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

Hai-Bin Zhang (zhanghaibin@bjut.edu.cn), Jiao-Jiao Jiang (jjiaoj@deakin.edu.au) and Yun-Bin Zhao (y.zhao.2@bham.ac.uk)

Computational Optimization and Applications, 2015, vol. 61, issue 1, 79-99

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

Keywords: Nonsmooth convex optimization; Proximal splitting method; Projected Landweber method; Newton’s method; Sparse group LASSO (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10589-014-9703-7

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