Antonio Sasaki, Sophie Demassey, Valentina Sessa, Localization of complementarity eigenvalues, Vol. 2027 (2027), No. 10, pp. 1-16

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DOI: 10.23952/cot.2027.10

Received September 27, 2025; Accepted January 21, 2026; Published online August 8, 2026

Abstract. Let $\mathbf{A},\mathbf{B}$ be symmetric $n\times n$ real matrices with $\mathbf{B}$ positive definite and strictly diagonally dominant. We derive two localization sets for the complementarity eigenvalues of $(\mathbf{A},\mathbf{B})$ , the tightest one assuming additionally that $\mathbf{A}$ is copositive. This extends He-Liu-Shen sets to the case where $\mathbf{B}$ is not the identity. Moreover, we compare the computable bounds obtained from these new sets with the extremal classical generalized eigenvalues.

How to Cite this Article:
A. Sasaki, S. Demassey, V. Sessa, Localization of complementarity eigenvalues, Commun. Optim. Theory 2027 (2027) 10.