Efficient optimization of constrained nonlinear resource allocation

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 that 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 provide a specific example of efficiently optimizing an admission control scheme.