  Consider a set of networked agents endowed with private cost functions and
seeking to find a consensus on the minimizer of the aggregate cost. A new class
of random asynchronous distributed optimization methods is introduced. The
methods generalize the standard Alternating Direction Method of Multipliers
(ADMM) to an asynchronous setting where isolated components of the network are
activated in an uncoordinated fashion. The algorithms rely on the introduction
of randomized Gauss-Seidel iterations of a Douglas-Rachford operator for
finding zeros of a sum of two monotone operators. Convergence to the sought
minimizers is provided under mild connectivity conditions. Numerical results
sustain our claims.
