— For wireless cellular and ad hoc networks with QoS constraints, we propose a suite of problem formulations that allocate network resources to optimize SIR, maximize throughput and minimize delay. The distinguishing characteristics of these resource allocation formulations is that, by using convex optimization, they accommodate a variety of realistic QoS and fairness constraints. Their globally optimal solutions can be computed efficiently through polynomial time interior point methods, even though they use nonlinear objectives and constraints. Through power control in wireless cellular networks, we optimize SIR and delay for a particular QoS class, subject to QoS constraints for all other QoS classes. For wireless ad hoc networks with multihop transmissions and Rayleigh fading, we optimize various objectives, such as the overall system throughput, subject to constraints on power, probability of outage, and data rates. These formulations can also be used for admission control and r...