  We present a new algorithmic paradigm for the decentralized solution of
graph-structured optimization problems that arise in the estimation and control
of network systems. A key and novel design concept of the proposed approach is
that it uses overlapping subdomains to promote and accelerate convergence. We
show that the algorithm converges if the size of the overlap is sufficiently
large and that the convergence rate improves exponentially with the size of the
overlap. The proposed approach provides a bridge between fully decentralized
and centralized architectures and is flexible in that it enables the
implementation of asynchronous schemes, handling of constraints, and balancing
of computing, communication, and data privacy needs. The proposed scheme is
tested in an estimation problem for a 9241-node power network and we show that
it outperforms the alternating direction method of multipliers.
