  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.
