Parabolic Regularity of Spectral Functions

Ashkan Mohammadi () and Ebrahim Sarabi ()
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Ashkan Mohammadi: Department of Mathematics, Georgetown University, Washington, District of Columbia 20057
Ebrahim Sarabi: Department of Mathematics, Miami University, Oxford, Ohio 45056

Mathematics of Operations Research, 2025, vol. 50, issue 3, 2017-2046

Abstract: 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.

Keywords: Primary: 49J52; 15A18; 49J53; spectral functions; parabolic regularity; twice epi-differentiability; composite optimization; second-order optimality conditions (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:50:y:2025:i:3:p:2017-2046

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