This paper proposes a validation method for solutions of linear complementarity problems. The validation procedure consists of two sufficient conditions that can be tested on a digital computer. If the first condition is satisfied then a given multidimensional interval centered at an approximate solution of the problem is guaranteed to contain an exact solution. If the second condition is satisfied then the multidimensional interval is guaranteed to contain no exact solution. This study is based on the mean value theorem for absolutely continuous functions and the reformulation of linear complementarity problems as nonsmooth nonlinear systems of equations.

Authors and Affiliations

1. Institut für Angewandte Mathematik, Universität Karlsruhe, Kaiserstrasse 12, D–76128 Karlsruhe, Germany, , , , , , DE

   G.E. Alefeld

2. Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan, , , , , , JP

   X. Chen

3. Department of Mathematics, University of Maryland, Baltimore, Md, USA, , , , , , US

   F.A. Potra

Received August 21, 1997 / Revised version July 2, 1998

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