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Interior Point Methods for Large-Scale Linear Programming

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Handbook of Optimization in Telecommunications

Abstract

We discuss interior point methods for large-scale linear programming, with an emphasis on methods that are useful for problems arising in telecommunications. We give the basic framework of a primal-dual interior point method, and consider the numerical issues involved in calculating the search direction in each iteration, including the use of factorization methods and/or preconditioned conjugate gradient methods. We also look at interior point column generation methods which can be used for very large scale linear programs or for problems where the data is generated only as needed.

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Author information

Authors and Affiliations

  1. Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    John E. Mitchell, Kris Farwell & Daryn Ramsden

Authors
  1. John E. Mitchell
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  2. Kris Farwell
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  3. Daryn Ramsden
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Editor information

Editors and Affiliations

  1. AT&T Labs Research, Florham Park, New Jersey

    Mauricio G. C. Resende

  2. University of Florida, Gainesville, Florida

    Panos M. Pardalos

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Mitchell, J.E., Farwell, K., Ramsden, D. (2006). Interior Point Methods for Large-Scale Linear Programming. In: Resende, M.G.C., Pardalos, P.M. (eds) Handbook of Optimization in Telecommunications. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30165-5_1

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