I. Introduction
In wireless cellular networks with users sharing scarce resources such as power and spectrum, appropriate radio resource and interference management (RRIM) mechanisms are key to achieve desired performance objectives with respect to rates, quality-of-service, and fairness. Therefore, over the last decade, researchers have proposed a plethora of RRIM strategies designed to target different objectives such as throughput maximization, proportional fairness, or max-min fairness. In this paper, we are primarily interested in maximizing the minimum observed rate, which we refer to as the max-min utility optimization problem. This problem belongs to a general class of network utility optimization tasks, and it is strongly related to the notion of max-min fairness, which is widely considered in networks where fairness among different users is of utmost importance when allocating wireless resources [1]–[7].