Combinatorial Characterizations of K-matrices
Optimization and Control
2013-01-23 v3 Combinatorics
Abstract
We present a number of combinatorial characterizations of K-matrices. This extends a theorem of Fiedler and Ptak on linear-algebraic characterizations of K-matrices to the setting of oriented matroids. Our proof is elementary and simplifies the original proof substantially by exploiting the duality of oriented matroids. As an application, we show that a simple principal pivot method applied to the linear complementarity problems with K-matrices converges very quickly, by a purely combinatorial argument.
Cite
@article{arxiv.0911.2171,
title = {Combinatorial Characterizations of K-matrices},
author = {Jan Foniok and Komei Fukuda and Lorenz Klaus},
journal= {arXiv preprint arXiv:0911.2171},
year = {2013}
}
Comments
17 pages; v2, v3: clarified proof of Thm 5.5, minor corrections