The Linearized Alternating Direction Method of Multipliers for Dantzig Selector

Xiangfeng Wang; Xiaoming Yuan

doi:10.1137/110833543

The Linearized Alternating Direction Method of Multipliers for Dantzig Selector

Xiangfeng Wang, Xiaoming Yuan^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

75 Citations (Scopus)

68 Downloads (Pure)

Abstract

The Dantzig selector was recently proposed to perform variable selection and model fitting in the linear regression model. It can be solved numerically by the alternating direction method of multipliers (ADM); and in this paper, we show that the application of ADM to the Dantzig selector can be speeded up significantly if one of its resulting subproblems at each iteration is linearized. The resulting linearized ADM for the Dantzig selector is shown to be efficient for solving both synthetic and real world data sets.

Original language	English
Pages (from-to)	A2792-A2811
Number of pages	20
Journal	SIAM Journal on Scientific Computing
Volume	34
Issue number	5
DOIs	https://doi.org/10.1137/110833543
Publication status	Published - 18 Oct 2012

Scopus Subject Areas

Computational Mathematics
Applied Mathematics

User-Defined Keywords

Alternating direction method of multipliers
Dantzig selector
Linear regression
Linearized

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10.1137/110833543

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Cite this

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abstract = "The Dantzig selector was recently proposed to perform variable selection and model fitting in the linear regression model. It can be solved numerically by the alternating direction method of multipliers (ADM); and in this paper, we show that the application of ADM to the Dantzig selector can be speeded up significantly if one of its resulting subproblems at each iteration is linearized. The resulting linearized ADM for the Dantzig selector is shown to be efficient for solving both synthetic and real world data sets.",

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note = "Funding information: Department of Mathematics, Nanjing University, 22 Hankou Road, Nanjing, 210093, People{\textquoteright}s Republic of China ([email protected]). This author{\textquoteright}s work was supported by NSFC grant 91130007. ^ Corresponding author. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, People{\textquoteright}s Republic of China ([email protected]). This author{\textquoteright}s work was supported by the Hong Kong General Research Fund, 203311. Publisher copyright: {\textcopyright} 2012, Society for Industrial and Applied Mathematics",

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The Linearized Alternating Direction Method of Multipliers for Dantzig Selector

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