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In this paper, we propose a convergent parallel best-response algorithm withthe exact line search for the nondifferentiable nonconvex sparsity-regularizedrank minimization problem. On the one hand, it exhibits a faster convergencethan subgradient algorithms and block coordinate descent algorithms. On theother hand, its convergence to a stationary point is guaranteed, while ADMMalgorithms only converge for convex problems. Furthermore, the exact linesearch procedure in the proposed algorithm is performed efficiently inclosed-form to avoid the meticulous choice of stepsizes, which is however acommon bottleneck in subgradient algorithms and successive convex approximationalgorithms. Finally, the proposed algorithm is numerically tested.

A Parallel Best-Response Algorithm with Exact Line Search for Nonconvex Sparsity-Regularized Rank Minimization