An alternating direction method for finding Dantzig selectors

Authors:
Zhaosong Lu;Ting Kei Pong;Yong Zhang
Affiliations:
Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada;Department of Mathematics, University of Washington, Seattle, Washington 98195, USA;Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada
Venue:
Computational Statistics & Data Analysis
Year:
2012

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Abstract

In this paper, we study the alternating direction method for finding the Dantzig selectors, which are first introduced in Candes and Tao (2007a). In particular, at each iteration we apply the nonmonotone gradient method proposed in Lu and Zhang (in press) to approximately solve one subproblem of this method. We compare our approach with a first-order method proposed in Becker et al. (2011). The computational results show that our approach usually outperforms that method in terms of CPU time while producing solutions of comparable quality.