Löwner's operator and spectral functions in Euclidean Jordan algebras

Defeng Sun, J. Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

106 Citations (Scopus)

Abstract

We study analyticity, differentiability, and semismoothness of Löwner's operator and spectral functions under the framework of Euclidean Jordan algebras. In particular, we show that many optimization-related classical results in the symmetric matrix space can be generalized within this framework. For example, the metric projection operator over any symmetric cone defined in a Euclidean Jordan algebra is shown to be strongly semismooth. The research also raises several open questions, whose answers would be of strong interest for optimization research. © 2008 INFORMS.
Original languageEnglish
Pages (from-to)421-445
Number of pages25
JournalMathematics of Operations Research
Volume33
Issue number2
DOIs
Publication statusPublished - 1 May 2008
Externally publishedYes

Keywords

  • Euclidean Jordan algebras
  • Löwner's operator
  • Semismoothness
  • Spectral functions

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

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