In this paper we consider nonconvex optimization and learning over a network of distributed nodes. We develop a Proximal Primal-Dual Algorithm (Prox-PDA), which enables the network nodes to distributedly and collectively compute the set of first-order stationary solutions in a global sublinear manner [with a rate of O(1/r), where r is the iteration counter]. To the best of our knowledge, this is the first algorithm that enables distributed nonconvex optimization with global sublinear rate guarantees. Our numerical experiments also demonstrate the effectiveness of the proposed algorithm.
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