Global attractor and limit points for nonsmooth ADMM

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.