Distributed convex optimization via proportional-integral-differential algorithm

Abstract

This paper studies the distributed convex optimization problem, where the global utility function is the sum of local cost functions associated to the individual agents. Only using the local information, a novel continuous-time distributed algorithm based on proportional-integral-differential (PID) control strategy is proposed. Under the assumption that the global utility function is strictly convex and local utility functions have locally Lipschitz gradients, the exponential convergence of the proposed algorithm is established with undirected and connected graph among these agents. Finally, numerical simulations are presented to illustrate the effectiveness of theoretical results.