Nonconvex Optimization for Communication Networks

Abstract

Convex optimization has provided both a powerful tool and an intriguing mentality to the analysis and design of communication systems over the last few years. A main challenge today is on nonconvex problems in these application. This paper presents an overview of some of the important nonconvex optimization problems in point-to-point and networked communication systems. Three typical applications are covered: Internet congestion control through nonconcave network utility maximization, wireless network power control through geometric and sigmoidal programming, and DSL spectrum management through distributed nonconvex optimization. A variety of nonconvex optimization techniques are showcased: from standard dual relaxation to sum-of-squares programming through successive SDP relaxation, signomial programming through successive GP relaxation, and leveraging the specific structures in problems for efficient and distributed heuristics.