Efficient Optimization of Constrained Nonlinear Resource Allocations

We present an efficient method to optimize network resource allocations under nonlinear Quality of Service (QoS) constraints. We first propose a suite of generalized proportional allocation schemes that can be obtained by minimizing the information-theoretic function of relative entropy. We then optimize over the allocation parameters, which are usually design variables an engineer can directly vary, either for a particular user or for the worst-case user, under constraints that lower bound the allocated resources for all other users. Despite the nonlinearity in the objective and constraints, we show this suite of resource allocation optimization can be efficiently solved for global optimality through a convex optimization technique called geometric programming. This general method and its extensions are applicable to a wide array of resource allocation problems, including processor sharing, congestion control, admission control, and wireless network power control. We focus on several specific formulations and numerical examples for an admission control scheme, and for power control problems of throughput maximization under outage and delay constraints for wireless multihop networks.