Local R-linear convergence of ADMM-based algorithm for ℓ1-norm minimization with linear and box constraints

This paper presents an efficient algorithm based on the alternating direction method of multipliers (ADMM) for an ℓ1-norm minimization problem with linear equality and box constraints. In the ADMM iterations, sub-problems, called proximal minimizations, are solved to obtain the next updating points...

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Bibliographic Details
Published inSystems & control letters Vol. 146
Main Authors Toyoda, Mitsuru, Tanaka, Mirai
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2020
Subjects
Alternating direction method of multipliers (ADMM)
Convergence analysis
Optimal control
Proximal algorithm
Sparse optimization
Sparse optimization
Optimal control
Proximal algorithm
Alternating direction method of multipliers (ADMM)
Convergence analysis
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ISSN0167-6911
1872-7956
DOI10.1016/j.sysconle.2020.104824

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Summary:This paper presents an efficient algorithm based on the alternating direction method of multipliers (ADMM) for an ℓ1-norm minimization problem with linear equality and box constraints. In the ADMM iterations, sub-problems, called proximal minimizations, are solved to obtain the next updating points by exploiting closed formulae. Furthermore, the local R-linear convergence is established by analysis, focusing on the dynamical structure of the ADMM iterations. Numerical examples illustrate obtained theoretical results and the effectiveness of the algorithm.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2020.104824