@article{jmsa2013112,
author={AUTHOR = {ELFOUTAYENI, Youssef and KHALADI, Mohamed},
title={A Min-Max Algorithm for Solving the Linear Complementarity Problem},
journal={Journal of Mathematical Sciences and Applications},
volume={1},
number={1},
pages={6--11},
year={2013},
url={http://pubs.sciepub.com/jmsa/1/1/2},
abstract={The Linear Complementarity Problem <i>LCP(M,q)</i> is to find a vector <i>x</i> in IR<SUP>n</SUP> satisfying <i>x</i>&#8805;<i>0, Mx+q</i>&#8805;<i>0</i> and <i>x</i><SUP><i>T</i></SUP><i>(Mx+q)</i>=0, where <i>M</i> as a matrix and <i>q</i> as a vector, are given data. In this paper we show that the linear complementarity problem is completely equivalent to finding the fixed point of the map <i>x</i> = max (0, <i>(I-M)x</i>-<i>q</i>); to find an approximation solution to the second problem, we propose an algorithm starting from any interval vector <i>X</i><SUP><i>(0)</i></SUP> and generating a sequence of the interval vector (<i>X</i><SUP><i>(k)</i></SUP>)<SUB><i>k=1</i></SUB> which converges to the exact solution of our linear complementarity problem. We close our paper with some examples which illustrate our theoretical results.},
doi={10.12691/jmsa-1-1-2}
publisher={Science and Education Publishing}
}