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A New Class of Semismooth Newton-Type Methods for Nonlinear Complementarity Problems

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Abstract

We introduce a new, one-parametric class of NCP-functions. This class subsumes the Fischer function and reduces to the minimum function in a limiting case of the parameter. This new class of NCP-functions is used in order to reformulate the nonlinear complementarity problem as a nonsmooth system of equations. We present a detailed investigation of the properties of the equation operator, of the corresponding merit function as well as of a suitable semismooth Newton-type method. Finally, numerical results are presented for this method being applied to a number of test problems.

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Authors and Affiliations

  1. Institute of Applied Mathematics, University of Hamburg, Bundesstrasse 55, D-20146, Hamburg, Germany

    Christian Kanzow

  2. Institute of Numerical Mathematics, Technical University of Dresden, D-01062, Dresden, Germany

    Helmut Kleinmichel

Authors
  1. Christian Kanzow
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  2. Helmut Kleinmichel
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Kanzow, C., Kleinmichel, H. A New Class of Semismooth Newton-Type Methods for Nonlinear Complementarity Problems. Computational Optimization and Applications 11, 227–251 (1998). https://doi.org/10.1023/A:1026424918464

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  • DOI: https://doi.org/10.1023/A:1026424918464