A parallel multi‐block alternating direction method of multipliers for tensor completion

Abstract

This paper proposes an algorithm for the tensor completion problem of estimating multi-linear data under the limitation of observation rate. Many tensor completion methods are based on nuclear norm minimization, they may fail to achieve the global solution for solving nuclear norm minimization in tensor completion problem with high missing ratio. To tackle this issue, an adaptive tensor completion method based on parallel multi-block alternating direction method of multipliers (ADMM) algorithm is proposed, it can derive the model from the initial estimate and compute the next estimate from the current solution. The parallel multi-block ADMM with global convergence is adopted to solve the dual problem, which greatly improves the processing power and reliability of the algorithm.