A Second-Order Proximal Algorithm for Consensus Optimization

We develop a distributed second-order proximal algorithm, referred to as SoPro, to address in-network consensus optimization. The proposed SoPro algorithm converges linearly to the exact optimal solution, provided that the global cost function is locally restricted strongly convex. This relaxes the standard global strong convexity condition required by the existing distributed optimization algorithms to establish linear convergence. In addition, we demonstrate that SoPro is computation- and communication-efficient in comparison with the state-of-the-art distributed second-order methods. Finally, extensive simulations illustrate the competitive convergence performance of SoPro.