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Subspace Newton method for sparse group $$\ell _0$$ ℓ 0 optimization problem

Author

Listed:
  • Shichen Liao

    (University of Chinese Academy of Sciences)

  • Congying Han

    (University of Chinese Academy of Sciences)

  • Tiande Guo

    (University of Chinese Academy of Sciences)

  • Bonan Li

    (University of Chinese Academy of Sciences)

Abstract

This paper investigates sparse optimization problems characterized by a sparse group structure, where element- and group-level sparsity are jointly taken into account. This particular optimization model has exhibited notable efficacy in tasks such as feature selection, parameter estimation, and the advancement of model interpretability. Central to our study is the scrutiny of the $$\ell _0$$ ℓ 0 and $$\ell _{2,0}$$ ℓ 2 , 0 norm regularization model, which, in comparison to alternative surrogate formulations, presents formidable computational challenges. We embark on our study by conducting the analysis of the optimality conditions of the sparse group optimization problem, leveraging the notion of a $$\gamma $$ γ -stationary point, whose linkage to local and global minimizer is established. In a subsequent facet of our study, we develop a novel subspace Newton algorithm for sparse group $$\ell _0$$ ℓ 0 optimization problem and prove its global convergence property as well as local second-order convergence rate. Experimental results reveal the superlative performance of our algorithm in terms of both precision and computational expediency, thereby outperforming several state-of-the-art solvers.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jglopt:v:90:y:2024:i:1:d:10.1007_s10898-024-01396-y
    DOI: 10.1007/s10898-024-01396-y
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    References listed on IDEAS

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    1. Yanming Li & Bin Nan & Ji Zhu, 2015. "Multivariate sparse group lasso for the multivariate multiple linear regression with an arbitrary group structure," Biometrics, The International Biometric Society, vol. 71(2), pages 354-363, June.
    2. 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.
    3. Jingnan Chen & Gengling Dai & Ning Zhang, 2020. "An application of sparse-group lasso regularization to equity portfolio optimization and sector selection," Annals of Operations Research, Springer, vol. 284(1), pages 243-262, January.
    4. Xiaotong Shen & Wei Pan & Yunzhang Zhu & Hui Zhou, 2013. "On constrained and regularized high-dimensional regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 807-832, October.
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