Distributed linear programming with event-triggered communication

TL;DR

This paper develops a distributed algorithm for linear programming where agents communicate asynchronously based on local triggers, ensuring convergence despite limited information and communication constraints.

Contribution

It introduces a novel set of state-based triggers and a distributed dynamics that guarantees convergence without requiring a common Lyapunov function.

Findings

Agents successfully converge to the linear program solution

Communication triggers are effectively detected using only local info

The method handles asynchronous and event-triggered communications

Abstract

We consider a network of agents whose objective is for the aggregate of their states to converge to a solution of a linear program in standard form. Each agent has limited information about the problem data and can communicate with other agents at discrete time instants of their choosing. Our main contribution is the synthesis of a distributed dynamics and a set of state-based rules, termed triggers, that individual agents use to determine when to opportunistically broadcast their state to neighboring agents to ensure asymptotic convergence to a solution of the linear program. Our technical approach to the algorithm design and analysis overcomes a number of challenges, including establishing convergence in the absence of a common smooth Lyapunov function, ensuring that the triggers are detectable by agents using only local information, accounting for asynchronism in the state broadcasts, and ruling out various causes of arbitrarily fast state broadcasting. Various simulations illustrate our results.