文献类型：期刊文献

英文题名：Generalized Nonconvex Nonsmooth Low-Rank Matrix Recovery Framework With Feasible Algorithm Designs and Convergence Analysis

作者：Zhang, Hengmin[1,2];Qian, Feng[1,3];Shi, Peng[4,5];Du, Wenli[1,3];Tang, Yang[1,3];Qian, Jianjun[6,7];Gong, Chen[6,7];Yang, Jian[6,7]

机构：[1]East China Univ Sci & Technol, Sch Informat Sci & Engn, Key Lab Adv Smart Mfg Energy Chem Proc, Minist Educ, Shanghai 200237, Peoples R China;[2]Univ Macau, Dept Comp & Informat Sci, Macau, Peoples R China;[3]Tongji Univ, Shanghai Inst Intelligent Sci & Technol, Shanghai 200092, Peoples R China;[4]Univ Adelaide, Sch Elect & Elect Engn, Adelaide, SA 5005, Australia;[5]Victoria Univ, Coll Engn & Sci, Melbourne, Vic 8001, Australia;[6]Nanjing Univ Sci & Technol, PCA Lab, Nanjing 210094, Peoples R China;[7]Nanjing Univ Sci & Technol, Key Lab Intelligent Percept & Syst High Dimens In, Minist Educ, Nanjing 210094, Peoples R China

年份：2023

卷号：34

期号：9

起止页码：5342

外文期刊名：IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS

收录：;EI(收录号：20222812349449);WOS:【SCI-EXPANDED(收录号:WOS:000826418000001)】；

基金：This work was supported in part by the National Natural Science Fund for Distinguished Young Scholars under Grant 61725301; in part by the National Key Research and Development Program of China under Grant 2021YFB1714300; in part by the General and Youth Programs under Grant 61906067, Grant 62176124, Grant 61973162, and Grant 61876083; in part by the China Postdoctoral Science Foundation under Grant 2019M651415 and Grant 2020T130191; and in part by the UM Macao Talent Programme under Grant UMMTP-2020-01.

语种：英文

外文关键词：Convergence; Optimization; Minimization; Linear programming; Matrix decomposition; Convex functions; Learning systems; Algorithm designs; convergence analysis; low-rank matrix recovery; multiple variables; nonconvex alternating direction method of multiplier (ADMM)

摘要：Decomposing data matrix into low-rank plus additive matrices is a commonly used strategy in pattern recognition and machine learning. This article mainly studies the alternating direction method of multiplier (ADMM) with two dual variables, which is used to optimize the generalized nonconvex nonsmooth low-rank matrix recovery problems. Furthermore, the minimization framework with a feasible optimization procedure is designed along with the theoretical analysis, where the variable sequences generated by the proposed ADMM can be proved to be bounded. Most importantly, it can be concluded from the Bolzano-Weierstrass theorem that there must exist a subsequence converging to a critical point, which satisfies the Karush-Kuhn-Tucher (KKT) conditions. Meanwhile, we further ensure the local and global convergence properties of the generated sequence relying on constructing the potential objective function Particularly, the detailed convergence analysis would be regarded as one of the core contributions besides the algorithm designs and the model generality. Finally, the numerical simulations and the real-world applications are both provided to verify the consistence of the theoretical results, and we also validate the superiority in performance over several mostly related solvers to the tasks of image inpainting and subspace clustering.