Open Access Peer-reviewed

A Min-Max Algorithm for Solving the Linear Complementarity Problem

Youssef ELFOUTAYENI1, 2,, Mohamed KHALADI1, 2

1UMI UMMISCO, IRD - UPMC, Paris, France

2MPD Laboratory, UCAM, Marrakech, Maroc

Journal of Mathematical Sciences and Applications. 2013, 1(1), 6-11. DOI: 10.12691/jmsa-1-1-2
Published online: August 25, 2017

Abstract

The Linear Complementarity Problem LCP(M,q) is to find a vector x in IRn satisfying x0, Mx+q0 and xT(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.

Keywords:

linear complementarity problem, min-max algorithm, fixed point, Brouwer theorem, interval vector, closed bounded convex set
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