ACCELERATED SYMMETRIC ADMM AND ITS APPLICATIONS IN LARGE-SCALE SIGNAL PROCESSING  

作　　者：Jianchao Bai Ke Guo Junli Liang Yang Jing H.C.So 

机构地区：[1]Research&Development Institute of Northwestern Polytechnical University in Shenzhen,Shenzhen 518057,China [2]School of Mathematics and Statistics,Northwestern Polytechnical University,Xi’an 710129,China [3]Key Laboratory of Optimization Theory and Applications at China West Normal University of Sichuan Province,School of Mathematics and Information,China West Normal University,Nanchong 637009,China [4]School of Electronics and Information,Northwestern Polytechnical University,Xi’an 710129,China [5]Department of Electrical Engineering,City University of Hong Kong,Hong Kong,SAR,China

出　　处：《Journal of Computational Mathematics》2024年第6期1605-1626,共22页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.12001430,11801455,11971238);by the Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515012405);by the Shanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSQ001);by the Sichuan Science and Technology Program(Grant No.2023NSFSC1922);by the Innovation Team Funds of China West Normal University(Grant No.KCXTD2023-3);by the Fundamental Research Funds of China West Normal University(Grant No.23kc010);by the Open Project of Key Laboratory(Grant No.CSSXKFKTM202004),School of Mathematical Sciences,Chongqing Normal University.

摘　　要：The alternating direction method of multipliers(ADMM)has been extensively investigated in the past decades for solving separable convex optimization problems,and surprisingly,it also performs efficiently for nonconvex programs.In this paper,we propose a symmetric ADMM based on acceleration techniques for a family of potentially nonsmooth and nonconvex programming problems with equality constraints,where the dual variables are updated twice with different stepsizes.Under proper assumptions instead of the socalled Kurdyka-Lojasiewicz inequality,convergence of the proposed algorithm as well as its pointwise iteration-complexity are analyzed in terms of the corresponding augmented Lagrangian function and the primal-dual residuals,respectively.Performance of our algorithm is verified by numerical examples corresponding to signal processing applications in sparse nonconvex/convex regularized minimization.

关 键 词：Nonconvex optimization Symmetric ADMM Acceleration technique COMPLEXITY Signal processing 

分 类 号：O17[理学—数学]