A Second-Order Multi-Agent Network for Bound-Constrained Distributed Optimization

TLDR

Agents communicate over an undirected graph, each knowing only its own objective and constraints. This note introduces a second‑order multi‑agent network that solves distributed optimization problems with convex objectives and bound constraints. The network achieves consensus by converting the distributed optimization into a second‑order dynamical system whose convergence is proven via a Lyapunov function. The network provably reaches optimal consensus under mild assumptions, outperforms existing first‑order networks by handling more general constraints, and is validated by simulations on two numerical examples.

Abstract

This technical note presents a second-order multi-agent network for distributed optimization with a sum of convex objective functions subject to bound constraints. In the multi-agent network, the agents connect each others locally as an undirected graph and know only their own objectives and constraints. The multi-agent network is proved to be able to reach consensus to the optimal solution under mild assumptions. Moreover, the consensus of the multi-agent network is converted to the convergence of a dynamical system, which is proved using the Lyapunov method. Compared with existing multi-agent networks for optimization, the second-order multi-agent network herein is capable of solving more general constrained distributed optimization problems. Simulation results on two numerical examples are presented to substantiate the performance and characteristics of the multi-agent network.