  We consider distributed smooth nonconvex unconstrained optimization over
networks, modeled as a connected graph. We examine the behavior of distributed
gradient-based algorithms near strict saddle points. Specifically, we establish
that (i) the renowned Distributed Gradient Descent (DGD) algorithm likely
converges to a neighborhood of a Second-order Stationary (SoS) solution; and
(ii) the more recent class of distributed algorithms based on gradient
tracking--implementable also over digraphs--likely converges to exact SoS
solutions, thus avoiding (strict) saddle-points. Furthermore, new convergence
rate results to first-order critical points is established for the latter class
of algorithms.
