Asynchronous Newton-Raphson Consensus for Distributed Convex Optimization !

We consider the distributed unconstrained minimization of separable convex cost functions, where the global cost is given by the sum of several local and private costs, each associated to a specific agent of a given communication network. We specifically address an asynchronous distributed optimization technique called Newton-Raphson Consensus. Beside having low computational complexity, low communication requirements and being interpretable as a distributed Newton-Raphson algorithm, the technique has also the beneficial properties of requiring very little coordination and naturally supporting time-varying topologies. In this work we analytically prove that under some assumptions it shows either local or global convergence properties, and corroborate this result by the means of numerical simulations.