A fast proximal iteratively reweighted nuclear norm algorithm for nonconvex low-rank matrix minimization problems

In this paper, we propose a fast proximal iteratively reweighted nuclear norm algorithm with extrapolation for solving a class of nonconvex low-rank matrix minimization problems. The proposed method incorporates two different extrapolation steps with respect to the previous iterations into the backward proximal step and the forward gradient step of the classic proximal iteratively reweighted method. We prove that the proposed method generates a convergent subsequence under general parameter constraints, and that any limit point is a stationary point of the problem. Furthermore, we prove that if the objective function satisfies the Kurdyka-Lojasiewicz property, the algorithm is globally convergent to a stationary point of the considered problem. Finally, we perform numerical experiments on a practical matrix completion problem with both synthetic and real data, the results of which demonstrate the efficiency and superior performance of the proposed algorithm. (C) 2022 IMACS. Published by Elsevier B.V. All rights reserved.