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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.09578 |
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Table of Contents:
- The commutation principle proved by Ramírez, Seeger, and Sossa (SIAM J Optim 23:687-694, 2013) in the setting of Euclidean Jordan algebras says that for a Fréchet differentiable function $Θ$ and a spectral function $F$, any local minimizer or maximizer $a$ of $Θ+F$ over a spectral set $\mathcal{E}$ operator commutes with the gradient of $Θ$ at $a$. In this paper, we improve this commutation principle by allowing $Θ$ to be nonsmooth with mild regularity assumptions over it. For example, for the case of local minimizer, we show that $a$ operator commutes with some element of the limiting (Mordukhovich) subdifferential of $Θ$ at $a$ provided that $Θ$ is subdifferentially regular at $a$ satisfying a qualification condition. For the case of local maximizer, we prove that $a$ operator commutes with each element of the (Fenchel) subdifferential of $Θ$ at $a$ whenever this subdifferential is nonempty. As an application, we characterize the local optimizers of shifted strictly convex spectral functions and norms over automorphism invariant sets.