Dual Pricing Algorithms by Wireless Network Duality for Utility Maximization

This chapter presents the wireless network utility maximization problem by parameterizing the global optimality in terms of signal‐to‐interference‐ and‐noise‐ratio (SINR) assignment, power and interference temperature allocation as optimization problems having spectral radius constraints. It also presents wireless network duality and characterizes analytically the power and interference temperature of the primal and dual networks. The relationship between them and the gradients of the spectral radius constraints in the utility maximization problem is established. The utility maximization problem is solved using an optimization technique that can be interpreted as iteratively minimizing the Linterference load in the network. The chapter describes the system model and reformulates our utility maximization problem in the SINR domain with spectral radius constraints. Using non‐negative matrix theory, the chapter illustrates the wireless network duality that is used to design a distributed algorithm to solve the utility maximization problem.