Youssef ELFOUTAYENI^{1, 2,}, Mohamed KHALADI^{1, 2}

The Linear Complementarity Problem LCP(M,q) is to find a vector x in IRⁿ 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.

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