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On finite termination of an iterative method for linear complementarity problems

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Abstract

Based on a well-known reformulation of the linear complementarity problem (LCP) as a nondifferentiable system of nonlinear equations, a Newton-type method will be described for the solution of LCPs. Under certain assumptions, it will be shown that this method has a finite termination property, i.e., if an iterate is sufficiently close to a solution of LCP, the method finds this solution in one step. This result will be applied to a recently proposed algorithm by Harker and Pang in order to prove that their algorithm also has the finite termination property.

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Authors and Affiliations

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

    Andreas Fischer

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

    Christian Kanzow

Authors
  1. Andreas Fischer
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  2. Christian Kanzow
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Correspondence to Christian Kanzow.

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Fischer, A., Kanzow, C. On finite termination of an iterative method for linear complementarity problems. Mathematical Programming 74, 279–292 (1996). https://doi.org/10.1007/BF02592200

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  • DOI: https://doi.org/10.1007/BF02592200

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