Smoothing composite proximal gradient algorithm for sparse group Lasso problems with nonsmooth loss functions

In recent years, the sparse and group sparse optimization problem has attracted extensive attention due to its wide applications in statistics, bioinformatics, signal interpretation and machine learning, which yields the sparsity both in group-wise and element-wise. In this paper, the sparse and gro...

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Bibliographic Details
Published in:Journal of applied mathematics & computing Vol. 70; no. 3; pp. 1887 - 1913
Main Authors: Shen, Huiling, Peng, Dingtao, Zhang, Xian
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2024
Springer Nature B.V
Subjects:
Algorithms
Approximation
Bioinformatics
Computational Mathematics and Numerical Analysis
Gene expression
Machine learning
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Optimization
Original Research
Smoothing
Sparsity
Theory of Computation
Smoothing composite proximal gradient algorithm
Anti-outlier
65K06
Nonsmooth loss function
90C30
90C06
Sublinear convergence rate
Sparse group Lasso problem
ISSN:1598-5865, 1865-2085
Online Access:Get full text
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Summary:In recent years, the sparse and group sparse optimization problem has attracted extensive attention due to its wide applications in statistics, bioinformatics, signal interpretation and machine learning, which yields the sparsity both in group-wise and element-wise. In this paper, the sparse and group sparse optimization problem with a nonsmooth loss function is considered, where the sparsity and group sparsity are induced by a penalty composed of a combination of ℓ 1 norm and ℓ 2 , 1 norm, so it is called the sparse group Lasso (SGLasso) problem. To solve this problem, the nonsmooth loss function is smoothed first. Then, based on the smooth approximation of the loss function, a smoothing composite proximal gradient (SCPG) algorithm is proposed. It is showed that any accumulation point of the sequence generated by SCPG algorithm is a global optimal solution of the problem. Moreover, it is proved that the convergence rate of the objective function value is O ( 1 k 1 - σ ) where σ ∈ ( 0.5 , 1 ) is a constant. Finally, numerical results illustrate that the proposed SCPG algorithm is effective and robust for sparse and group sparse optimization problems. Especially, compared with some popular algorithms, SCPG algorithm has obvious advantages in anti-outlier.
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ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-024-02034-2