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An active set Barzilar–Borwein algorithm for $$l_{0}$$l0 regularized optimization

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  • Wanyou Cheng

    (Dongguan University of Technology)

  • Zixin Chen

    (Dongguan University of Technology)

  • Qingjie Hu

    (Guilin University of Electronic Technology)

Abstract

In this paper, we develop an active set identification technique for the $$\ell _0$$ℓ0 regularization optimization. Such a technique has a strong ability to identify the zero components in a neighbourhood of a strict L-stationary point. Based on the identification technique, we propose an active set Barzilar–Borwein algorithm and prove that any limit point of the sequence generated by the algorithm is a strong stationary point. Some preliminary numerical results are provided, showing that the method is promising.

Suggested Citation

  • Wanyou Cheng & Zixin Chen & Qingjie Hu, 2020. "An active set Barzilar–Borwein algorithm for $$l_{0}$$l0 regularized optimization," Journal of Global Optimization, Springer, vol. 76(4), pages 769-791, April.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:4:d:10.1007_s10898-019-00830-w
    DOI: 10.1007/s10898-019-00830-w
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    References listed on IDEAS

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    1. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    2. Yulan Liu & Shujun Bi & Shaohua Pan, 2018. "Equivalent Lipschitz surrogates for zero-norm and rank optimization problems," Journal of Global Optimization, Springer, vol. 72(4), pages 679-704, December.
    3. P. Tseng & S. Yun, 2009. "Block-Coordinate Gradient Descent Method for Linearly Constrained Nonsmooth Separable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 513-535, March.
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    Cited by:

    1. Shichen Liao & Congying Han & Tiande Guo & Bonan Li, 2024. "Subspace Newton method for sparse group $$\ell _0$$ ℓ 0 optimization problem," Journal of Global Optimization, Springer, vol. 90(1), pages 93-125, September.

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