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Global convergence of proximal iteratively reweighted algorithm

Author

Listed:
  • Tao Sun

    (National University of Defense Technology)

  • Hao Jiang

    (National University of Defense Technology)

  • Lizhi Cheng

    (National University of Defense Technology
    National University of Defense Technology)

Abstract

In this paper, we investigate the convergence of the proximal iteratively reweighted algorithm for a class of nonconvex and nonsmooth problems. Such problems actually include numerous models in the area of signal processing and machine learning research. Two extensions of the algorithm are also studied. We provide a unified scheme for these three algorithms. With the Kurdyka–Łojasiewicz property, we prove that the unified algorithm globally converges to a critical point of the objective function.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:68:y:2017:i:4:d:10.1007_s10898-017-0507-z
    DOI: 10.1007/s10898-017-0507-z
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    References listed on IDEAS

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    1. Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
    2. 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.
    3. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
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    Cited by:

    1. 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.

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