An Alternating Direction Method for Finding Dantzig Selectors

TL;DR

This paper introduces an alternating direction method for efficiently computing Dantzig selectors, demonstrating improved computational performance over existing first-order methods while maintaining solution quality.

Contribution

The paper proposes a novel alternating direction method combined with a nonmonotone gradient approach for Dantzig selector computation, showing superior efficiency.

Findings

Outperforms existing first-order methods in CPU time

Produces solutions of comparable quality

Effective for large-scale problems

Abstract

In this paper, we study the alternating direction method for finding the Dantzig selectors, which are first introduced in [8]. In particular, at each iteration we apply the nonmonotone gradient method proposed in [17] to approximately solve one subproblem of this method. We compare our approach with a first-order method proposed in [3]. The computational results show that our approach usually outperforms that method in terms of CPU time while producing solutions of comparable quality.