A linear programming approach to network utility maximization

This paper describes a linear programming (LP) approach for solving the network utility maximization problem. The developed approach is inspired by a convex relaxation technique from non-convex polynomial optimization methods. In contrast to most of the existing results where concavity of the network's utility function is often assumed, the proposed LP approach may still be used to solve the NUM problem even in the absence of such a concavity assumption. Although the presented LP approach is originally formulated to compute upper bounds for the global optima of the NUM problem, we illustrate through simulation examples that the obtained bounds often correspond to the exact global optima.