  Network utility maximization is the most important problem in network traffic
management. Given the growth of modern communication networks, we consider the
utility maximization problem in a network with a large number of connections
(links) that are used by a huge number of users. To solve this problem an
adaptive mirror descent algorithm for many constraints is proposed. The key
feature of the algorithm is that it has a dimension-free convergence rate. The
convergence of the proposed scheme is proved theoretically. The theoretical
analysis is verified with numerical simulations. We compare the algorithm with
another approach, using the ellipsoid method (EM) for the dual problem.
Numerical experiments showed that the performance of the proposed algorithm
against EM is significantly better in large networks and when very high
solution accuracy is not required. Our approach can be used in many network
design paradigms, in particular, in software-defined networks.
