Title: Distributed Nesterov gradient methods over arbitrary graphs,
Abstract: In this letter, we introduce a distributed Nesterov method, termed as
$\mathcal{ABN}$, that does not require doubly-stochastic weight matrices.
Instead, the implementation is based on a simultaneous application of both row-
and column-stochastic weights that makes this method applicable to arbitrary
(strongly-connected) graphs. Since constructing column-stochastic weights needs
additional information (the number of outgoing neighbors at each agent), not
available in certain communication protocols, we derive a variation, termed as
FROZEN, that only requires row-stochastic weights but at the expense of
additional iterations for eigenvector learning. We numerically study these
algorithms for various objective functions and network parameters and show that
the proposed distributed Nesterov methods achieve acceleration compared to the
current state-of-the-art methods for distributed optimization.