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Interior Point Methods for Large-Scale Linear Programming

In: Handbook of Optimization in Telecommunications

Author

Listed:
  • John E. Mitchell

    (Rensselaer Polytechnic Institute, Mathematical Sciences)

  • Kris Farwell

    (Rensselaer Polytechnic Institute, Mathematical Sciences)

  • Daryn Ramsden

    (Rensselaer Polytechnic Institute, Mathematical Sciences)

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.

Suggested Citation

  • John E. Mitchell & Kris Farwell & Daryn Ramsden, 2006. "Interior Point Methods for Large-Scale Linear Programming," Springer Books, in: Mauricio G. C. Resende & Panos M. Pardalos (ed.), Handbook of Optimization in Telecommunications, chapter 1, pages 3-25, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-30165-5_1
    DOI: 10.1007/978-0-387-30165-5_1
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