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Interior-point methods

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Encyclopedia of Operations Research and Management Science

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INTRODUCTION

Notwithstanding the success of the simplex method for linear programming (LP), there was, even from the earliest days of operations research, a desire to create an algorithm for solving linear programming problems that proceeded on a path through the polytope rather than around its perimeter. Indeed, methods were considered, but until recently, none was as effective as the simplex method. In this article, the motivation for desiring an “interior” path, the concept of the complexity of solving a linear programming problem, a brief his-tory of the developments in the area, and the status of the subject as of this writing are discussed. More complete surveys are given in Gonzaga (1991a, 1991b, 1992), Goldfarb and Todd (1989), Roos and Terlaky (1997), Roos, Terlaky and Vial (1997), Terlaky (1996), Ye (1997), Wright (1996) and Wright (1998). Generalizations to nonlinear problems are briefly discussed as well. For a thorough treatment of interior-point algorithms on those...

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Author information

Authors and Affiliations

  1. McMaster University, Hamilton, Ontario, Canada

    Tamaás Terlaky

  2. Sandia National Laboratories, Livermore, California, USA

    Paul T. Boggs

Authors
  1. Tamaás Terlaky
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  2. Paul T. Boggs
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Editor information

Editors and Affiliations

  1. Robert H. Smith School of Business, University of Maryland, College Part, Maryland, USA

    Saul I. Gass

  2. School of Information Technology & Engineering, George Mason University, Fairfax, Virginia, USA

    Carl M. Harris

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© 2001 Kluwer Academic Publishers

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Terlaky, T., Boggs, P.T. (2001). Interior-point methods. In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_475

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  • DOI: https://doi.org/10.1007/1-4020-0611-X_475

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-7923-7827-3

  • Online ISBN: 978-1-4020-0611-1

  • eBook Packages: Springer Book Archive

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