Numerical methods for the resource allocation problem in networks

TL;DR

This paper explores various numerical optimization techniques for resource allocation in large-scale networks, focusing on dual problem formulations, convergence rates, and distributed computation adaptations.

Contribution

It introduces and analyzes multiple numerical methods for solving the network resource allocation problem, emphasizing primal-dual analysis and distributed implementation strategies.

Findings

Convergence rates are estimated for each optimization method.

Modified algorithms are proposed for distributed network environments.

The dual problem approach effectively addresses large-scale resource allocation.

Abstract

In this paper, we consider the resource allocation problem in a network with a large number of connections which are used by a huge number of users. The resource allocation problem under discussion is a maximization problem with linear inequality constraints. To solve this problem we construct the dual problem and propose to use the following numerical optimization methods for the dual: a fast gradient method, a stochastic projected subgradient method, an ellipsoid method, and a random gradient extrapolation method. A special focus is made on the primal-dual analysis of these methods. For each method we estimate the convergence rate. We also provide some modifications of these methods in the setup of distributed computations, taking into account their application to networks.