The New Method To Solve The Problem Of Matrix Rank Minimization

Matrix rank minimization problem is a hot problem in operations research, hasbeen widely used in the practical application, such as in the fields of control, signalprocessing, system identification. In the study of afne constraints matrix rankminimization problem, because the nuclear norm is the best convex approximationfor matrix rank function on the unit ball, the afne constraints matrix rank min-imization problem is transformed to afne constraints nuclear norm minimizationproblem.This paper presents two methods for solving nuclear norm minimization prob-lem, called the new algorithm and the accelerating algorithm respectively. The newalgorithm is based on gradient algorithm, and uses the average operator obtainedby composing non-expansive operator and identical operator as a convex combina-tion. Finally, through the experimental data, we can observe, the two algorithm isefective.