Conference · 2020
Gradient-Consensus Method for Distributed Optimization in Directed Multi-Agent Networks,
V. Khatana, G. Saraswat, S. Patel and M. V. Salapaka
2020 American Control Conference (ACC), Denver, CO, USA
Abstract
In this article, a distributed optimization problem for minimizing a sum, Pn i=1 fi, of convex objective functions, fi, on directed graph topologies is addressed. Here each function fi is a function of n variables, private to agent i which defines the agent’s objective. These fi’s are assumed to be Lipschitz-differentiable convex functions. For solving this optimization problem, we develop a novel distributed algorithm, which we term as the gradient-consensus method. The gradient-consensus scheme uses a finite-time terminated consensus protocol called ρ-consensus, which allows each local estimate to be ρ-close to each other at every iteration. The parameter ρ is a fixed constant independent of the network size and topology. It is shown that the estimate of the optimal solution at any local agent i converges geometrically to the optimal solution within an O(ρ) neighborhood, where ρ can be chosen to be arbitrarily small.
BibTeX
@inproceedings{khatana-2020-gradient-consensus-method-for-distributed-optimization-in-di,
title = {Gradient-Consensus Method for Distributed Optimization in Directed Multi-Agent Networks,},
author = {V. Khatana and G. Saraswat and S. Patel and M. V. Salapaka},
booktitle = {2020 American Control Conference (ACC), Denver, CO, USA},
year = {2020},
doi = {10.23919/ACC45564.2020.9147544}
}