The Practical Performance of Subgradient Computational Techniques for Mesh Network Utility Optimization

Abstract

In the networking research literature, the problem of network utility optimization is often converted to the dual problem which, due to nondifferentiability, is solved with a particular subgradient technique. This technique is not an ascent scheme, hence each iteration does not necessarily improve the value of the dual function. This paper examines the performance of this computational technique in realistic mesh network settings. The traditional subgradient technique is compared to a subgradient technique that is an ascent algorithm. It is found that the traditional subgradient techniques suffer from poor performance. Specifically, for large networks, the convergence is slow. While increasing the step size improves convergence speed, due to stability problems, the step size cannot be set arbitrarily high, and suitable step sizes result in slow convergence. The traditional subgradient technique also suffers from difficulties when used online. The ascent scheme performs well in all respects, however, it is not a distributed technique.