Localization of complementarity eigenvalues
Optimization and Control
2026-01-23 v1 Spectral Theory
Abstract
Let A, B be symmetric n x n real matrices with B positive definite and strictly diagonally dominant. We derive two localization sets for the complementarity eigenvalues of (A, B), the tightest one assuming additionally that A is copositive. This extends He-Liu-Shen sets to the case where B is not the identity. Moreover, we compare the computable bounds obtained from these new sets with the extreme classical generalized eigenvalues.
Cite
@article{arxiv.2601.15789,
title = {Localization of complementarity eigenvalues},
author = {Antonio Sasaki and Sophie Demassey and Valentina Sessa},
journal= {arXiv preprint arXiv:2601.15789},
year = {2026}
}