Lowner's operator and spectral functions in euclidean Jordan algebras

• 成果类型: Article
• 署名作者: Sun, Defeng; Sun, Jie
• 署名单位: National University of Singapore; National University of Singapore
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1070.0300
• 发表日期: 2008
• 页码: 421-445
• 关键词: valued functions; p-properties; semidefinite; inverse; transformations; homeomorphisms; version

摘要

We study analyticity, differentiability, and semismoothness of Lowner'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.