Adaptive Mirror Descent for the Network Utility Maximization Problem

TL;DR

This paper introduces an adaptive mirror descent algorithm with dimension-free convergence for network utility maximization, demonstrating superior performance over existing methods in large-scale networks.

Contribution

It proposes a novel adaptive mirror descent method for large-scale network utility maximization with theoretical convergence guarantees.

Findings

Algorithm outperforms ellipsoid method in large networks

Convergence rate is dimension-free

Numerical simulations confirm theoretical results

Abstract

Network utility maximization is the most important problem in network traffic management. Given the growth of modern communication networks, we consider the utility maximization problem in a network with a large number of connections (links) that are used by a huge number of users. To solve this problem an adaptive mirror descent algorithm for many constraints is proposed. The key feature of the algorithm is that it has a dimension-free convergence rate. The convergence of the proposed scheme is proved theoretically. The theoretical analysis is verified with numerical simulations. We compare the algorithm with another approach, using the ellipsoid method (EM) for the dual problem. Numerical experiments showed that the performance of the proposed algorithm against EM is significantly better in large networks and when very high solution accuracy is not required. Our approach can be used in many network design paradigms, in particular, in software-defined networks.