ROBUST INEXACT ALTERNATING OPTIMIZATION FOR MATRIX COMPLETION WITH OUTLIERS  

作　　者：Ji Li Jian-Feng Cai Hongkai Zhao 

机构地区：[1]Beijing Computational Science Research Center,Beijing 100193,China [2]Department of Mathematics,Hong Kong University of Science and Technology,Clear Water Bay,Kowloon,Hong Kong [3]Department of Mathematics,University of California,Irvine,CA,USA

出　　处：《Journal of Computational Mathematics》2020年第2期337-354,共18页计算数学（英文）

基　　金：JL was supported by China Postdoctoral Science Foundation grant No.2017M620589;JFC was supported in part by Hong Kong Research Grant Council(HKRGC)grants 16300616 and 16306317;HK Zhao was supported in part by NSF grants DMS-1418422 and DMS-1622490.

摘　　要：We investigate the problem of robust matrix completion with a fraction of observation corrupted by sparsity outlier noise.We propose an algorithmic framework based on the ADMM algorithm for a non-convex optimization,whose objective function consists of an l1 norm data fidelity and a rank constraint.To reduce the computational cost per iteration,two inexact schemes are developed to replace the most time-consuming step in the generic ADMM algorithm.The resulting algorithms remarkably outperform the existing solvers for robust matrix completion with outlier noise.When the noise is severe and the underlying matrix is ill-conditioned,the proposed algorithms are faster and give more accurate solutions than state-of-the-art robust matrix completion approaches.

关 键 词：Matrix completion ADMM Outlier noise Inexact projection 

分 类 号：O24[理学—计算数学]