  In this paper, we consider the problem of minimizing the sum of nonconvex and
possibly nonsmooth functions over a connected multi-agent network, where the
agents have partial knowledge about the global cost function and can only
access the zeroth-order information (i.e., the functional values) of their
local cost functions. We propose and analyze a distributed primal-dual
gradient-free algorithm for this challenging problem. We show that by
appropriately choosing the parameters, the proposed algorithm converges to the
set of first order stationary solutions with a provable global sublinear
convergence rate. Numerical experiments demonstrate the effectiveness of our
proposed method for optimizing nonconvex and nonsmooth problems over a network.
