Nonconvex Optimization for Communication Networks
نویسندگان
چکیده
Nonlinear convex optimization has provided both an insightful modeling language and a powerful solution tool to the analysis and design of communication systems over the last decade. A main challenge today is on nonconvex problems in these applications. This chapter presents an overview on some of the important nonconvex optimization problems in communication networks. Four typical applications are covered: Internet congestion control through nonconcave network utility maximization, wireless network power control through geometric and sigmoidal programming, DSL spectrummanagement through distributed nonconvex optimization, and Internet intra-domain routing through nonconvex, non-smooth optimization. A variety of nonconvex optimization techniques are showcased: sum-of-squares programming through successive SDP relaxation, signomial programming through successive GP relaxation, leveraging specific structures in these engineering problems for efficient and distributed heuristics, and changing the underlying protocol to enable a different problem formulation in the first place. Collectively, they illustrate three alternatives of tackling nonconvex optimization for communication networks: going “through” nonconvexity, “around” nonconvexity, and “above” nonconvexity.
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