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 non-linearity 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 provide a specific example to efficiently optimize an admission control scheme.