Iteratively Linearized Reweighted Alternating Direction Method of Multipliers for a Class of Nonconvex Problems
This addresses computational and mathematical difficulties for researchers in signal processing and machine learning, but it is incremental as it builds on existing methods.
The paper tackles the challenge of solving nonconvex and nonsmooth problems in signal processing and machine learning by proposing a reweighted alternating direction method of multipliers, which ensures convex subproblems and demonstrates global convergence to a critical point with numerical efficiency.
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-Łojasiewicz property. Several numerical results are presented to demonstrate the efficiency of the proposed algorithm.