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Interior-Point Methods for Conic-Linear Optimization

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Encyclopedia of Operations Research and Management Science

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Introduction

Even with the success of the simplex method for linear programming (LP), there was from the earliest days of operations research a desire to create an algorithm for solving LP problems that proceeded on a path through the polytope rather than around its perimeter. Interior point methods (IPMs) were first developed in 1950s, analyzed and first implemented in the 1960s. At that time the conclusion was made that IPMs were not competitive with other algorithms, especially with simplex methods. The continuous effort to find a polynomial algorithm for LP problems led to the revitalization of IPMs. In 1984 Karmarkar first proved the polynomial complexity of an IPM, which led to the “Interior Point Revolution” (Wright 2004) in mathematical programming. In this article the motivation for desiring an interior path, the concept of the complexity of solving LP problems, a brief history of the developments in the area, and the research state of the art are discussed, including...

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Author information

Authors and Affiliations

  1. Lehigh University, Harold S. Mohler Laboratory, 200 West Packer Avenue, Bethlehem, PA, 18015-1582, USA

    Tamás Terlaky

  2. Sandia National Laboratories, Livermore, CA, USA

    Paul T. Boggs

  3. National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA

    Paul T. Boggs

Authors
  1. Tamás Terlaky
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  2. Paul T. Boggs
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Correspondence to Tamás Terlaky .

Editor information

Editors and Affiliations

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

    Saul I. Gass

  2. Robert H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, MD, USA

    Michael C. Fu

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Terlaky, T., Boggs, P.T. (2013). Interior-Point Methods for Conic-Linear Optimization. In: Gass, S.I., Fu, M.C. (eds) Encyclopedia of Operations Research and Management Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1153-7_475

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  • DOI: https://doi.org/10.1007/978-1-4419-1153-7_475

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