# On properties of univariate max functions at local maximizers

@article{Mitchell2022OnPO,
title={On properties of univariate max functions at local maximizers},
author={Tim Mitchell and Michael L. Overton},
journal={Optimization Letters},
year={2022}
}
• Published 17 August 2021
• Mathematics
• Optimization Letters
More than three decades ago, Boyd and Balakrishnan established a regularity result for the two-norm of a transfer function at maximizers. Their result extends easily to the statement that the maximum eigenvalue of a univariate real analytic Hermitian matrix family is twice continuously differentiable, with Lipschitz second derivative, at all local maximizers, a property that is useful in several applications that we describe. We also investigate whether this smoothness property extends to max…
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