We consider problems where multiple agents cooperate to control their individual state so as to optimize a common objective while communicating with each other to exchange state information. Since communication costs can be significant, especially when the agents are wireless devices with limited energy, we seek conditions under which communication of state information among nodes can be restricted while still ensuring that the optimization process converges. We propose an asynchronous (event-driven) optimization scheme that limits communication to instants when some state estimation error function at a node exceeds a threshold and prove that, under certain conditions, such convergence is guaranteed when communication delays are negligible. We subsequently extend the analysis to include communication delays as long as they are bounded. We apply this approach to a sensor network coverage control problem where the objective is to maximize the probability of detecting events occurring in a given region and show that the proposed asynchronous approach may significantly reduce communication costs, hence also prolonging the system's lifetime, without any performance degradation.