@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 *LCP(M,q)* is to find a vector *x* in IR^{n} satisfying *x*≥*0, Mx+q*≥*0* and *x*^{T}*(Mx+q)*=0, where *M* as a matrix and *q* 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 *x* = max (0, *(I-M)x*-*q*); to find an approximation solution to the second problem, we propose an algorithm starting from any interval vector *X*^{(0)} and generating a sequence of the interval vector (*X*^{(k)})_{k=1} 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}
}