[Dottorcomp] Seminari di Matematica Applicata, 03/03/2026, Emanuele Naldi

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

*Martedì 3 Marzo 2026*, alle *ore 16* precise, presso l'aula Beltrami del
Dipartimento di Matematica,

Emanuele Naldi (Università di Genova)

terrà un seminario dal titolo:

Proximal methods in the Wasserstein space: links and differences from the
Hilbert case.

Abstract: In this talk, we revisit the proximal point method, known in the
Wasserstein setting as the Jordan–Kinderlehrer–Otto (JKO) scheme. While the
classical JKO scheme assumes exact minimization at each step, practical
implementations rely on approximate solutions due to computational
constraints. We therefore investigate the asymptotic convergence properties
of the inexact JKO scheme and its generalization, the proximal-gradient
algorithm in the Wasserstein space. We analyze two types of inexactness:
errors in Wasserstein distance and errors in functional evaluations. We
establish rigorous convergence guarantees under controlled error
conditions. Beyond the inexact setting, we also extend the convergence
results by considering varying stepsizes. Our analysis expands previous
approaches, providing new insights into discrete Wasserstein gradient
flows. We finish the talk with a comparison to the Hilbert space setting,
where the proximity operator is nonexpansive, a property that plays a
central role in many classical convergence results. In the Wasserstein
setting, the nonexpansivity of the proximity operator generally fails, even
for geodesically convex functionals. We discuss the class of functions for
which this property still holds and highlight potential directions for
future research.

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https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/