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An Efficient Algorithm for Minimizing Multi Non-Smooth Component Functions

Pham, Minh and Ninh, Anh and Le, Hoang and Liu, Yufeng (2020) An Efficient Algorithm for Minimizing Multi Non-Smooth Component Functions. Journal of Computational and Graphical Statistics . ISSN 1061-8600. (In Press)

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Many problems in statistics and machine learning can be formulated as an optimization problem of a finite sum of nonsmooth convex functions. We propose an algorithm to minimize this type of objective functions based on the idea of alternating linearization. Our algorithm retains the simplicity of contemporary methods without any restrictive assumptions on the smoothness of the loss function. We apply our proposed method to solve two challenging problems: overlapping group lasso and convex regression with sharp partitions. Numerical experiments show that our method is superior to the state-of-the-art algorithms, many of which are based on the accelerated proximal gradient method. Supplementary materials for this article are available online.

Item Type:Article
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Liu, Yufeng0000-0002-1686-0545
Additional Information:© 2020 Taylor & Francis. Received 08 Sep 2018, Accepted 24 May 2020, Accepted author version posted online: 05 Aug 2020, Published online: 29 Sep 2020. The author was supported by NSF grant DMS-1821231 and NIH grant R01GM126550.
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Subject Keywords:Nonsmooth optimization, Penalized regression, Regularization
Record Number:CaltechAUTHORS:20201019-134117484
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Official Citation:Minh Pham, Anh Ninh, Hoang Le & Yufeng Liu (2020) An Efficient Algorithm for Minimizing Multi Non-Smooth Component Functions, Journal of Computational and Graphical Statistics, DOI: 10.1080/10618600.2020.1804390
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106149
Deposited By: Tony Diaz
Deposited On:20 Oct 2020 16:02
Last Modified:20 Oct 2020 16:02

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