Global attractor and limit points for nonsmooth ADMM. (June 2022)

• Record Type: Journal Article
• Authors: Jung, Yoon Mo; Shin, Bomi; Yun, Sangwoon
• Is Part Of: Applied mathematics letters. Volume 128(2022)
• Publication Date: 2022-06
• Subjects: Set-valued dynamical system -- Differential inclusion -- ADMM -- Global attractor -- ω-limit set; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107890
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: The alternating direction method of multipliers (ADMM) is frequently used to solve optimization problems derived from machine learning and statistics. Hence it is important to investigate the asymptotic behavior of ADMM. Most works in this direction deal with smooth objective functions excluding various important applications in the nonsmooth case. In this paper, we study the asymptotic behavior of the solutions of differential inclusions arising from ADMM applied to nonsmooth objective functions. More precisely, we associate a multiflow to this differential inclusion and analyze the structure of both ω -limit points and global attractors for this multiflow.