The successive approximation approach for multi-path utility maximization problem

In this paper, we solve the network utility maximization (NUM) problem for networks with both multi-path and single-path users. To deal with the non-strictly convexity and non-separability of the problem, we approximate it to a new strictly convex and separable problem which is efficiently solved by the standard dual-based decomposition approach. After a sequence of approximations, the solution to the approximation problem converges to a globally optimal solution of the original NUM. From the theoretical analysis, we also introduce a design of multi-path Reno (mReno) based on the reverse engineering framework of TCP Reno. The fairness among multi-path users and single-path users is guaranteed.