Distributed Optimization Algorithm for Composite Optimization Problems with Non-Smooth Function

This paper mainly studies the distributed optimization problems in a class of undirected networks. The objective function problem consists smooth convex and non-smooth function. Each agent network needs to optimize sum two functions. For this kind problem, based on operator splitting method, uses proximal deal with term further designs algorithm that allows use uncoordinated step-sizes. At same time, by introducing random-block coordinate mechanism, develops an asynchronous iterative version synchronous algorithm. Finally, convergence algorithms is proven, effectiveness verified through numerical simulations.