# Generalized subdifferentials of spectral functions over Euclidean Jordan algebras

arXiv: https://arxiv.org/abs/1902.05270 · HTML: https://mlsanity.com/paper/1902.05270/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2019.

## Built on by (most cited first, 2 of 2)

- [SG-PALM: a Fast Physically Interpretable Tensor Graphical Model](https://mlsanity.com/paper/2105.12271/) (2021)
- [Interpretable and Scalable Graphical Models for Complex Spatio-temporal Processes](https://mlsanity.com/paper/2301.06021/) (2023)

## Abstract (arXiv)

This paper is devoted to the study of generalized subdifferentials of spectral functions over Euclidean Jordan algebras. Spectral functions appear often in optimization problems playing the role of "regularizer", "barrier", "penalty function" and many others. We provide formulae for the regular, approximate and horizon subdifferentials of spectral functions. In addition, under local lower semicontinuity, we also furnish a formula for the Clarke subdifferential, thus extending an earlier result by Baes. As application, we compute the generalized subdifferentials of the function that maps an element to its k-th largest eigenvalue. Furthermore, in connection with recent approaches for nonsmooth optimization, we present a study of the Kurdyka-Lojasiewicz (KL) property for spectral functions and prove a transfer principle for the KL-exponent. In our proofs, we make extensive use of recent tools such as the commutation principle of Ram'irez, Seeger and Sossa and majorization principles developed by Gowda.