Löwner’s Operator and Spectral Functions in Euclidean Jordan Algebras - Sun, D.; Sun, Jie (Institute for Operations Research and the Management Sciences (I N F O R M S), 2008)
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 solution would be of general interest for optimization.