Towards Fast-Convergence, Low-Delay and Low-Complexity Network Optimization

Distributed network optimization has been studied several years. However, we still do not have a good idea of how to design schemes that can simultaneously provide good performance across the dimensions of utility optimality, convergence speed, and delay. To address these challenges, in this paper, we propose a new algorithmic framework with all these metrics approaching optimality. The salient features of our new algorithm are three-fold: (i) fast convergence: it converges with only O(log(1/ε)) iterations, that is the fastest speed among all the existing algorithms; (ii) low delay: it guarantees optimal utility with finite queue length; (iii) simple implementation: the control variables of this algorithm are based on virtual queues that do not require maintaining per-flow information. The new technique builds on a kind of inexact Uzawa method in the Alternating Directional Method of Multiplier. A theoretical contribution of independent interest is a new pathway we provide to prove global and linear convergence rate of Uzawa-ADMM without requiring the full rank assumption of the constraint matrix.