Linearly Convergent Second-Order Distributed Optimization Algorithms

This article studies distributed optimization problems whose goal is to minimize the sum of cost functions located among agents in a network, where communications are described by a connected and undirected graph. Two novel second-order methods with adapt-then-combine strategy are developed. For the algorithms, explicit convergence rates are established under strongly convex and the Lipschitz gradient assumptions. Finally, numerical examples demonstrate the efficiency of algorithms and are in line with theoretical results.