The Linearized Alternating Direction Method of Multipliers for Dantzig Selector

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 spee...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2012-01, Vol.34 (5), p.A2792-A2811
Main Authors: Wang, Xiangfeng, Yuan, Xiaoming
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Feature selection
Fourier transforms
Lagrange multiplier
Linear programming
Regression analysis
Variables
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Summary: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. [PUBLICATION ABSTRACT]
ISSN:1064-8275
1095-7197
DOI:10.1137/110833543