Abstract

Important properties such as differentiability and convexity of symmetric functions in Rn\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 ⁣:Sn→R∪{+∞}F\colon {\bf S}^n \rightarrow \mathbb{R\cup \{+\infty \}} is prox-regular if and only if the underlying symmetric function f ⁣:Rn→R∪{+∞}f\colon\mathbb{R}^{n}\rightarrow \mathbb{R\cup \{+\infty \}} is prox-regular. Relevant properties of symmetric sets are also discussed.

Author information

Contact details are reproduced from the original publication and may be historical.

Aris Daniilidis

Dep. de Matemàtiques C1/308, Universitat Autònoma de Barcelona, 08193 Bellaterra - Cerdanyola del Vallès, Spain

arisd@mat.uab.es

Adrian Lewis

School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, U.S.A.

aslewis@orie.cornell.edu

Hristo Sendov

Dept. of Statistical and Actuarial Sciences, The University of Western Ontario, London, Ontario, Canada

hssendov@stats.uwo.ca

Keywords

  • Spectral function
  • prox-regular function
  • eigenvalue optimization
  • invariant function
  • permutation theory

Mathematics Subject Classification

15A18, 49J52; 47A75, 90C22

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Suggested citation

A. Daniilidis, A. Lewis, J. Malick, H. Sendov. “Prox-Regularity of Spectral Functions and Spectral Sets.” Journal of Convex Analysis 15 (2008), No. 3, 547–560. https://doi.org/10.68381/jca15039

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Published by Heldermann Verlag, 2008. Rights now held by Banach Press LLC.