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Consensus-based distributed optimisation of multi-agent networks via a two level subgradient-proximal algorithm

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Listed:
  • Bin Hu
  • Zhi-Hong Guan
  • Rui-Quan Liao
  • Ding-Xue Zhang
  • Gui-Lin Zheng

Abstract

This paper presents a consensus-based stochastic subgradient algorithm for multi-agent networks to minimise multiple convex but not necessarily differential objective functions, subject to an intersection set of multiple closed convex constraint sets. Compared with the existing results an alternative subgradient algorithm is first introduced based on two level subgradient iterations, where the first level is to minimise the component functions, and the second to enforce the iterates not oscillate from the constraint set wildly. In addition, a distributed consensus-based type of the proposed subgradient algorithm is constructed within the framework of multi-agent networks for the case when the iteration index of local objective functions and local constraint sets is not homologous. Detailed convergence analysis of the proposed algorithms is established using matrix theories and super-martingale convergence theorem. In addition, a pre-step convergence factor is obtained in this study to characterise the distance between the iterations and the optimal set, while some existing literatures only present a convergence work. Simulation results are given to demonstrate the effectiveness of the developed theoretical results.

Suggested Citation

  • Bin Hu & Zhi-Hong Guan & Rui-Quan Liao & Ding-Xue Zhang & Gui-Lin Zheng, 2015. "Consensus-based distributed optimisation of multi-agent networks via a two level subgradient-proximal algorithm," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(7), pages 1307-1318, May.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:7:p:1307-1318
    DOI: 10.1080/00207721.2013.822122
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    References listed on IDEAS

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    1. Fenglan Sun & Zhi-Hong Guan & Li Ding & Yan-Wu Wang, 2013. "Mean square average-consensus for multi-agent systems with measurement noise and time delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(6), pages 995-1005.
    2. Jiahu Qin & Huijun Gao & Wei Xing Zheng, 2011. "On average consensus in directed networks of agents with switching topology and time delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(12), pages 1947-1956.
    3. S. Sundhar Ram & A. Nedić & V. V. Veeravalli, 2010. "Distributed Stochastic Subgradient Projection Algorithms for Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 516-545, December.
    4. Quanjun Wu & Jin Zhou & Lan Xiang, 2012. "Impulsive consensus seeking in directed networks of multi-agent systems with communication time delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(8), pages 1479-1491.
    5. Lina Rong & Shengyuan Xu & Baoyong Zhang & Yun Zou, 2013. "Accelerating average consensus by using the information of second-order neighbours with communication delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(6), pages 1181-1188.
    6. Fenglan Sun & Zhi-Hong Guan, 2013. "Finite-time consensus for leader-following second-order multi-agent system," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(4), pages 727-738.
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