Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras
Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras
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DOI：
10.1287/moor.1070.0300
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发表时间：
2008-05
期刊：
影响因子：
--
通讯作者：
Defeng Sun;Jie Sun
中科院分区：
文献类型：
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作者：
Defeng Sun;Jie Sun
本文在欧氏若当代数的框架下研究了Lowner算子和谱函数的解析性、可微性和半光滑性。特别是，我们表明，许多优化相关的经典结果在对称矩阵空间可以推广到这个框架内。例如，度量投影算子在任何对称锥定义在欧几里德约当代数被证明是强半光滑的。该研究还提出了几个开放的问题，其答案将是最优化研究的浓厚兴趣。
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.