  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.
