Isotone projection cones and Q-matrices
Abstract
Proper cones with the property that the projection onto them is isotone with respect to the order they induce are called isotone projection cones. Isotone projection cones and their extensions have been used to solve complementarity problems and variational inequalities. Q-matrices are matrices with the property that all classical linear complementarity problems defined by them are solvable. This note will use the isotone projection cones to generate a large class of Q-matrices. More specifically, it will be shown that the product between a non-negative matrix with positive diagonal elements and a Stieltjes matrix is a Q-matrix.
Cite
@article{arxiv.1608.06958,
title = {Isotone projection cones and Q-matrices},
author = {A. B. Németh and S. Z. Németh},
journal= {arXiv preprint arXiv:1608.06958},
year = {2016}
}
Comments
We found a counterexample for Theorem 1 which shows that the result is not true. We also found the mistake in the proof. The sequence $x_n$ is not $\leq_K$-decreasing. It seems that there is no way of correcting the result of Theorem 1. Therefore, we would like to immediately withdraw the paper. We apologise for any inconvenience we caused