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.
@article{arxiv.1707.09178,
title = {Newton-Raphson Consensus under asynchronous and lossy communications for peer-to-peer networks},
author = {Nicoletta Bof and Ruggero Carli and Giuseppe Notarstefano and Luca Schenato and Damiano Varagnolo},
journal= {arXiv preprint arXiv:1707.09178},
year = {2017}
}