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Properties and Iterative Methods for the Q‐Lasso

Author

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  • 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.

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Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:250943
DOI: 10.1155/2013/250943
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