Data e orario: Martedì, 1 aprile 2025, 14:30,  Aula Dal Passo

Relatore: Alessandro Scagliotti (Technical University of Munich)

Titolo: Trade-off Invariance Principle for regularized functionals

Abstract: When minimizing a regularized functional - i.e., one of the form $H(u) = F(u) + \alpha G(u)$, where $G$ is a regularization term and $\alpha$ is the regularization parameter - one generally expects multiple minimizers to exist; one might furthermore expect the term $G$ to assume different values in correspondence of different minimizers. We show, however, that for most choices of the parameter $\alpha$, all minimizers of the regularized functional share the same value of $G$. This holds without requiring any assumptions on the domain nor on the smoothness/convexity properties of the involved functionals.
We also prove a stronger result concerning the invariance of the limit of $G$ along minimizing sequences. Moreover, we demonstrate how these findings extend to multi-regularized functionals and - when an underlying differentiable structure is present- to critical points.

Nota: Questo seminario rientra tra le attività del progetto MUR "Dipartimenti d'eccellenza" MatMod@TOV (2023-27)
--
FROM 117.143.179.*