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Properties and Iterative Methods for the Q‐Lasso

Author

Listed:
  • Maryam A. Alghamdi
  • Mohammad Ali Alghamdi
  • Naseer Shahzad
  • Hong-Kun Xu

Abstract

We introduce the Q‐lasso which generalizes the well‐known lasso of Tibshirani (1996) with Q a closed convex subset of a Euclidean m‐space for some integer m ≥ 1. This set Q can be interpreted as the set of errors within given tolerance level when linear measurements are taken to recover a signal/image via the lasso. Solutions of the Q‐lasso depend on a tuning parameter γ. In this paper, we obtain basic properties of the solutions as a function of γ. Because of ill posedness, we also apply l1‐l2 regularization to the Q‐lasso. In addition, we discuss iterative methods for solving the Q‐lasso which include the proximal‐gradient algorithm and the projection‐gradient algorithm.

Suggested Citation

  • Maryam A. Alghamdi & Mohammad Ali Alghamdi & Naseer Shahzad & Hong-Kun Xu, 2013. "Properties and Iterative Methods for the Q‐Lasso," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:250943
    DOI: 10.1155/2013/250943
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    References listed on IDEAS

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    1. 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.
    2. 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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