Geodesic
Prox-Regularity of Spectral Functions and Spectral Sets
Journal of convex analysis, Tome 15 (2008) no. 3, pp. 547-56.

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 15A18, 49J52, 47A75, 90C22
Mots-clés : Spectral function, prox-regular function, eigenvalue optimization, invariant function, permutation theory 
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     title = {Prox-Regularity of {Spectral} {Functions} and {Spectral} {Sets}},
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A. Daniilidis; A. Lewis; J. Malick; H. Sendov. Prox-Regularity of Spectral Functions and Spectral Sets. Journal of convex analysis, Tome 15 (2008) no. 3, pp. 547-56. http://geodesic.mathdoc.fr/item/JCA_2008_15_3_JCA_2008_15_3_a7/