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Inertial proximal incremental aggregated gradient method with linear convergence guarantees

Author

Listed:
  • Xiaoya Zhang

    (Defense Innovation Institute, Chinese Academy of Military Science)

  • Wei Peng

    (Defense Innovation Institute, Chinese Academy of Military Science)

  • Hui Zhang

    (National University of Defense Technology)

Abstract

In this paper, we propose an inertial version of the Proximal Incremental Aggregated Gradient (abbreviated by iPIAG) method for minimizing the sum of smooth convex component functions and a possibly nonsmooth convex regularization function. First, we prove that iPIAG converges linearly under the gradient Lipschitz continuity and the strong convexity, along with an upper bound estimation of the inertial parameter. Then, by employing the recent Lyapunov-function-based method, we derive a weaker linear convergence guarantee, which replaces the strong convexity by the quadratic growth condition. At last, we present two numerical tests to illustrate that iPIAG outperforms the original PIAG.

Suggested Citation

  • Xiaoya Zhang & Wei Peng & Hui Zhang, 2022. "Inertial proximal incremental aggregated gradient method with linear convergence guarantees," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(2), pages 187-213, October.
    • Handle: RePEc:spr:mathme:v:96:y:2022:i:2:d:10.1007_s00186-022-00790-0
    DOI: 10.1007/s00186-022-00790-0
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    References listed on IDEAS

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