Strictly contractive Peaceman–Rachford splitting method to recover the corrupted low rank matrix

Abstract

Abstract The strictly contractive Peaceman–Rachford splitting method (SC-PRSM) attracts much attention on solving the separable convex programming. In this paper, the SC-PRSM is first applied to recover the corrupted low rank matrix, which extends the application of the SC-PRSM. At each iteration, we just solve two easy subproblems, where one subproblem has a closed solution and another needs to solve linear equations by the conjugate gradient method. Finally, numerical comparisons with the existing types of the alternating direction method of multipliers show that the SC-PRSM is efficient and competitive for recovering the low rank matrix problems.

Keywords

• Low rank matrix
• Strictly contractive Peaceman–Rachford splitting method
• Nuclear norm minimization