Motivated by a variety of applications in control engineering and informationsciences, we study network resource allocation problems where the goal is tooptimally allocate a fixed amount of resource over a network of nodes. In theseproblems, due to the large scale of the network and complicatedinter-connections between nodes, any solution must be implemented in paralleland based only on local data resulting in a need for distributed algorithms. Inthis paper, we propose a novel distributed Lagrangian method, which requiresonly local computation and communication. Our focus is to understand theperformance of this algorithm on the underlying network topology. Specifically,we obtain an upper bound on the rate of convergence of the algorithm as afunction of the size and the topology of the underlying network. Theeffectiveness and applicability of the proposed method is demonstrated by itsuse in solving the important economic dispatch problem in power systems,specifically on the benchmark IEEE-14 and IEEE-118 bus systems.
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