  This paper considers the distributed optimization of a sum of locally
observable, non-convex functions. The optimization is performed over a
multi-agent networked system, and each local function depends only on a subset
of the variables. An asynchronous and distributed alternating directions method
of multipliers (ADMM) method that allows the nodes to defer or skip the
computation and transmission of updates is proposed in the paper. The proposed
algorithm utilizes different approximations in the update step, resulting in
proximal and majorized ADMM variants. Both variants are shown to converge to a
local minimum, under certain regularity conditions. The proposed asynchronous
algorithms are also applied to the problem of cooperative localization in
wireless ad hoc networks, where it is shown to outperform the other
state-of-the-art localization algorithms.
