Distributed sub-optimal resource allocation over weight-balanced graph via singular perturbation

TL;DR

This paper introduces a distributed sub-optimal resource allocation algorithm for weight-balanced graphs, utilizing singular perturbation analysis to ensure convergence and near-optimality with adjustable parameters.

Contribution

It proposes a simple continuous-time algorithm with proven convergence and sub-optimality, advancing distributed optimization methods over weight-balanced graphs.

Findings

Proven existence and uniqueness of the algorithm's equilibrium

Exponential convergence rate of the algorithm

Approaches optimal solution as parameter tends to zero

Abstract

In this paper, we consider distributed optimization design for resource allocation problems over weight-balanced graphs. With the help of singular perturbation analysis, we propose a simple sub-optimal continuous-time optimization algorithm. Moreover, we prove the existence and uniqueness of the algorithm equilibrium, and then show the convergence with an exponential rate. Finally, we verify the sub-optimality of the algorithm, which can approach the optimal solution as an adjustable parameter tends to zero.