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Complementarity Problems

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Interior Point Methods of Mathematical Programming

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

Abstract

This chapter deals with the interior point methods for solving complementarity problems. Complementarity problems provide generalized forms for nonlinear and/or linear programs and equilibrium problems. Among others, the monotone linear complementarity problem has two important applications in the mathematical programming, the linear program and the convex quadratic program. We focus on this problem and state its properties which serve as the theoretical backgrounds of various interior point methods. We provide two prototype algorithms in the class of interior point methods for the monotone linear complementarity problem and their theoretical views. Also we briefly refer to recent developments and further extensions on this subject.

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Authors and Affiliations

  1. Institute of Socio-Economic Planning, University of Tsukuba, Tsukuba, Ibaraki, 305, Japan

    Akiko Yoshise

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  1. Akiko Yoshise
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  1. Delft University of Technology, The Netherlands

    Tamás Terlaky

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© 1996 Kluwer Academic Publishers

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Yoshise, A. (1996). Complementarity Problems. 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_8

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  • DOI: https://doi.org/10.1007/978-1-4613-3449-1_8

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