  This paper aims to solve a distributed resource allocation problem with
binary local constraints. The problem is formulated as a binary program with a
cost function defined by the summation of agent costs plus a global
mismatch/penalty term. We propose a modification of the Hopfield Neural Network
(HNN) dynamics in order to solve this problem while incorporating a novel
Newton-like weighting factor. This addition lends itself to fast avoidance of
saddle points, which the gradient-like HNN is susceptible to. Turning to a
multi-agent setting, we reformulate the problem and develop a distributed
implementation of the Newton-like dynamics. We show that if a local solution to
the distributed reformulation is obtained, it is also a local solution to the
centralized problem. A main contribution of this work is to show that the
probability of converging to a saddle point of an appropriately defined energy
function in both the centralized and distributed settings is zero under light
assumptions. Finally, we enlarge our algorithm with an annealing technique
which gradually learns a feasible binary solution. Simulation results
demonstrate that the proposed methods are competitive with centralized greedy
and SDP relaxation approaches in terms of solution quality, while the main
advantage of our approach is a significant improvement in runtime over the SDP
relaxation method and the distributed quality of implementation.
