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Distributed and iterative network utility maximization algorithms, such asthe primal-dual algorithms or the network-user decomposition algorithms, ofteninvolve trajectories where the iterates may be infeasible, convergence to theoptimal points of relaxed problems different from the original, or convergenceto local maxima. In this paper, we highlight the three issues with iterativealgorithms. We then propose a distributed and iterative algorithm that does notsuffer from the three issues. In particular, we assert the feasibility of thealgorithm's iterates at all times, convergence to the global maximum of thegiven problem (rather than to global maximum of a relaxed problem), andavoidance of any associated spurious rest points of the dynamics. A benchmarkalgorithm due to Kelly, Maulloo and Tan (1998) [Rate control for communicationnetworks: shadow prices, proportional fairness and stability, Journal of theOperational Research Society, 49(3), 237-252] involves fast user updatescoupled with slow network updates in the form of additive-increasemultiplicative-decrease of suggested user flows. The proposed algorithm may beviewed as one with fast user updates and fast network updates that keeps theiterates feasible at all times. Simulations suggest that the convergence rateof the ordinary differential equation (ODE) tracked by our proposed algorithm'siterates is comparable to that of the ODE for the aforementioned benchmarkalgorithm.

Network Utility Maximization Revisited: Three Issues and Their Resolution