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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
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    References listed on IDEAS

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    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.
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    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.

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