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Advances in Applied Mathematics and Global Optimization pp 137–196Cite as

Nonconvex Optimization for Communication Networks

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Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 17))

Summary

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 spectrum management through distributed nonconvex optimization, and Internet intradomain routing through nonconvex, nonsmooth 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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Authors and Affiliations

  1. Electrical Engineering Department, Princeton University, 08544, Princeton, NJ, U.S.A

    Mung Chiang

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  1. Mung Chiang
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Correspondence to Mung Chiang .

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Editors and Affiliations

  1. Dept. Mathematics, Virginia Tech, McBryde Hall 524, Blacksburg, 24061, U.S.A.

    David Y. Gao

  2. State University, Dept. Industrial & Systems Engineering, Virginia Polytechnic Institute &, Whittemore Hall 547, Blacksburg, 24061, U.S.A.

    Hanif D. Sherali

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Chiang, M. (2009). Nonconvex Optimization for Communication Networks. In: Gao, D., Sherali, H. (eds) Advances in Applied Mathematics and Global Optimization. Advances in Mechanics and Mathematics, vol 17. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-75714-8_5

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