  This paper addresses a class of constrained optimization problems over
networks in which local cost functions and constraints can be nonconvex. We
propose an asynchronous distributed optimization algorithm, relying on the
centralized Method of Multipliers, in which each node wakes up in an
uncoordinated fashion and performs either a descent step on a local Augmented
Lagrangian or an ascent step on the local multiplier vector. These two phases
are regulated by a distributed logic-AND, which allows nodes to understand when
the descent on the (whole) Augmented Lagrangian is sufficiently small. We show
that this distributed algorithm is equivalent to a block coordinate descent
algorithm for the minimization of the Augmented Lagrangian followed by an
update of the whole multiplier vector. Thus, the proposed algorithm inherits
the convergence properties of the Method of Multipliers.
