Alternating direction method of multipliers for nonconvex fused regression problems

Xianchao Xiu, Wanquan Liu, Ling Li and Lingchen Kong

Computational Statistics & Data Analysis, 2019, vol. 136, issue C, 59-71

Abstract: It is well-known that the fused least absolute shrinkage and selection operator (FLASSO) has been playing an important role in signal and image processing. Recently, the nonconvex penalty is extensively investigated due to its success in sparse learning. In this paper, a novel nonconvex fused regression model, which integrates FLASSO and the nonconvex penalty nicely, is proposed. The developed alternating direction method of multipliers (ADMM) approach is shown to be very efficient owing to the fact that each derived subproblem has a closed-form solution. In addition, the convergence is discussed and proved mathematically. This leads to a fast and convergent algorithm. Extensive numerical experiments show that our proposed nonconvex fused regression outperforms the state-of-the-art approach FLASSO.

Keywords: Fused LASSO; Alternating direction method of multipliers; Variable selection; Nonconvex optimization (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:136:y:2019:i:c:p:59-71

DOI: 10.1016/j.csda.2019.01.002

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