A Distributed Methodology for Approximate Uniform Global Minimum Sharing

TL;DR

This paper introduces a scalable distributed approach for approximate global minimum sharing among decision-makers, ensuring stability and near-optimal solutions without increasing local variables with network size.

Contribution

It presents a novel adjustable approximate method that maintains decentralization, scalability, and uniform asymptotic stability in distributed minimum sharing problems.

Findings

Method achieves near-minimum solutions with stability guarantees.

Scalability: local variables do not grow with network size.

Uniform asymptotic stability towards a steady state.

Abstract

The paper deals with the distributed minimum sharing problem: a set of decision-makers compute the minimum of some local quantities of interest in a distributed and decentralized way by exchanging information through a communication network. We propose an adjustable approximate solution which enjoys several properties of crucial importance in applications. In particular, the proposed solution has good decentralization properties and it is scalable in that the number of local variables does not grow with the size or topology of the communication network. Moreover, a global and uniform (both in the initial time and in the initial conditions) asymptotic stability result is provided towards a steady state which can be made arbitrarily close to the sought minimum. Exact asymptotic convergence can be recovered at the price of losing uniformity with respect to the initial time.