Distributed ADMM over directed graphs.
Kiran Rokade, Rachel Kalpana Kalaimani · arXiv (Cornell University) · 2020
We consider the problem of minimizing the sum of convex functions, where each function is privately known to an agent which is part of a communication network. We consider the case where the communication links in the network are directed. Assuming that the network is strongly connected and the objective functions are strongly convex with Lipschitz-continuous gradients, we propose an ADMM algorithm to solve the optimization problem in a distributed manner. We show that if the parameters of the algorithm are chosen appropriately, then the primal-dual iterates of the algorithm converge to their unique optimal points at a geometric rate. Through numerical examples, we observe that the performance of our algorithm is comparable with some state-of-the-art algorithms for solving distributed optimization problems over directed graphs.