Distributed event-triggered optimization for linear programming

This paper considers a network of agents whose objective is for the aggregate of their states to converge to a solution of a linear program. We assume that each agent has limited information about the problem data and communicates with other agents at discrete times of its choice. Our main contribution is the development of a distributed continuous-time dynamics and a set of state-based rules, termed triggers, that an individual agent can use to determine when to broadcast its state to neighboring agents to ensure convergence. 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, and accounting for the asynchronism in the state broadcasts of the agents. Simulations illustrate our results.