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 
@article{JCA_2008_15_3_JCA_2008_15_3_a7,
     author = {A. Daniilidis and A. Lewis and J. Malick and H. Sendov},
     title = {Prox-Regularity of {Spectral} {Functions} and {Spectral} {Sets}},
     journal = {Journal of convex analysis},
     pages = {547--56},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JCA_2008_15_3_JCA_2008_15_3_a7/}
}
TY  - JOUR
AU  - A. Daniilidis
AU  - A. Lewis
AU  - J. Malick
AU  - H. Sendov
TI  - Prox-Regularity of Spectral Functions and Spectral Sets
JO  - Journal of convex analysis
PY  - 2008
SP  - 547
EP  - 56
VL  - 15
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCA_2008_15_3_JCA_2008_15_3_a7/
ID  - JCA_2008_15_3_JCA_2008_15_3_a7
ER  - 
%0 Journal Article
%A A. Daniilidis
%A A. Lewis
%A J. Malick
%A H. Sendov
%T Prox-Regularity of Spectral Functions and Spectral Sets
%J Journal of convex analysis
%D 2008
%P 547-56
%V 15
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCA_2008_15_3_JCA_2008_15_3_a7/
%F JCA_2008_15_3_JCA_2008_15_3_a7
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/