Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras

Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras

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Article ID: iaor200954168
Country: United States
Volume: 33
Issue: 2
Start Page Number: 421
End Page Number: 445
Publication Date: May 2008
Journal: Mathematics of Operations Research
Authors: ,
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.

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