An alternating direction method for finding Dantzig selectors

In this paper, we study the alternating direction method for finding the Dantzig selectors, which are first introduced in Candès and Tao (2007a). In particular, at each iteration we apply the nonmonotone gradient method proposed in Lu and Zhang (in press) to approximately solve one subproblem of this method. We compare our approach with a first-order method proposed in Becker et al. (2011). The computational results show that our approach usually outperforms that method in terms of CPU time while producing solutions of comparable quality.