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Feasible descent algorithms for mixed complementarity problems

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Abstract.

In this paper we consider a general algorithmic framework for solving nonlinear mixed complementarity problems. The main features of this framework are: (a) it is well-defined for an arbitrary mixed complementarity problem, (b) it generates only feasible iterates, (c) it has a strong global convergence theory, and (d) it is locally fast convergent under standard regularity assumptions. This framework is applied to the PATH solver in order to show viability of the approach. Numerical results for an appropriate modification of the PATH solver indicate that this framework leads to substantial computational improvements.

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Authors and Affiliations

  1. University of Wisconsin – Madison, Computer Sciences Department, 1210 West Dayton Street, Madison, WI 53706, USA, e-mail: ferris@cs.wisc.edu, , , , , , US

    Michael C. Ferris

  2. University of Hamburg, Institute of Applied Mathematics, Bundesstrasse 55, D-20146 Hamburg, Germany, e-mail: kanzow@math.uni-hamburg.de, , , , , , DE

    Christian Kanzow

  3. University of Wisconsin – Madison, Computer Sciences Department, 1210 West Dayton Street, Madison, WI 53706, USA, e-mail: tmunson@cs.wisc.edu, , , , , , US

    Todd S. Munson

Authors
  1. Michael C. Ferris
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  2. Christian Kanzow
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  3. Todd S. Munson
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Received April 9, 1998 / Revised version received November 23, 1998¶Published online March 16, 1999

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Ferris, M., Kanzow, C. & Munson, T. Feasible descent algorithms for mixed complementarity problems. Math. Program. 86, 475–497 (1999). https://doi.org/10.1007/s101070050101

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  • DOI: https://doi.org/10.1007/s101070050101

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