Max-Weight Revisited: Sequences of Non-Convex Optimisations Solving Convex Optimisations

TL;DR

This paper unifies max-weight and dual subgradient methods within a single theoretical framework, revealing their deep connections in convex optimization using elementary, non-asymptotic analysis.

Contribution

It establishes a clear, elementary, non-asymptotic framework linking max-weight algorithms with dual subgradient methods for convex optimization.

Findings

Unified theoretical framework for max-weight and dual subgradient methods

Explicit connection between queue occupancies and Lagrange multipliers

Elementary, non-asymptotic analysis of the methods

Abstract

We investigate the connections between max-weight approaches and dual subgradient methods for convex optimisation. We find that strong connections exist and we establish a clean, unifying theoretical framework that includes both max-weight and dual subgradient approaches as special cases. Our analysis uses only elementary methods, and is not asymptotic in nature. It also allows us to establish an explicit and direct connection between discrete queue occupancies and Lagrange multipliers.