Subdifferentiation with symmetry

Fuente: arXiv
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Autor principal: Josz, Cédric
Formato: Preprint
Publicado: 2025
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author Josz, Cédric
author_facet Josz, Cédric
contents Given an objective function that is invariant under an action of a Lie group, we study how its subgradients relate to the orbits of the action. Our main finding is that they satisfy projection formulae analogous to those stemming from the Whitney and Verdier stratifications. If the function is definable in an o-minimal structure on the real field, then we also obtain an invariant variational stratification. On the application side, we derive a conservation law for subgradient dynamics under minimal assumptions. It can be used to detect instability in discrete subgradient dynamics.
format Preprint
id arxiv_https___arxiv_org_abs_2509_11422
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Subdifferentiation with symmetry
Josz, Cédric
Optimization and Control
Given an objective function that is invariant under an action of a Lie group, we study how its subgradients relate to the orbits of the action. Our main finding is that they satisfy projection formulae analogous to those stemming from the Whitney and Verdier stratifications. If the function is definable in an o-minimal structure on the real field, then we also obtain an invariant variational stratification. On the application side, we derive a conservation law for subgradient dynamics under minimal assumptions. It can be used to detect instability in discrete subgradient dynamics.
title Subdifferentiation with symmetry
topic Optimization and Control
url https://arxiv.org/abs/2509.11422