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Title: Parabolic Regularity of Spectral Functions
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 second-order 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.  more » « less
Award ID(s):
2108546
PAR ID:
10534375
Author(s) / Creator(s):
;
Publisher / Repository:
Informs
Date Published:
Journal Name:
Mathematics of Operations Research
ISSN:
0364-765X
Subject(s) / Keyword(s):
spectral functions, parabolic regularity, twice epi-differentiability, composite optimization, second-order optimality conditions
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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