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Implementation of Interior-Point Methods for Large Scale Linear Programs

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Interior Point Methods of Mathematical Programming

Part of the book series: Applied Optimization ((APOP,volume 5))

Abstract

In the past 10 years the interior point methods (IPM) for linear programming have gained extraordinary interest as an alternative to the sparse simplex based methods. This has initiated a fruitful competition between the two types of algorithms which has led to very efficient implementations on both sides. The significant difference between interior point and simplex based methods is reflected not only in the theoretical background but also in the practical implementation. In this paper we give an overview of the most important characteristics of advanced implementations of interior point methods. First, we present the infeasible-primal-dual algorithm which is widely considered the most efficient general purpose IPM. Our discussion includes various algorithmic enhancements of the basic algorithm. The only shortcoming of the “traditional” infeasible-primal-dual algorithm is to detect a possible primal or dual infeasibility of the linear program. We discuss how this problem can be solved with the homogeneous and self-dual model.

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Authors and Affiliations

  1. Department of Management, Odense University, Campusvej 55, DK-5230, Odense M, Denmark

    Erling D. Anderson

  2. Logilab, HEC Geneva, Section of Management Studies, University of Geneva, 102 Bd Carl Vogt, CH-1211, Geneva 4, Switzerland

    Jacek Gondzio

  3. Department of Operations Research and Decision Support Systems, Computer and Automation Research Institute, Hungarian Academy of Sciences, Lágymányosi u.11, Budapest, Hungary

    Csaba Mészáros

  4. Institute of Systems Science, Academia Sinica, Beijing, 100080, China

    Xiaojie Xu

  5. Systems Research Institute, Polish Academy of Sciences, Newelska 6, Warsaw, 01-447, Poland

    Jacek Gondzio

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  1. Erling D. Anderson
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  4. Xiaojie Xu
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Editors and Affiliations

  1. Delft University of Technology, The Netherlands

    Tamás Terlaky

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Anderson, E.D., Gondzio, J., Mészáros, C., Xu, X. (1996). Implementation of Interior-Point Methods for Large Scale Linear Programs. In: Terlaky, T. (eds) Interior Point Methods of Mathematical Programming. Applied Optimization, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3449-1_6

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