• Corpus ID: 253761006

# Descent modulus and applications

@inproceedings{Daniilidis2022DescentMA,
title={Descent modulus and applications},
author={Aris Daniilidis and Laurent Miclo and David Salas},
year={2022}
}
• Published 21 November 2022
• Mathematics
. The norm of the gradient k∇ f ( x ) k measures the maximum descent of a real-valued smooth function f at x . For (nonsmooth) convex functions, this is expressed by the distance dist(0 , ∂f ( x )) of the subdiﬀerential to the origin, while for general real-valued functions deﬁned on metric spaces by the notion of metric slope |∇ f | ( x ). In this work we propose an axiomatic deﬁnition of descent modulus T [ f ]( x ) of a real-valued function f at every point x , deﬁned on a general (not…

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