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A smoothing proximal gradient algorithm with extrapolation for the relaxation of $${\ell_{0}}$$ ℓ 0 regularization problem

Author

Listed:
  • Jie Zhang

    (Sichuan University)

  • Xinmin Yang

    (Chongqing Normal University)

  • Gaoxi Li

    (Chongqing Technology and Business University)

  • Ke Zhang

    (National Center for Applied Mathematics in Chongqing)

Abstract

In this paper, we consider the exact continuous relaxation model of $${\ell_{0}}$$ ℓ 0 regularization problem, which was given by Bian and Chen (SIAM J Numer Anal 58:858–883, 2020) and propose a smoothing proximal gradient algorithm with extrapolation (SPGE) for this kind of problems. Under a general choice of extrapolation parameter, it is proved that all the accumulation points have a common support set, and the ability of the SPGE algorithm to identify the zero entries of the accumulation point within finite iterations is available. We show that any accumulation point of the sequence generated by the SPGE algorithm is a lifted stationary point of the relaxation model. Moreover, a convergence rate concerning proximal residual is established. Finally, we conduct three numerical experiments to illustrate the efficiency of the SPGE algorithm compared with the smoothing proximal gradient (SPG) algorithm proposed by Bian and Chen (2020).

Suggested Citation

  • Jie Zhang & Xinmin Yang & Gaoxi Li & Ke Zhang, 2023. "A smoothing proximal gradient algorithm with extrapolation for the relaxation of $${\ell_{0}}$$ ℓ 0 regularization problem," Computational Optimization and Applications, Springer, vol. 84(3), pages 737-760, April.
    • Handle: RePEc:spr:coopap:v:84:y:2023:i:3:d:10.1007_s10589-022-00446-z
    DOI: 10.1007/s10589-022-00446-z
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    References listed on IDEAS

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    1. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. NESTEROV, Yurii, 2007. "Smoothing technique and its applications in semidefinite optimization," LIDAM Reprints CORE 1951, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Jong-Shi Pang & Meisam Razaviyayn & Alberth Alvarado, 2017. "Computing B-Stationary Points of Nonsmooth DC Programs," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 95-118, January.
    4. Ming Hu & Masao Fukushima, 2012. "Smoothing approach to Nash equilibrium formulations for a class of equilibrium problems with shared complementarity constraints," Computational Optimization and Applications, Springer, vol. 52(2), pages 415-437, June.
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