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On the proximal Landweber Newton method for a class of nonsmooth convex problems

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  • Hai-Bin Zhang
  • Jiao-Jiao Jiang
  • Yun-Bin Zhao

Abstract

We consider a class of nonsmooth convex optimization problems where the objective function is a convex differentiable function regularized by the sum of the group reproducing kernel norm and $$\ell _1$$ ℓ 1 -norm of the problem variables. This class of problems has many applications in variable selections such as the group LASSO and sparse group LASSO. In this paper, we propose a proximal Landweber Newton method for this class of convex optimization problems, and carry out the convergence and computational complexity analysis for this method. Theoretical analysis and numerical results show that the proposed algorithm is promising. Copyright Springer Science+Business Media New York 2015

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  • Hai-Bin Zhang & Jiao-Jiao Jiang & Yun-Bin Zhao, 2015. "On the proximal Landweber Newton method for a class of nonsmooth convex problems," Computational Optimization and Applications, Springer, vol. 61(1), pages 79-99, May.
    • Handle: RePEc:spr:coopap:v:61:y:2015:i:1:p:79-99
    DOI: 10.1007/s10589-014-9703-7
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    References listed on IDEAS

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    1. Vincent, Martin & Hansen, Niels Richard, 2014. "Sparse group lasso and high dimensional multinomial classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 771-786.
    2. Haibin Zhang & Juan Wei & Meixia Li & Jie Zhou & Miantao Chao, 2014. "On proximal gradient method for the convex problems regularized with the group reproducing kernel norm," Journal of Global Optimization, Springer, vol. 58(1), pages 169-188, January.
    3. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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