remove the need for such a master node and still enable the computing nodes to generate an approximate dual solution for the underlying convex optimization problem. In addition, we provide a primal recovery mechanism to allow the nodes to have access to approximate near-optimal primal solutions. Our scheme is based on a constant stepsize choice, and the dual and primal objective convergence are achieved up to a bounded error floor dependent on the stepsize and on the number of consensus steps among the nodes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:1:d:10.1007_s10957-015-0758-0
    DOI: 10.1007/s10957-015-0758-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-015-0758-0
    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/s10957-015-0758-0?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. A. Nedić & A. Ozdaglar, 2009. "Subgradient Methods for Saddle-Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 205-228, July.
    2. L. Xiao & S. Boyd, 2006. "Optimal Scaling of a Gradient Method for Distributed Resource Allocation," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 469-488, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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. 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.
    3. 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.

    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. Ion Necoara & Yurii Nesterov & François Glineur, 2017. "Random Block Coordinate Descent Methods for Linearly Constrained Optimization over Networks," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 227-254, April.
    2. Hua Han & Lang Li & Lina Wang & Mei Su & Yue Zhao & Josep M. Guerrero, 2017. "A Novel Decentralized Economic Operation in Islanded AC Microgrids," Energies, MDPI, vol. 10(6), pages 1-18, June.
    3. Vinayaka G. Yaji & Shalabh Bhatnagar, 2020. "Stochastic Recursive Inclusions in Two Timescales with Nonadditive Iterate-Dependent Markov Noise," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1405-1444, November.
    4. Liusheng Hou & Hongjin He & Junfeng Yang, 2016. "A partially parallel splitting method for multiple-block separable convex programming with applications to robust PCA," Computational Optimization and Applications, Springer, vol. 63(1), pages 273-303, January.
    5. William La Cruz, 2022. "A genetic algorithm with a self-reproduction operator to solve systems of nonlinear equations," Journal of Global Optimization, Springer, vol. 84(4), pages 1005-1032, December.
    6. Guangming Zhou & Qin Wang & Wenjie Zhao, 2020. "Saddle points of rational functions," Computational Optimization and Applications, Springer, vol. 75(3), pages 817-832, April.
    7. Huang, Lei & Sun, Wei & Li, Qiyue & Li, Weitao, 2023. "Distributed real-time economic dispatch for islanded microgrids with dynamic power demand," Applied Energy, Elsevier, vol. 342(C).
    8. Yajie Jiang & Siyuan Cheng & Haoze Wang, 2023. "Distributed Integral Convex Optimization-Based Current Control for Power Loss Optimization in Direct Current Microgrids," Energies, MDPI, vol. 16(24), pages 1-17, December.
    9. Hongsheng Liu & Shu Lu, 2019. "Convergence of the augmented decomposition algorithm," Computational Optimization and Applications, Springer, vol. 72(1), pages 179-213, January.
    10. Desmond Cai & Subhonmesh Bose & Adam Wierman, 2019. "On the Role of a Market Maker in Networked Cournot Competition," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1122-1144, August.
    11. Denizalp Goktas & Amy Greenwald, 2022. "Gradient Descent Ascent in Min-Max Stackelberg Games," Papers 2208.09690, arXiv.org.
    12. Flåm, Sjur Didrik, 2015. "Bilateral exchange and competitive equilibrium," Working Papers in Economics 05/15, University of Bergen, Department of Economics.
    13. Sjur Didrik Flåm, 2016. "Noncooperative games, coupling constraints, and partial efficiency," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 213-229, October.
    14. Wenjie Zhao & Guangming Zhou, 2022. "Local saddle points for unconstrained polynomial optimization," Computational Optimization and Applications, Springer, vol. 82(1), pages 89-106, May.
    15. Regina S. Burachik & Alfredo N. Iusem & Jefferson G. Melo, 2013. "An Inexact Modified Subgradient Algorithm for Primal-Dual Problems via Augmented Lagrangians," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 108-131, April.
    16. Samira Mir Mazhari Anvar & Sohrab Khanmohammadi & Javad Musevi niya, 2016. "Game theoretic power allocation for fading MIMO multiple access channels with imperfect CSIR," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 61(4), pages 875-886, April.
    17. Avinash N. Madavan & Subhonmesh Bose, 2021. "A Stochastic Primal-Dual Method for Optimization with Conditional Value at Risk Constraints," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 428-460, August.
    18. Ion Necoara & Andrei Patrascu, 2014. "A random coordinate descent algorithm for optimization problems with composite objective function and linear coupled constraints," Computational Optimization and Applications, Springer, vol. 57(2), pages 307-337, March.
    19. Sjur Didrik Flåm, 2019. "Blocks of coordinates, stochastic programming, and markets," Computational Management Science, Springer, vol. 16(1), pages 3-16, February.
    20. Guigues, Vincent & Shapiro, Alexander & Cheng, Yi, 2023. "Duality and sensitivity analysis of multistage linear stochastic programs," European Journal of Operational Research, Elsevier, vol. 308(2), pages 752-767.

    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:168:y:2016:i:1:d:10.1007_s10957-015-0758-0. 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.