# 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} }

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…

## 2 Citations

### Root-max Problems, Hybrid Expansion-Contraction, and Quadratically Convergent Optimization of Passive Systems

- Mathematics, Computer ScienceArXiv
- 2021

We present quadratically convergent algorithms to compute the extremal value of a real parameter for which a given rational transfer function of a linear time-invariant system is passive. This…

### Convergence rate analysis and improved iterations for numerical radius computation

- Computer ScienceArXiv
- 2020

An improved level-set method is introduced that is often significantly faster than the existing approach of Mengi and Overton and the first rate of convergence results for any numerical radius method are established, showing how the convergence of Uhlig's cutting-plane method varies from superlinear to linear based on the normalized curvature at outermost points in the field of values.

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