Distributed continuous-time convex optimization: discrete-time communication and privacy preservation

Solmaz Sajjadi Kia, Jorge Cortes, and Sonia Martinez
2014 American Control Conference

Abstract- We propose a distributed continuous-time algorithm to solve a network optimization problem where the global cost function is a strictly convex function composed of the sum of the local cost functions of the agents. We prove that this algorithm, when implemented over strongly connected and weight-balanced directed graph topologies, converges exponentially fast when the local cost functions are strongly convex and their gradients are globally Lipschitz. We extend such guarantees for time-varying strongly connected and weight-balanced digraphs. When the network topology is a connected undirected graph, we show that exponential convergence is still preserved if the gradients of the strongly convex local functions are Lipschitz on compact sets, while it is asymptotic if the local cost functions are convex. We also study discrete-time and event-triggered communication implementations. Specifically, we provide an upper bound on the stepsize that guarantees convergence over connected undirected graph topologies and, building on this result, desig a centralized event-triggered implementation that is free of Zeno behavior. Finally, we characterize the privacy preservation properties of our algorithm. Simulations illustrate our results.

Bib-tex entry:

@InProceedings{SSK-JC-SM:14,
author = {S. S. Kia and J. Cortes and S. Mart{\'\i}nez},
booktitle = {Proceedings of the American Control Conference, Portland, Oregon, USA, 2014},
title = {Distributed continuous-time convex optimization: discrete-time communication and privacy preservation},
year = {2014},
month = {June},
address = {Portland, OR}
}