Parabolic Regularity of Spectral Functions

• 成果类型: Article
• 署名作者: Mohammadi, Ashkan; Sarabi, Ebrahim
• 署名单位: Georgetown University; University System of Ohio; Miami University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0010
• 发表日期: 2025
• 关键词: 2nd-order epi-differentiability; 1st

摘要

This paper is devoted to the study of the second-order variational analysis of spectral functions. It is well-known that spectral functions can be expressed as a composite function of symmetric functions and eigenvalue functions. We establish several secondorder properties of spectral functions when their associated symmetric functions enjoy these properties. Our main attention is given to characterize parabolic regularity for this class of functions. It was observed recently that parabolic regularity can play a central rule in ensuring the validity of important second-order variational properties, such as twice epi-differentiability. We demonstrates that for convex spectral functions, their parabolic regularity amounts to that of their symmetric functions. As an important consequence, we calculate the second subderivative of convex spectral functions, which allows us to establish second-order optimality conditions for a class of matrix optimization problems.