  In this article, we focus on solving a class of distributed optimization
problems involving $n$ agents with the local objective function at every agent
$i$ given by the difference of two convex functions $f_i$ and $g_i$
(difference-of-convex (DC) form), where $f_i$ and $g_i$ are potentially
nonsmooth. The agents communicate via a directed graph containing $n$ nodes. We
create smooth approximations of the functions $f_i$ and $g_i$ and develop a
distributed algorithm utilizing the gradients of the smooth surrogates and a
finite-time approximate consensus protocol. We term this algorithm as
DDC-Consensus. The developed DDC-Consensus algorithm allows for non-symmetric
directed graph topologies and can be synthesized distributively. We establish
that the DDC-Consensus algorithm converges to a stationary point of the
nonconvex distributed optimization problem. The performance of the
DDC-Consensus algorithm is evaluated via a simulation study to solve a
nonconvex DC-regularized distributed least squares problem. The numerical
results corroborate the efficacy of the proposed algorithm.
