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

Authors:
Christian Kanzow;Helmut Kleinmichel
Affiliations:
University of Hamburg, Institute of Applied Mathematics, Bundesstrasse 55, D-20146 Hamburg, Germany. E-mail: Email: kanzow@math.uni-hamburg.de;Technical University of Dresden, Institute of Numerical Mathematics, D-01062 Dresden, Germany. E-mail: Email: kleinmi@math.tu-dresden.de
Venue:
Computational Optimization and Applications
Year:
1998

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Abstract

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