Applied and Computational Mathematics

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Distributed Subgradient Algorithm for Multi-agent Convex Optimization with Local Constraint Sets

Received: 12 June 2016    Accepted: 20 June 2016    Published: 13 July 2016
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Abstract

This paper considers a distributed constrained optimization problem, where the objective function is the sum of local objective functions of distributed nodes in a network. The estimate of each agent is restricted to different convex sets. To solve this optimization problem which is not necessarily smooth, we study a novel distributed projected subgradient algorithm for multi-agent optimization with nonidentical constraint sets and switching topologies. The algorithm shows that each agent minimizes its own objective function while communicating information locally with other agents over a network with time-varying topologies but satisfying a standard connectivity property. Under the assumption that the network topology is weight-balanced, the novel distributed subgradient algorithm we proposed is proven to be convergent. Particularly, we suppose the step-size is various, which is different from previous work on multi-agent optimization that makes worst-case assumption with constant step-size.

DOI 10.11648/j.acm.20160503.19
Published in Applied and Computational Mathematics (Volume 5, Issue 3, June 2016)
Page(s) 150-159
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Distributed Optimization, Subgradient Algorithm, Multi-agent Network, Weight-Balanced

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Author Information
  • College of Electronic and Information Engineering, Southwest University, Chongqing, PR China

  • College of Electronic and Information Engineering, Southwest University, Chongqing, PR China; State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing, PR China

  • Department of Mathematics and Information Engineering, Chongqing University of Education, Chongqing, PR China

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  • APA Style

    Qingguo Lü, Huaqing Li, Li Xiao. (2016). Distributed Subgradient Algorithm for Multi-agent Convex Optimization with Local Constraint Sets. Applied and Computational Mathematics, 5(3), 150-159. https://doi.org/10.11648/j.acm.20160503.19

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    ACS Style

    Qingguo Lü; Huaqing Li; Li Xiao. Distributed Subgradient Algorithm for Multi-agent Convex Optimization with Local Constraint Sets. Appl. Comput. Math. 2016, 5(3), 150-159. doi: 10.11648/j.acm.20160503.19

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    AMA Style

    Qingguo Lü, Huaqing Li, Li Xiao. Distributed Subgradient Algorithm for Multi-agent Convex Optimization with Local Constraint Sets. Appl Comput Math. 2016;5(3):150-159. doi: 10.11648/j.acm.20160503.19

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  • @article{10.11648/j.acm.20160503.19,
      author = {Qingguo Lü and Huaqing Li and Li Xiao},
      title = {Distributed Subgradient Algorithm for Multi-agent Convex Optimization with Local Constraint Sets},
      journal = {Applied and Computational Mathematics},
      volume = {5},
      number = {3},
      pages = {150-159},
      doi = {10.11648/j.acm.20160503.19},
      url = {https://doi.org/10.11648/j.acm.20160503.19},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20160503.19},
      abstract = {This paper considers a distributed constrained optimization problem, where the objective function is the sum of local objective functions of distributed nodes in a network. The estimate of each agent is restricted to different convex sets. To solve this optimization problem which is not necessarily smooth, we study a novel distributed projected subgradient algorithm for multi-agent optimization with nonidentical constraint sets and switching topologies. The algorithm shows that each agent minimizes its own objective function while communicating information locally with other agents over a network with time-varying topologies but satisfying a standard connectivity property. Under the assumption that the network topology is weight-balanced, the novel distributed subgradient algorithm we proposed is proven to be convergent. Particularly, we suppose the step-size is various, which is different from previous work on multi-agent optimization that makes worst-case assumption with constant step-size.},
     year = {2016}
    }
    

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    T1  - Distributed Subgradient Algorithm for Multi-agent Convex Optimization with Local Constraint Sets
    AU  - Qingguo Lü
    AU  - Huaqing Li
    AU  - Li Xiao
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    DO  - 10.11648/j.acm.20160503.19
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
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    EP  - 159
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20160503.19
    AB  - This paper considers a distributed constrained optimization problem, where the objective function is the sum of local objective functions of distributed nodes in a network. The estimate of each agent is restricted to different convex sets. To solve this optimization problem which is not necessarily smooth, we study a novel distributed projected subgradient algorithm for multi-agent optimization with nonidentical constraint sets and switching topologies. The algorithm shows that each agent minimizes its own objective function while communicating information locally with other agents over a network with time-varying topologies but satisfying a standard connectivity property. Under the assumption that the network topology is weight-balanced, the novel distributed subgradient algorithm we proposed is proven to be convergent. Particularly, we suppose the step-size is various, which is different from previous work on multi-agent optimization that makes worst-case assumption with constant step-size.
    VL  - 5
    IS  - 3
    ER  - 

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