Communications in Mathematical Sciences

Volume 15 (2017)

Number 8

On robust width property for Lasso and Dantzig selector

Pages: 2387 – 2393

(Fast Communication)



Hui Zhang (College of Science, National University of Defense Technology, Changsha, Hunan, China)


Recently, Cahill and Mixon completely characterized sensing operators in many compressed sensing instances with a robust width property, which allows uniformly stable and robust reconstruction via certain convex optimization. However, their current theory does not cover the Lasso and Dantzig selector models, both of which are popular alternatives in statistics and optimization community. In this short note, we show that the robust width property can be perfectly applied to these two types of models as well. Our main results affirmatively answer the question left by Cahill and Mixon.


robust width property, compressed sensing, Lasso model, Dantzig selector model

2010 Mathematics Subject Classification

65F22, 65K05, 90C25

This work is supported by the National Science Foundation of China (No. 11501569 and No. 61571008).

Received 8 May 2017

Accepted 24 August 2017

Published 20 December 2017