  In this paper, we develop a distributed mixing-accelerated primal-dual
proximal algorithm, referred to as MAP-Pro, which enables nodes in multi-agent
networks to cooperatively minimize the sum of their nonconvex, smooth local
cost functions in a decentralized fashion. The proposed algorithm is
constructed upon minimizing a computationally inexpensive
augmented-Lagrangian-like function and incorporating a time-varying mixing
polynomial to expedite information fusion across the network. The convergence
results derived for MAP-Pro include a sublinear rate of convergence to a
stationary solution and, under the Polyak-{\L}ojasiewics (P-{\L}) condition, a
linear rate of convergence to the global optimal solution. Additionally, we may
embed the well-noted Chebyshev acceleration scheme in MAP-Pro, which generates
a specific sequence of mixing polynomials with given degrees and enhances the
convergence performance based on MAP-Pro. Finally, we illustrate the
competitive convergence speed and communication efficiency of MAP-Pro via a
numerical example.
