A Proximal ADMM for Decentralized Composite Optimization

In this letter, we propose a proximal alternating direction method of multiplier (ADMM) to solve the composite optimization problem over a decentralized network. Compared with existing methods, such as PG-EXTRA and IC-ADMM, the proposed decentralized proximal ADMM method does not rely on assuming a smooth + nonsmooth structure on the objective functions, thus covering a wider range of composite optimization problems. Simulation results show that the proposed proximal ADMM presents a considerable performance advantage over existing state-of-the-art algorithms for both nonsmooth + nonsmooth and smooth + nonsmooth composite optimization problems.