Convergence Analysis of Quantized Primal-Dual Algorithms in Network Utility Maximization Problems

Abstract

This paper investigates the asymptotic and nonasymptotic behavior of the quantized primal-dual (PD) algorithm in network utility maximization (NUM) problems, in which a group of agents maximizes the sum of their individual concave objective functions under linear constraints. In the asymptotic scenario, we use the information-theoretic notion of differential entropy power to establish universal bounds on the maximum exponential convergence rates of joint PD, primal and dual variables under optimum-achieving quantization schemes. These results provide tradeoffs between the speed of exponential convergence, the agents' objective functions, the communication bit rates, and the number of agents ..