Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 250943, 8 pages
http://dx.doi.org/10.1155/2013/250943
Research Article

Properties and Iterative Methods for the -Lasso

1Department of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, P.O. Box 4087, Jeddah 21491, Saudi Arabia
2Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
3Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan

Received 24 September 2013; Accepted 27 November 2013

Academic Editor: Chi-Keung Ng

Copyright © 2013 Maryam A. Alghamdi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of the Royal Statistical Society B, vol. 58, no. 1, pp. 267–288, 1996. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Journal on Scientific Computing, vol. 20, no. 1, pp. 33–61, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  3. D. L. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289–1306, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 489–509, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Communications on Pure and Applied Mathematics, vol. 59, no. 8, pp. 1207–1223, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. E. Candès and T. Tao, “The Dantzig selector: statistical estimation when p is much larger than n,” Annals of Statistics, vol. 35, no. 6, pp. 2313–2351, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. T. T. Cai, G. Xu, and J. Zhang, “On recovery of sparse signals via l1 minimization,” IEEE Transactions on Information Theory, vol. 55, no. 7, pp. 3388–3397, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  8. Y. Censor and T. Elfving, “A multiprojection algorithm using Bregman projections in a product space,” Numerical Algorithms, vol. 8, no. 2–4, pp. 221–239, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H.-K. Xu, “Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces,” Inverse Problems, vol. 26, no. 10, Article ID 105018, 17 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J.-J. Moreau, “Propriétés des applications ‘prox’,” Comptes Rendus de l'Académie des Sciences, vol. 256, pp. 1069–1071, 1963. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J.-J. Moreau, “Proximité et dualité dans un espace hilbertien,” Bulletin de la Société Mathématique de France, vol. 93, pp. 273–299, 1965. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. P. L. Combettes and V. R. Wajs, “Signal recovery by proximal forward-backward splitting,” Multiscale Modeling & Simulation, vol. 4, no. 4, pp. 1168–1200, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. C. A. Micchelli, L. Shen, and Y. Xu, “Proximity algorithms for image models: denoising,” Inverse Problems, vol. 27, no. 4, Article ID 045009, 30 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. H. K. Xu, “Properties and iterative methods for the Lasso and its variants,” Chinese Annals of Mathematics B, vol. 35, no. 3, 2014. View at Google Scholar
  15. H. Zou and T. Hastie, “Regularization and variable selection via the elastic net,” Journal of the Royal Statistical Society B, vol. 67, no. 2, pp. 301–320, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet