  In this paper, we propose a convergent parallel best-response algorithm with
the exact line search for the nondifferentiable nonconvex sparsity-regularized
rank minimization problem. On the one hand, it exhibits a faster convergence
than subgradient algorithms and block coordinate descent algorithms. On the
other hand, its convergence to a stationary point is guaranteed, while ADMM
algorithms only converge for convex problems. Furthermore, the exact line
search procedure in the proposed algorithm is performed efficiently in
closed-form to avoid the meticulous choice of stepsizes, which is however a
common bottleneck in subgradient algorithms and successive convex approximation
algorithms. Finally, the proposed algorithm is numerically tested.
