A distributed alternating direction method of multipliers algorithm for consensus optimization

The Alternating Directions Methods of Multipliers (ADMM) are widely used in many fields of scientific computing in recent years. This method applies iterative computation to the information exchange between individual agent and neighbor. However, despite the success of traditional centralized ADMM in some application environments, its applicability is limited in global convergence center by its communication requirements. In our paper, we provide the linear convergence rate for this distributed consensus optimization problem, which satisfies strongly convex local objective functions. Then, the properties of the local objective function and the parameters of the algorithm, the theoretical convergence rate is given according to the network topology.