DEXTRA: A Fast Algorithm for Optimization Over Directed Graphs

Abstract

This paper develops a fast distributed algorithm, termed DEXTRA , to solve the optimization problem when $n$ agents reach agreement and collaboratively minimize the sum of their local objective functions over the network, where the communication between the agents is described by a directed graph. Existing algorithms solve the problem restricted to directed graphs with convergence rates of $O(\ln k/\sqrt{k})$ for general convex objective functions and $O(\ln k/k)$ when the objective functions are strongly convex, where $k$ is the number of iterations. We show that, with the appropriate step-size, DEXTRA converges at a linear rate $O(\tau ^{k})$ for $0 , given that the objective functions are restricted strongly convex. The implementation of DEXTRA requires each agent to know its local out-degree. Simulation examples further illustrate our findings.