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Title: An efficient augmented Lagrangian-based method for linear equality-constrained Lasso
Authors: Deng, Z
Yue, MC 
Issue Date: 2020
Source: 2020 IEEE International Conference on Acoustics, Speech,and Signal Processing : proceedings, May 4–8, 2020, Centre de Convencions Internacional de Barcelona (CCIB), Barcelona, Spain, p. 5760-5764. Piscataway, NJ: IEEE, 2020
Abstract: Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, various constrained Lasso models have been proposed in the literature. Compared with the classic (unconstrained) Lasso model, the algorithmic aspects of constrained Lasso models are much less explored. In this paper, we demonstrate how the recently developed semis-mooth Newton-based augmented Lagrangian framework can be extended to solve a linear equality-constrained Lasso model. A key technical challenge that is not present in prior works is the lack of strong convexity in our dual problem, which we overcome by adopting a regularization strategy. We show that under mild assumptions, our proposed method will converge superlinearly. Moreover, extensive numerical experiments on both synthetic and real-world data show that our method can be substantially faster than existing first-order methods while achieving a better solution accuracy.
Keywords: Constrained Lasso
Augmented Lagrangian
Semismooth Newton
Superlinear convergence
Publisher: Institute of Electrical and Electronics Engineers
ISBN: 978-1-5090-6631-5 (Electronic ISBN)
DOI: 10.1109/ICASSP40776.2020.9053722
Description: 2020 IEEE International Conference on Acoustics, Speech and Signal Processing, May 4-8 2020, Centre de Convencions Internacional de Barcelona (CCIB), Barcelona, Spain.
Rights: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.
© 2020 IEEE
The following publication Z. Deng, M. -C. Yue and A. M. -C. So, "An Efficient Augmented Lagrangian-Based Method for Linear Equality-Constrained Lasso," ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Barcelona, Spain, 2020, pp. 5760-5764 is available at
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