Network utility maximisation: A DC programming approach for Sigmoidal utility function

Network Utility Maximisation for nonconcave utility functions is a challenging problem in Communication Systems. We propose an innovative approach in nonconvex programming framework for the Network Sigmoidal Utility Maximisation which has many applications, in particular in Multimedia and Internet congestion control. Our method is based on DC (Difference of Convex functions) programming and DCA (DC Algorithms) which have been successfully applied to many large-scale (smooth or nonsmooth) nonconvex programs in various areas. A simple DC formulation is proposed that leads to a fast and scalable DCA based algorithm. A distributed version of DCA is developed and some numerical examples are considered. Our algorithm given a global optimal solution in all cases.