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An extrapolated proximal iteratively reweighted method for nonconvex composite optimization problems

Author

Listed:
  • Zhili Ge

    (Nanjing Normal University of Special Education)

  • Zhongming Wu

    (Nanjing University of Information Science and Technology)

  • Xin Zhang

    (Suqian University)

  • Qin Ni

    (Nanjing University of Aeronautics and Astronautics)

Abstract

We consider a class of problems where the objective function is the sum of a smooth function and a composition of nonconvex and nonsmooth functions. Such optimization problems arise frequently in machine learning and data processing. The proximal iteratively reweighted method has been widely used and popularized in solving these problems. In this paper, we develop an extrapolated proximal iteratively reweighted method that incorporates two different flexible inertial steps at each iteration. We first prove the subsequential convergence of the proposed method under parameter constraints. Moreover, if the objective function satisfies the Kurdyka-Łojasiewicz property, the global convergence of the new method is established. In addition, we analyze the local convergence rate by making assumptions on the Kurdyka-Łojasiewicz exponent of the objective function. Finally, numerical results on $$l_p$$ l p minimization and feature selection problems are reported to show the effectiveness and superiority of the proposed algorithm.

Suggested Citation

  • Zhili Ge & Zhongming Wu & Xin Zhang & Qin Ni, 2023. "An extrapolated proximal iteratively reweighted method for nonconvex composite optimization problems," Journal of Global Optimization, Springer, vol. 86(4), pages 821-844, August.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:4:d:10.1007_s10898-023-01299-4
    DOI: 10.1007/s10898-023-01299-4
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    References listed on IDEAS

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    1. Zhongming Wu & Chongshou Li & Min Li & Andrew Lim, 2021. "Inertial proximal gradient methods with Bregman regularization for a class of nonconvex optimization problems," Journal of Global Optimization, Springer, vol. 79(3), pages 617-644, March.
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    4. Xiaojun Chen & Weijun Zhou, 2014. "Convergence of the reweighted ℓ 1 minimization algorithm for ℓ 2 –ℓ p minimization," Computational Optimization and Applications, Springer, vol. 59(1), pages 47-61, October.
    5. Tao Sun & Hao Jiang & Lizhi Cheng, 2017. "Global convergence of proximal iteratively reweighted algorithm," Journal of Global Optimization, Springer, vol. 68(4), pages 815-826, August.
    6. Radu Ioan Boţ & Ernö Robert Csetnek & Szilárd Csaba László, 2016. "An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 4(1), pages 3-25, February.
    7. Bo Wen & Xiaoping Xue, 2019. "On the convergence of the iterates of proximal gradient algorithm with extrapolation for convex nonsmooth minimization problems," Journal of Global Optimization, Springer, vol. 75(3), pages 767-787, November.
    8. Ke Guo & Deren Han, 2018. "A note on the Douglas–Rachford splitting method for optimization problems involving hypoconvex functions," Journal of Global Optimization, Springer, vol. 72(3), pages 431-441, November.
    9. Zhongming Wu & Min Li, 2019. "General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems," Computational Optimization and Applications, Springer, vol. 73(1), pages 129-158, May.
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