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Distributed Communication-Sliding Mirror-Descent Algorithm for Nonsmooth Resource Allocation Problem

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Abstract

This paper considers a distributed nonsmooth resource allocation problem of minimizing a global convex function formed by a sum of local nonsmooth convex functions with coupled constraints. A distributed communication-efficient mirror-descent algorithm, which can reduce communication rounds between agents over the network, is designed for the distributed resource allocation problem. By employing communication-sliding methods, agents can find a ε-solution in \(O\left( {{1 \over \varepsilon }} \right)\) communication rounds while maintaining \(O\left( {{1 \over {{\varepsilon ^2}}}} \right)\) subgradient evaluations for nonsmooth convex functions. A numerical example is also given to illustrate the effectiveness of the proposed algorithm.

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References

  1. Yi P, Hong Y, and Liu F, Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems, Automatica, 2016, 74: 259–269.

    Article  MathSciNet  Google Scholar 

  2. Zeng X, Yi P, and Hong Y, Distributed algorithm for robust resource allocation with polyhedral uncertain allocation parameters, Journal of Systems Science & Complexity, 2018, 31(1): 103–119.

    Article  MathSciNet  Google Scholar 

  3. Nedi A, Olshevsky A, and Shi W, Improved convergence rates for distributed resource allocation, 2018 IEEE Conference on Decision and Control (CDC), IEEE, 2018, 172–177.

  4. Wang Y, Tu Z, and Qin H, Distributed stochastic mirror descent algorithm for resource allocation problem, Control Theory and Technology, 2020, 18(4): 339–347.

    Article  MathSciNet  Google Scholar 

  5. Zhu M and Martnez S, On distributed convex optimization under inequality and equality constraints, IEEE Transactions on Automatic Control, 2011, 57(1): 151–164.

    MathSciNet  Google Scholar 

  6. Zhang J, You K, and Cai K, Distributed dual gradient tracking for resource allocation in unbalanced networks, IEEE Transactions on Signal Processing, 2020, 68: 2186–2198.

    Article  MathSciNet  Google Scholar 

  7. Xu J, Zhu S, Soh Y C, et al., A dual splitting approach for distributed resource allocation with regularization, IEEE Transactions on Control of Network Systems, 2018, 6(1): 403–414.

    Article  MathSciNet  Google Scholar 

  8. Roth V, The generalized LASSO, IEEE Transactions on Neural Networks, 2004, 15(1): 16–28.

    Article  Google Scholar 

  9. Deng Z, Nian X, and Hu C, Distributed algorithm design for nonsmooth resource allocation problems, IEEE transactions on cybernetics, 2019, 50(7): 3208–3217.

    Article  Google Scholar 

  10. Zhu Y, Wen G, Yu W, et al., Continuous-time distributed proximal gradient algorithms for nonsmooth resource allocation over general digraphs, IEEE Transactions on Network Science and Engineering, 2021, DOI: https://doi.org/10.1109/TNSE.2021.3070398.

  11. Wei Y, Shang C, Fang H, et al. Solving a class of nonsmooth resource allocation problems with directed graphs though distributed smooth multi-proximal algorithms, Automatica, 2022, 136: 110071.

    Article  Google Scholar 

  12. Iiduka H, Distributed optimization for network resource allocation with nonsmooth utility functions, IEEE Transactions on Control of Network Systems, 2018, 6(4): 1354–1365.

    Article  MathSciNet  Google Scholar 

  13. Nesterov Y and Shikhman V, Dual subgradient method with averaging for optimal resource allocation, European Journal of Operational Research, 2018, 270(3): 907–916.

    Article  MathSciNet  Google Scholar 

  14. Bregman L M, The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming, USSR Computational Mathematics and Mathematical Physics, 1967, 7(3): 200–217.

    Article  MathSciNet  Google Scholar 

  15. Yuan D, Hong Y, Ho D W C, et al., Optimal distributed stochastic mirror descent for strongly convex optimization, Automatica, 2018, 90: 196–203.

    Article  MathSciNet  Google Scholar 

  16. Lan G, Lee S, and Zhou Y, Communication-efficient algorithms for decentralized and stochastic optimization, Mathematical Programming, 2020, 180(1): 237–284.

    Article  MathSciNet  Google Scholar 

  17. Ouyang Y, Chen Y, Lan G, et al., An accelerated linearized alternating direction method of multipliers, SIAM Journal on Imaging Sciences, 2015, 8(1): 644–681.

    Article  MathSciNet  Google Scholar 

  18. Ghadimi S and Lan G, Optimal stochastic approximation algorithms for strongly convex stochastic composite optimization i: A generic algorithmic framework, SIAM Journal on Optimization, 2012, 22(4): 1469–1492.

    Article  MathSciNet  Google Scholar 

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Correspondence to Yinghui Wang, Zhipeng Tu or Huashu Qin.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 72101026, 61621063, and the State Key Laboratory of Intelligent Control and Decision of Complex Systems.

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Wang, Y., Tu, Z. & Qin, H. Distributed Communication-Sliding Mirror-Descent Algorithm for Nonsmooth Resource Allocation Problem. J Syst Sci Complex 35, 1244–1261 (2022). https://doi.org/10.1007/s11424-022-0187-8

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  • DOI: https://doi.org/10.1007/s11424-022-0187-8

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