Distributed Augmented Lagrangian Method for Link-Based Resource Sharing Problems of Multi-Agent Systems

TL;DR

This paper introduces a distributed augmented Lagrangian algorithm for multi-agent energy management problems with edge-based constraints, capable of handling time-varying and asynchronous communication networks, with proven convergence properties.

Contribution

It presents a novel distributed dual-based augmented Lagrangian method that accommodates asynchronous updates and time-varying communication networks in multi-agent systems.

Findings

Algorithm converges under asynchronous and time-varying network conditions.

Convergence rate of the proposed method is established.

Applicable to energy systems with separable convex cost functions.

Abstract

A multi-agent optimization problem motivated by the management of energy systems is discussed. The associated cost function is separable and convex although not necessarily strongly convex and there exist edge-based coupling equality constraints. In this regard, we propose a distributed algorithm based on solving the dual of the augmented problem. Furthermore, we consider that the communication network might be time-varying and the algorithm might be carried out asynchronously. The time-varying nature and the asynchronicity are modeled as random processes. Then, we show the convergence and the convergence rate of the proposed algorithm under the aforementioned conditions.