A smoothing majorization method for l22-lpp matrix minimization

We discuss the l2-lp (with p ∈ (0, 1)) matrix minimization for recovering low rank matrix. A smoothing approach is developed for solving this non-smooth, non-Lipschitz and non-convex optimization problem, in which the smoothing parameter is used as a variable and a majorization method is adopted to solve the smoothing problem. The convergence theorem shows that any accumulation point of the sequence generated by the smoothing approach satisfies the necessary optimality condition for the l2-lp problem. As an application, we use the proposed smoothing majorization method to solve matrix completion problems. Numerical experiments indicate that our method is very efficient for obtaining the high quality recovery solution for matrix completion problems.