26 citations · 63 across the 25 of their papers we have counts for
5 papers · 1 filter
All convex bodies are in the subdifferential of some everywhere differentiable locally Lipschitz function
Aris Daniilidis, Robert Deville, Sebastian Tapia-Garcia
We construct a differentiable locally Lipschitz function in with the property that for every convex body there exists $\bar x \in \math…
Extending Rademacher Theorem to Set-Valued Maps
Aris Daniilidis, Marc Quincampoix
Rademacher theorem asserts that Lipschitz continuous functions between Euclidean spaces are differentiable almost everywhere. In this work we extend this result to set-valued maps…
Descent modulus and applications
Aris Daniilidis, Laurent Miclo, David Salas
The norm of the gradient f (x) measures the maximum descent of a real-valued smooth function f at x. For (nonsmooth) convex functions, this is expressed by the distance dis…
Orbits of geometric descent
Aris Daniilidis, Dmitriy Drusvyatskiy, A. S. Lewis
We prove that quasiconvex functions always admit descent trajectories bypassing all non-minimizing critical points.
Rectifiability of Self-contracted curves in the Euclidean space and applications
Aris Daniilidis, Guy David, Estibalitz Durand-Cartagena +1
It is hereby established that, in Euclidean spaces of finite dimension, bounded self-contracted curves have finite length. This extends the main result of Daniilidis, Ley, and Sabo…