Abstract
This chapter provides an introductory analysis of linear programming foundations and large-scale methods. The chapter begins by discussing the basics of linear programming modeling and solution properties, duality principles for linear programming problems, and extensions to integer programming methods. We then develop Benders decomposition, Dantzig-Wolfe decomposition, and Lagrangian optimization procedures in the context of network design and routing problems that arise in telecommunications operations research studies. The chapter closes with a brief discussion and list of basic references for other large-scale optimization algorithms that are commonly used to optimize telecommunications systems, including basis partitioning, interior point, and heuristic methods.
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Smith, J.C., Sonuc, S.B. (2011). An Introduction to Integer and Large-Scale Linear Optimization. In: Kennington, J., Olinick, E., Rajan, D. (eds) Wireless Network Design. International Series in Operations Research & Management Science, vol 158. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6111-2_4
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DOI: https://doi.org/10.1007/978-1-4419-6111-2_4
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