Distributed Lagrangian Methods for Network Resource Allocation

TL;DR

This paper introduces a distributed Lagrangian algorithm for network resource allocation that operates with local data and communication, providing convergence guarantees and demonstrating effectiveness on power system benchmarks.

Contribution

It presents a novel distributed Lagrangian method with convergence analysis based on network topology, applicable to large-scale network resource problems.

Findings

Convergence rate depends on network size and topology.

Effective in solving power system economic dispatch problems.

Validated on IEEE benchmark power systems.

Abstract

Motivated by a variety of applications in control engineering and information sciences, we study network resource allocation problems where the goal is to optimally allocate a fixed amount of resource over a network of nodes. In these problems, due to the large scale of the network and complicated inter-connections between nodes, any solution must be implemented in parallel and based only on local data resulting in a need for distributed algorithms. In this paper, we propose a novel distributed Lagrangian method, which requires only local computation and communication. Our focus is to understand the performance of this algorithm on the underlying network topology. Specifically, we obtain an upper bound on the rate of convergence of the algorithm as a function of the size and the topology of the underlying network. The effectiveness and applicability of the proposed method is demonstrated by its use in solving the important economic dispatch problem in power systems, specifically on the benchmark IEEE-14 and IEEE-118 bus systems.