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Zero gradient sum algorithm of arbitrary initial value with constraints and communication delay based on directed graph.

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Titel: Zero gradient sum algorithm of arbitrary initial value with constraints and communication delay based on directed graph.
Autoren: Lin, Siman, Zhang, Xiaotang, Ren, Junwu, Tan, Manchun
Quelle: International Journal of Systems Science; Jan2025, Vol. 56 Issue 2, p267-292, 26p
Schlagwörter: LYAPUNOV functions, MACHINE learning, TOPOLOGY, ALGORITHMS, SAMPLING methods
Abstract: The distributed convex optimisation issue with inequality constraints and box constraints on the directed communication topology is examined in this paper. In the case of the communication delay between agents, we propose a piecewise zero-gradient-sum triggered control algorithm that allows arbitrary initial values. Using the log-barrier penalty method, we only need to study an unconstrained approximation problem of the original problem. Firstly, each agent's state converges to the optimal value of the related local objective function in a fixed time. Simultaneously, the upper bound of fixed time in this paper is smaller than some existing results. Then, in the case of communication delay, time-triggered and event-triggered methods with non-uniform sampling interval are proposed in this paper, which make the communication cost lower and the application broader. Using the Lyapunov function method, the sufficient conditions for each agent's state to converge to the optimal point are given, and the Zeno behaviour is excluded. Finally, to confirm the algorithm's effectiveness, we provide two numerical examples and one machine learning example as demonstrations. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Systems Science is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Label: Title
  Group: Ti
  Data: Zero gradient sum algorithm of arbitrary initial value with constraints and communication delay based on directed graph.
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  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Lin%2C+Siman%22">Lin, Siman</searchLink><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Xiaotang%22">Zhang, Xiaotang</searchLink><br /><searchLink fieldCode="AR" term="%22Ren%2C+Junwu%22">Ren, Junwu</searchLink><br /><searchLink fieldCode="AR" term="%22Tan%2C+Manchun%22">Tan, Manchun</searchLink>
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  Data: International Journal of Systems Science; Jan2025, Vol. 56 Issue 2, p267-292, 26p
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  Data: <searchLink fieldCode="DE" term="%22LYAPUNOV+functions%22">LYAPUNOV functions</searchLink><br /><searchLink fieldCode="DE" term="%22MACHINE+learning%22">MACHINE learning</searchLink><br /><searchLink fieldCode="DE" term="%22TOPOLOGY%22">TOPOLOGY</searchLink><br /><searchLink fieldCode="DE" term="%22ALGORITHMS%22">ALGORITHMS</searchLink><br /><searchLink fieldCode="DE" term="%22SAMPLING+methods%22">SAMPLING methods</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The distributed convex optimisation issue with inequality constraints and box constraints on the directed communication topology is examined in this paper. In the case of the communication delay between agents, we propose a piecewise zero-gradient-sum triggered control algorithm that allows arbitrary initial values. Using the log-barrier penalty method, we only need to study an unconstrained approximation problem of the original problem. Firstly, each agent's state converges to the optimal value of the related local objective function in a fixed time. Simultaneously, the upper bound of fixed time in this paper is smaller than some existing results. Then, in the case of communication delay, time-triggered and event-triggered methods with non-uniform sampling interval are proposed in this paper, which make the communication cost lower and the application broader. Using the Lyapunov function method, the sufficient conditions for each agent's state to converge to the optimal point are given, and the Zeno behaviour is excluded. Finally, to confirm the algorithm's effectiveness, we provide two numerical examples and one machine learning example as demonstrations. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Systems Science is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1080/00207721.2024.2392829
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      – Code: eng
        Text: English
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        PageCount: 26
        StartPage: 267
    Subjects:
      – SubjectFull: LYAPUNOV functions
        Type: general
      – SubjectFull: MACHINE learning
        Type: general
      – SubjectFull: TOPOLOGY
        Type: general
      – SubjectFull: ALGORITHMS
        Type: general
      – SubjectFull: SAMPLING methods
        Type: general
    Titles:
      – TitleFull: Zero gradient sum algorithm of arbitrary initial value with constraints and communication delay based on directed graph.
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            NameFull: Lin, Siman
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            NameFull: Zhang, Xiaotang
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            NameFull: Ren, Junwu
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          Dates:
            – D: 15
              M: 01
              Text: Jan2025
              Type: published
              Y: 2025
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