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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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    1. Hui Zhang & Yu-Hong Dai & Lei Guo & Wei Peng, 2021. "Proximal-Like Incremental Aggregated Gradient Method with Linear Convergence Under Bregman Distance Growth Conditions," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 61-81, February.
    2. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
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    4. Zehui Jia & Jieru Huang & Xingju Cai, 2021. "Proximal-like incremental aggregated gradient method with Bregman distance in weakly convex optimization problems," Journal of Global Optimization, Springer, vol. 80(4), pages 841-864, August.
    5. Ion Necoara & Yurii Nesterov & François Glineur, 2019. "Linear convergence of first order methods for non-strongly convex optimization," LIDAM Reprints CORE 3000, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Wei Peng & Hui Zhang & Xiaoya Zhang, 2019. "Nonconvex Proximal Incremental Aggregated Gradient Method with Linear Convergence," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 230-245, October.
    7. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Patrick R. Johnstone & Pierre Moulin, 2017. "Local and global convergence of a general inertial proximal splitting scheme for minimizing composite functions," Computational Optimization and Applications, Springer, vol. 67(2), pages 259-292, June.
    9. Peter Ochs, 2018. "Local Convergence of the Heavy-Ball Method and iPiano for Non-convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 153-180, April.
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