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Iterative reweighted methods for $$\ell _1-\ell _p$$ ℓ 1 - ℓ p minimization

Author

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  • Xianchao Xiu

    (Beijing Jiaotong University)

  • Lingchen Kong

    (Beijing Jiaotong University)

  • Yan Li

    (University of International Business and Economics)

  • Houduo Qi

    (University of Southampton)

Abstract

In this paper, we focus on the $$\ell _1-\ell _p$$ ℓ 1 - ℓ p minimization problem with $$0

Suggested Citation

  • Xianchao Xiu & Lingchen Kong & Yan Li & Houduo Qi, 2018. "Iterative reweighted methods for $$\ell _1-\ell _p$$ ℓ 1 - ℓ p minimization," Computational Optimization and Applications, Springer, vol. 70(1), pages 201-219, May.
    • Handle: RePEc:spr:coopap:v:70:y:2018:i:1:d:10.1007_s10589-017-9977-7
    DOI: 10.1007/s10589-017-9977-7
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    References listed on IDEAS

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    1. Jelena Bradic & Jianqing Fan & Weiwei Wang, 2011. "Penalized composite quasi‐likelihood for ultrahigh dimensional variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 325-349, June.
    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. Wang, Lie, 2013. "The L1 penalized LAD estimator for high dimensional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 135-151.
    4. Lan Wang & Yichao Wu & Runze Li, 2012. "Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 214-222, March.
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    Cited by:

    1. Sining Huang & Yupeng Chen & Tiantian Qiao, 2021. "An Extended Reweighted ℓ 1 Minimization Algorithm for Image Restoration," Mathematics, MDPI, vol. 9(24), pages 1-15, December.
    2. Liu, Jingjing & Ma, Ruijie & Zeng, Xiaoyang & Liu, Wanquan & Wang, Mingyu & Chen, Hui, 2021. "An efficient non-convex total variation approach for image deblurring and denoising," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    3. Xiu, Xianchao & Liu, Wanquan & Li, Ling & Kong, Lingchen, 2019. "Alternating direction method of multipliers for nonconvex fused regression problems," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 59-71.

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