Prox-regularity of spectral functions and spectral sets

Aris Daniilidis, Adrian Lewis, Jérôme Malick, Hristo Sendov

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15 Citations (Scopus)

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 languageEnglish
Pages (from-to)547-560
JournalJournal of Convex Analysis
Volume15
Issue number3
Publication statusPublished - 7 Aug 2008

Keywords

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

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    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.