Finding Dantzig selectors with a proximity operator based fixed-point algorithm

A simple iterative method for finding the Dantzig selector, designed for linear regression problems, is introduced. The method consists of two stages. The first stage approximates the Dantzig selector through a fixed-point formulation of solutions to the Dantzig selector problem; the second stage constructs a new estimator by regressing data onto the support of the approximated Dantzig selector. The proposed method is compared to an alternating direction method. The results of numerical simulations using both the proposed method and the alternating direction method on synthetic and real-world data sets are presented. The numerical simulations demonstrate that the two methods produce results of similar quality; however the proposed method tends to be significantly faster.