  We consider the consensual distributed optimization problem and propose an
asynchronous version of the Alternating Direction Method of Multipliers (ADMM)
algorithm to solve it. The `asynchronous' part here refers to the fact that
only one node/processor is updated (i.e. performs a minimization step) at each
iteration of the algorithm. The selection of the node to be updated is decided
by simulating a Markov chain. The proposed algorithm is shown to have a linear
convergence property in expectation for the class of functions which are
strongly convex and continuously differentiable.
