  Large scale, non-convex optimization problems arising in many complex
networks such as the power system call for efficient and scalable distributed
optimization algorithms. Existing distributed methods are usually iterative and
require synchronization of all workers at each iteration, which is hard to
scale and could result in the under-utilization of computation resources due to
the heterogeneity of the subproblems. To address those limitations of
synchronous schemes, this paper proposes an asynchronous distributed
optimization method based on the Alternating Direction Method of Multipliers
(ADMM) for non-convex optimization. The proposed method only requires local
communications and allows each worker to perform local updates with information
from a subset of but not all neighbors. We provide sufficient conditions on the
problem formulation, the choice of algorithm parameter and network delay, and
show that under those mild conditions, the proposed asynchronous ADMM method
asymptotically converges to the KKT point of the non-convex problem. We
validate the effectiveness of asynchronous ADMM by applying it to the Optimal
Power Flow problem in multiple power systems and show that the convergence of
the proposed asynchronous scheme could be faster than its synchronous
counterpart in large-scale applications.
