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An alternating direction method for finding Dantzig selectors

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  • Lu, Zhaosong
  • Pong, Ting Kei
  • Zhang, Yong

Abstract

In this paper, we study the alternating direction method for finding the Dantzig selectors, which are first introduced in Candès 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.

Suggested Citation

  • Lu, Zhaosong & Pong, Ting Kei & Zhang, Yong, 2012. "An alternating direction method for finding Dantzig selectors," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4037-4046.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4037-4046
    DOI: 10.1016/j.csda.2012.04.019
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    References listed on IDEAS

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    1. Gareth M. James & Peter Radchenko & Jinchi Lv, 2009. "DASSO: connections between the Dantzig selector and lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 127-142, January.
    2. NESTEROV, Yu., 2007. "Gradient methods for minimizing composite objective function," LIDAM Discussion Papers CORE 2007076, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    4. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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    Cited by:

    1. Hongjin He & Xingju Cai & Deren Han, 2015. "A fast splitting method tailored for Dantzig selector," Computational Optimization and Applications, Springer, vol. 62(2), pages 347-372, November.
    2. Tianxiang Liu & Ting Kei Pong, 2017. "Further properties of the forward–backward envelope with applications to difference-of-convex programming," Computational Optimization and Applications, Springer, vol. 67(3), pages 489-520, July.
    3. Guoyin Li & Tianxiang Liu & Ting Kei Pong, 2017. "Peaceman–Rachford splitting for a class of nonconvex optimization problems," Computational Optimization and Applications, Springer, vol. 68(2), pages 407-436, November.

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