### Abstract

Important properties such as differentiability and convexity of symmetric functions in Rn 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 : Sn → R U {+00} is prox-regular if and only if the underlying symmetric function f: Rn → RU {+00} is prox-regular. Relevant properties of symmetric sets are also discussed.

Original language | English |
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Pages (from-to) | 547-560 |

Journal | Journal of Convex Analysis |

Volume | 15 |

Issue number | 3 |

Publication status | Published - 7 Aug 2008 |

### Keywords

- Eigenvalue optimization
- Invariant function
- Permutation theory
- Prox-regular function
- Spectral function

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## Cite this

Daniilidis, A., Lewis, A., Malick, J., & Sendov, H. (2008). Prox-regularity of spectral functions and spectral sets.

*Journal of Convex Analysis*,*15*(3), 547-560.