Matrix completion via extended linearized augmented Lagrangian method of multipliers

The problem of recovering low-rank matrix from only a subset of observed entries is known as the matrix completion problem. Many problems arising in compressive sensing, image processing, machine learning, can be usefully cast as this problem. In this paper, we propose an extended linearized augmented Lagrangian method of multipliers for the problem, and prove its global convergence. We show that all the resulting subproblems have closed-forms solutions. Finally, some numerical experiments are conducted to show its efficiency.