  In this paper, we consider solving a class of nonconvex and nonsmooth
problems frequently appearing in signal processing and machine learning
research. The traditional alternating direction method of multipliers
encounters troubles in both mathematics and computations in solving the
nonconvex and nonsmooth subproblem. In view of this, we propose a reweighted
alternating direction method of multipliers. In this algorithm, all subproblems
are convex and easy to solve. We also provide several guarantees for the
convergence and prove that the algorithm globally converges to a critical point
of an auxiliary function with the help of the Kurdyka-{\L}ojasiewicz property.
Several numerical results are presented to demonstrate the efficiency of the
proposed algorithm.
