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Alternating direction method of multipliers for nonconvex fused regression problems

Author

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  • Xiu, Xianchao
  • Liu, Wanquan
  • Li, Ling
  • Kong, Lingchen

Abstract

It is well-known that the fused least absolute shrinkage and selection operator (FLASSO) has been playing an important role in signal and image processing. Recently, the nonconvex penalty is extensively investigated due to its success in sparse learning. In this paper, a novel nonconvex fused regression model, which integrates FLASSO and the nonconvex penalty nicely, is proposed. The developed alternating direction method of multipliers (ADMM) approach is shown to be very efficient owing to the fact that each derived subproblem has a closed-form solution. In addition, the convergence is discussed and proved mathematically. This leads to a fast and convergent algorithm. Extensive numerical experiments show that our proposed nonconvex fused regression outperforms the state-of-the-art approach FLASSO.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:136:y:2019:i:c:p:59-71
    DOI: 10.1016/j.csda.2019.01.002
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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. 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.
    3. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    4. 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.
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    Cited by:

    1. 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).
    2. Maneesha, Ampolu & Swarup, K. Shanti, 2021. "A survey on applications of Alternating Direction Method of Multipliers in smart power grids," Renewable and Sustainable Energy Reviews, Elsevier, vol. 152(C).

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