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2013 Properties and Iterative Methods for the Q -Lasso
Maryam A. Alghamdi, Mohammad Ali Alghamdi, Naseer Shahzad, Hong-Kun Xu
Abstr. Appl. Anal. 2013(SI45): 1-8 (2013). DOI: 10.1155/2013/250943

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 l 1 - l 2 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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Maryam A. Alghamdi. Mohammad Ali Alghamdi. Naseer Shahzad. Hong-Kun Xu. "Properties and Iterative Methods for the Q -Lasso." Abstr. Appl. Anal. 2013 (SI45) 1 - 8, 2013. https://doi.org/10.1155/2013/250943

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1359.94052
MathSciNet: MR3147855
Digital Object Identifier: 10.1155/2013/250943

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI45 • 2013
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