An Implementable Accelerated Alternating Direction Method of Multipliers for Low-Rank Tensor Completion

Low-rank tensor completion has attracted much interest in many applications such as image processing, data mining and machine learning. A widely used method is to minimize the sum of nuclear norms of unfolding matrices of a tensor. In this paper, we study a accelerated alternating direction method of multipliers (ADMM) for solving the sum of nuclear norms of unfolding matrices of a tensor. The basic idea of accelerated ADMM is to incorporate a multistep acceleration scheme into the classical ADMM. We design efficient implementations of the algorithm and present its convergence result. Extensive numerical examples on both random and real world data are presented to validate the superiority of our proposed algorithm over class ADMM.