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Modified graph systems for distributed optimization

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Abstract

In distributed optimization theory, network topology graphs are important in communications among multiple agents. However, distributed optimization approaches cannot solve optimization problems well if the graphs are infeasible or tampered. To this end, this paper develops two types of modified graph systems for modifying or recovering the communication graphs among agents employed in distributed optimization. Two optimization problems for obtaining feasible graphs are formulated. Based on the two optimization problems, two modified graph systems are derived accordingly and their convergence to the optimal solution is proven. Via a coordination mechanism consisting of a distributed optimization approach and a modified graph system, we can modify an infeasible communication graph into a feasible one or recover a tampered graph, and the distributed optimization approach can resume its solver capability with the modified graphs. Several examples are provided to demonstrate the efficiency of the main results.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 62173308), Natural Science Foundation of Zhejiang Province of China (Grant Nos. LR20F030001, LD19A010001), and Jinhua Science and Technology Project (Grant No. 2022-1-042).

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Authors and Affiliations

  1. Key Laboratory of Intelligent Education Technology and Application of Zhejiang Province, Jinhua, 321004, China

    Zicong Xia & Yang Liu

  2. School of Mathematical Sciences, Zhejiang Normal University, Jinhua, 321004, China

    Zicong Xia & Yang Liu

  3. College of Engineering, Zhejiang Normal University, Jinhua, 321004, China

    Dongyun Wang

  4. School of Information Science and Engineering, Central South University, Changsha, 410083, China

    Weihua Gui

Authors
  1. Zicong Xia
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  2. Yang Liu
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  3. Dongyun Wang
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  4. Weihua Gui
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Correspondence to Yang Liu.

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Xia, Z., Liu, Y., Wang, D. et al. Modified graph systems for distributed optimization. Sci. China Inf. Sci. 66, 222202 (2023). https://doi.org/10.1007/s11432-022-3781-4

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  • DOI: https://doi.org/10.1007/s11432-022-3781-4

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