Network Utility Maximization Problem with Monotonic Functions

摘要

We consider the Network Utility Maximization ProbleM with a non-concave, monotonically increasing objective functioa Non-concave utility functions model inelastic traffic flows. Maximization of a nonconcave function over a closed, convex set is a nonconvex programming problem. In this paper we establish a necessary and sufficient global optimality condition for problems with a monotonic objective function. On the basis of this result we propose a numerical method for solving a class of monotonic problems.