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Exact spectral-like gradient method for distributed optimization

Author

Listed:
  • Dušan Jakovetić

    (University of Novi Sad)

  • Nataša Krejić

    (University of Novi Sad)

  • Nataša Krklec Jerinkić

    (University of Novi Sad)

Abstract

Since the initial proposal in the late 80s, spectral gradient methods continue to receive significant attention, especially due to their excellent numerical performance on various large scale applications. However, to date, they have not been sufficiently explored in the context of distributed optimization. In this paper, we consider unconstrained distributed optimization problems where n nodes constitute an arbitrary connected network and collaboratively minimize the sum of their local convex cost functions. In this setting, building from existing exact distributed gradient methods, we propose a novel exact distributed gradient method wherein nodes’ step-sizes are designed according to the novel rules akin to those in spectral gradient methods. We refer to the proposed method as Distributed Spectral Gradient method. The method exhibits R-linear convergence under standard assumptions for the nodes’ local costs and safeguarding on the algorithm step-sizes. We illustrate the method’s performance through simulation examples.

Suggested Citation

  • Dušan Jakovetić & Nataša Krejić & Nataša Krklec Jerinkić, 2019. "Exact spectral-like gradient method for distributed optimization," Computational Optimization and Applications, Springer, vol. 74(3), pages 703-728, December.
    • Handle: RePEc:spr:coopap:v:74:y:2019:i:3:d:10.1007_s10589-019-00131-8
    DOI: 10.1007/s10589-019-00131-8
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    Cited by:

    1. Juan Gao & Xin-Wei Liu & Yu-Hong Dai & Yakui Huang & Junhua Gu, 2023. "Distributed stochastic gradient tracking methods with momentum acceleration for non-convex optimization," Computational Optimization and Applications, Springer, vol. 84(2), pages 531-572, March.
    2. Dušan Jakovetić & Nataša Krejić & Nataša Krklec Jerinkić, 2023. "EFIX: Exact fixed point methods for distributed optimization," Journal of Global Optimization, Springer, vol. 85(3), pages 637-661, March.

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