Iteratively Linearized Reweighted Alternating Direction Method of Multipliers for a Class of Nonconvex Problems

Abstract: 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.