Integer matrices that are not copositive have certificates of less than quadratic complexity
Optimization and Control
2013-06-18 v1
Abstract
A real symmetric n times n matrix is called copositive if the corresponding quadratic form is non-negative on the closed first orthant. If the matrix fails to be copositive there exists some non-negative certificate for which the quadratic form is negative. Due to the scaling property, we can find such certificates in every neighborhood of the origin but their properties depend on the matrix of course and are hard to describe. If it is an integer matrix however, we are guaranteed certificates of a complexity that is at most a constant times the binary encoding length of the matrix raised to the power 3/2.
Cite
@article{arxiv.1306.3867,
title = {Integer matrices that are not copositive have certificates of less than quadratic complexity},
author = {Timo Hirscher},
journal= {arXiv preprint arXiv:1306.3867},
year = {2013}
}