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

Shichen Liao (), Congying Han (), Tiande Guo () and Bonan Li ()
Additional contact information
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

Journal of Global Optimization, 2024, vol. 90, issue 1, No 5, 93-125

Abstract: 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.

Keywords: Sparse group $$\ell _0$$ ℓ 0 optimization; Subspace Newton method; Global convergence; Second-order convergence rate; 90C26; 90C46; 49M15 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10898-024-01396-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:90:y:2024:i:1:d:10.1007_s10898-024-01396-y

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-024-01396-y

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().