Lowner's Operator and Spectral Functions in Euclidean Jordan Algebras

D SUN (matsundfnus.edu.sg)
J SUN (jsunnus.edu.sg)

Abstract: 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 solution would be of general interest for optimization.

Keywords: Differentiability, Jordan Algebra, Semismooth, Spectral Function

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Complementarity and Variational Inequalities

Category 3: Convex and Nonsmooth Optimization

Citation: Tech. Report, Dept. of Mathematics, National University of Singapore, Dec. 2004

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Entry Submitted: 12/26/2004
Entry Accepted: 12/28/2004
Entry Last Modified: 12/26/2004

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