DEXTRA: A Fast Algorithm for Optimization Over Directed Graphs

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/root 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 < tau < 1, given that the objective functions are restricted strongly convex. The implementation of DEXTRA requires each agent to know its local out-egree. Simulation examples further illustrate our findings.