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...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.展开更多
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)+4 种基金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.
文摘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.
