  In this work we study the problem of unconstrained convex-optimization in a
fully distributed multi-agent setting which includes asynchronous computation
and lossy communication. In particular, we extend a recently proposed algorithm
named Newton-Raphson Consensus by integrating it with a broadcast-based average
consensus algorithm which is robust to packet losses. We show via the
separation of time scales principle that under mild conditions (i.e.,
persistency of the agents activation and bounded consecutive communication
failures) the proposed algorithm is proved to be locally exponentially stable
with respect to the optimal global solution. Finally, we complement the
theoretical analysis with numerical simulations that are based on real
datasets.
