ADD-OPT: Accelerated Distributed Directed Optimization

In this paper, we consider distributed optimization problems where the goal is to minimize a sum of objective functions over a multiagent network. We focus on the case when the interagent communication is described by a strongly connected, <italic>directed</italic> graph. The proposed algorithm, Accelerated Distributed Directed OPTimization (ADD-OPT), achieves the best known convergence rate for this class of problems, <inline-formula> <tex-math notation="LaTeX">$O(\mu ^{k}),0<\mu <1$</tex-math></inline-formula>, given strongly convex, objective functions with globally Lipschitz-continuous gradients, where <inline-formula><tex-math notation="LaTeX">$k$ </tex-math></inline-formula> is the number of iterations. Moreover, ADD-OPT supports a wider and more realistic range of step sizes in contrast to existing work. In particular, we show that ADD-OPT converges for arbitrarily small (positive) step sizes. Simulations further illustrate our results.