Pivoting in Linear Complementarity: Two Polynomial-Time Cases
Optimization and Control
2010-06-24 v2
Abstract
We study the behavior of simple principal pivoting methods for the P-matrix linear complementarity problem (P-LCP). We solve an open problem of Morris by showing that Murty's least-index pivot rule (under any fixed index order) leads to a quadratic number of iterations on Morris's highly cyclic P-LCP examples. We then show that on K-matrix LCP instances, all pivot rules require only a linear number of iterations. As the main tool, we employ unique-sink orientations of cubes, a useful combinatorial abstraction of the P-LCP.
Cite
@article{arxiv.0807.1249,
title = {Pivoting in Linear Complementarity: Two Polynomial-Time Cases},
author = {Jan Foniok and Komei Fukuda and Bernd Gärtner and Hans-Jakob Lüthi},
journal= {arXiv preprint arXiv:0807.1249},
year = {2010}
}
Comments
20 pages, v2: restructured and shortened, implemented referees' suggestions