Löwner’s Operator and Spectral Functions in Euclidean Jordan Algebras
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. Fo...
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| Format: | Journal Article |
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Institute for Operations Research and the Management Sciences (I N F O R M S)
2008
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| Online Access: | http://hdl.handle.net/20.500.11937/30342 |
| Summary: | 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. |
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