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: | Sun Jie, Sun Defeng |
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.