The convergence properties of hierarchical overlapping coordination

Hierarchical overlapping coordination (HOC) has been developed in order to coordinate decision-making in a large-scale system in terms of its various hierarchical structures (i.e. decompositions) which are derived from the various aspects and databased on the system. The main drawback of HOC has been the convergence problem. The properties of convergence to the optimal point for HOC problems that have linear equality constraints and linear inequality constraints, respectively, are explored in this paper. Sufficient conditions for achieving convergence are presented and several examples are given.