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This paper establishes a framework for designing fast, robust, and distributed algorithms for solving network utility maximization problems with coupled objective functions. The authors use two case studies in wireless communications to illustrate the key ideas: reverse-engineering the algorithm based on the KKT conditions of the optimization problem, and proving the properties of the algorithms using monotone mapping, contraction mapping, and super-modular game theory. In order to optimize the performance of communication and networking systems, they often model it mathematically as a Network Utility Maximization (NUM) problem.
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