Tapia Garcia, Sebastian (TU Wien, Austria): Sensitivity analysis of the slopes of convex functions

Vineri, 19 aprilie, ora 10, va invitam sa participati în cadrul colectivului de Geometrie la prelegerea invitată cu titlul:

Sensitivity analysis of the slopes of convex functions

susținută de Tapia Garcia, Sebastian (TU Wien, Austria).

Prelegerea va avea loc online, folosind Microsoft Teams. Linkul de acces este:


Alternativ se pot utiliza:

Meeting ID: 375 567 286 039
Passcode: Pik7Mr

Abstract: After the surprising result that asserts that two smooth convex functions, bounded by below, coincide up to a constant if and only if the norm of their gradients coincide [Boulmezaoud, Cieutat, Daniilidis 2018. SIOPT], there has been a considerable effort to extend it to more general settings. In this talk we focus our attention on the approximation results obtained in [Daniilidis, Drusvyatskiy 2023. PAMS] and [Daniilidis, Salas, Tapia-García 2023. Arxiv]. In the former one, roughly speaking, it is shown that the value of the difference of two convex functions is controlled by the uniform difference of their slopes and the uniform difference of the functions in the set of critical points. In the last one, for finite dimensional spaces, we show that Attouch theorem can be extended by means of the epigraphical-convergence of the sequence of the slopes (and a normalization condition), i.e. a sequence of lower semicontinuous convex functions converges epigraphically to a proper convex bounded by below function if and only if the sequence of slopes converges epigraphically to the slope of the limit (and a normalization condition).

This is a joint work with Aris Daniilidis and David Salas.