Distributed Optimization for Network Resource Allocation With Nonsmooth Utility Functions

The network utility maximization problem is the problem of maximizing the overall utility of a network under capacity constraints, where each source in the network has its own private nonsmooth concave utility function (which allows the true utility to be modeled accurately) and each link in the network has only its capacity constraint. To solve this problem, two distributed optimization algorithms are proposed: a projected proximal algorithm and a projected subgradient algorithm. These algorithms can be implemented for the case that each source tries to maximize only its utility by using its proximity operator or subdifferential and each link tries to satisfy only its capacity constraint by using the metric projection onto its capacity constraint set. A convergence analysis indicates that these algorithms are sufficient for each source to find the optimal resource allocation. The convergence, optimality, and performance of the proposed algorithms are demonstrated through numerical comparisons with the existing decentralized network flow control algorithm.