Decomposition methods for network utility maximization

Abstract

Network Utility Maximization (NUM) is the problem of allocating the right amount of resources to the nodes of a network, in order to maximize an overall utility function. There are many optimization tools to solve this problem in a centralized manner. In this thesis, we discuss distributed ways to solve various formulations of NUM problems. We decompose the problems into subproblems using Primal Decomposition, by applying direct resource allocation and then adjust the resources by small steps until equilibrium, and Dual Decomposition by pricing the resource in such manner that each node achieves the optimal utility. Many alternatives can be derived from these two methods, in different NUM formulations, with the use of multilevel decompositions. These decompositions may lead to better understanding of existing networks, reverse engineering of network protocols like TCP, better management of existing networks, and ways to design and operate new networks by layering as optimization. Finally, we experiment with the message passing of these algorithms and try to minimize the data transferred by quantizing the values.