Distributed Optimization in Locally-Coupled Systems, with Applications to LTE Networks
16 February 2011
We develop a generic methodology for distributed optimization in locally-coupled systems, i.e., networked systems where the mutual impact among the various nodes is restricted to relatively small neighborhoods. The proposed approach is inspired by interacting-particle systems, linking the set of global optima with the steady-state distribution of a process that is driven by simple local interactions. In contrast to earlier studies, our method does not rely on any concavity/convexity assumptions, customized objective functions, or an ad hoc breakdown of the global optimization problem. Rather, our framework guarantees consistent treatment of the global optimization criterion, and allows for completely arbitrary objective functions as well as integrality constraints. The distributed nature of our method is a natural consequence of the inherent locality of the system and the additivity of the global objective function. We apply the proposed approach to resource allocation problems arising in LTE networks. In particular, we describe how generalized Network Utility Maximization problems, with nonconcave objective functions (due to interference) and discrete decision variables, can be solved in a distributed way. Extensive numerical experiments are presented to illustrate convergence and performance of the proposed method.
