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Journal Articles Journal of Convex Analysis Year : 2008

## Prox-Regularity of Spectral Functions and Spectral Sets

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Aris Daniilidis
• Function : Author
• PersonId : 843792
Jérôme Malick

#### Abstract

Important properties such as differentiability and convexity of symmetric functions in $\mathbb{R}^{n}$ can be transferred to the corresponding spectral functions and vice-versa. Continuing to built on this line of research, we hereby prove that a spectral function $F\colon {\bf S}^n \rightarrow \mathbb{R\cup \{+\infty \}}$ is prox-regular if and only if the underlying symmetric function $f\colon\mathbb{R}^{n}\rightarrow \mathbb{R\cup \{+\infty \}}$ is prox-regular. Relevant properties of symmetric sets are also discussed.

### Dates and versions

hal-00317203 , version 1 (03-09-2008)

### Identifiers

• HAL Id : hal-00317203 , version 1

### Cite

Aris Daniilidis, Adrian Lewis, Jérôme Malick, Hristo Sendov. Prox-Regularity of Spectral Functions and Spectral Sets. Journal of Convex Analysis, 2008, 15 (3), pp.547-560. ⟨hal-00317203⟩

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