On Computing the Copositive Minimum and its Representatives
Number Theory
2025-09-30 v1 Metric Geometry
Optimization and Control
Abstract
Computing the copositive minimum of a strictly copositive quadratic form is a natural generalization of computing the arithmetical minimum of a positive definite one. In this paper we show that this generalized problem is NP-complete. Moreover, we describe a practical method to calculate all shortest vectors using the LDLT-decomposition in a big class of special cases. Our numerical tests show that our method performs significantly better than previous approaches.
Cite
@article{arxiv.2509.23696,
title = {On Computing the Copositive Minimum and its Representatives},
author = {Alexander Oertel and Achill Schürmann},
journal= {arXiv preprint arXiv:2509.23696},
year = {2025}
}
Comments
19 pages, 2 figures