  In this paper, we focus on solving an important class of nonconvex
optimization problems which includes many problems for example signal
processing over a networked multi-agent system and distributed learning over
networks. Motivated by many applications in which the local objective function
is the sum of smooth but possibly nonconvex part, and non-smooth but convex
part subject to a linear equality constraint, this paper proposes a proximal
zeroth-order primal dual algorithm (PZO-PDA) that accounts for the information
structure of the problem. This algorithm only utilize the zeroth-order
information (i.e., the functional values) of smooth functions, yet the
flexibility is achieved for applications that only noisy information of the
objective function is accessible, where classical methods cannot be applied. We
prove convergence and rate of convergence for PZO-PDA. Numerical experiments
are provided to validate the theoretical results.
