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Global convergence in infeasible-interior-point algorithms

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Abstract

This paper presents a wide class of globally convergent interior-point algorithms for the nonlinear complementarity problem with a continuously differentiable monotone mapping in terms of a unified global convergence theory given by Polak in 1971 for general nonlinear programs. The class of algorithms is characterized as: Move in a Newton direction for approximating a point on the path of centers of the complementarity problem at each iteration. Starting from a strictly positive but infeasible initial point, each algorithm in the class either generates an approximate solution with a given accuracy or provides us with information that the complementarity problem has no solution in a given bounded set. We present three typical examples of our interior-point algorithms, a horn neighborhood model, a constrained potential reduction model with the use of the standard potential function, and a pure potential reduction model with the use of a new potential function.

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Author information

Authors and Affiliations

  1. Department of Information Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, 152, Tokyo, Japan

    Masakazu Kojima

  2. Ships Division, Equipment Bureau, Defense Agency, Minato-ku, 102, Tokyo, Japan

    Toshihito Noma

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

    Akiko Yoshise

Authors
  1. Masakazu Kojima
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  2. Toshihito Noma
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  3. Akiko Yoshise
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Research supported in part by Grant-in-Aids for Co-Operative Research (03832017) of the Japan Ministry of Education, Science and Culture.

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Kojima, M., Noma, T. & Yoshise, A. Global convergence in infeasible-interior-point algorithms. Mathematical Programming 65, 43–72 (1994). https://doi.org/10.1007/BF01581689

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  • DOI: https://doi.org/10.1007/BF01581689

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