  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.
