Distributed Safe Resource Allocation using Barrier Functions

TL;DR

This paper introduces a distributed feasible method using barrier functions for safe resource allocation in networked systems, ensuring each step is feasible and converges to near-optimal solutions efficiently.

Contribution

The paper presents a novel distributed algorithm that guarantees feasibility at every iteration for resource allocation problems, unlike traditional methods.

Findings

DFM ensures all iterates are feasible and safe.

DFM converges to an arbitrarily small neighborhood of the optimal solution.

Numerical experiments show DFM's competitive performance.

Abstract

Resource allocation plays a central role in many networked systems such as smart grids, communication networks and urban transportation systems. In these systems, many constraints have physical meaning and having feasible allocation is often vital to avoid system breakdown. Hence, algorithms with asymptotic feasibility guarantees are often insufficient since it is impractical to run algorithms for an infinite number of rounds. This paper proposes a distributed feasible method (DFM) for safe resource allocation based on barrier functions. In DFM, every iterate is feasible and thus safe to implement. We prove that under mild conditions, DFM converges to an arbitrarily small neighbourhood of the optimal solution. Numerical experiments demonstrate the competitive performance of DFM.