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Path constrained unbalanced optimal transport

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Auteurs : Charon, Nicolas (Auteur de la conférence)
CIRM (Editeur )

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Résumé : We will present a variation of the unbalanced optimal transport model and Wasserstein Fisher-Rao metric on positive measures, in which one imposes additional affine integral equality constraints. This is motivated by multiple examples from mathematics and applied mathematics that naturally involve comparing and interpolating between two measures in particular subspaces or in which one enforces some constraints on the interpolating path itself. Building from the dynamic formulation of the Wasserstein Fisher-Rao metric, we introduce a class of constrained problems where the interpolating measure at each time must satisfy a given stationary or time-dependent constraint in measure space. We then specifically derive general conditions under which the existence of minimizing paths can be guaranteed, and then examine some of the properties of the resulting models and the metrics that are induced on measures. We will further hint at the potential of this approach in various specific situations such as the comparison of measures with prescribed moments, the unbalanced optimal transport under global mass evolution or obstacle constraints, and emphasize some connections with the construction of Riemannian metrics on the space of all convex shapes in an Euclidean space. We shall conclude with a few remaining unsolved/open questions.

Mots-Clés : unbalanced optimal transport; affine constraints; existence of minimizers

Codes MSC :
49Q22 - Optimal transportation

    Informations sur la Vidéo

    Réalisateur : Recanzone, Luca
    Langue : Anglais
    Date de Publication : 21/06/2024
    Date de Captation : 28/05/2024
    Sous Collection : Research talks
    Catégorie arXiv : Optimization and Control
    Domaine(s) : Théorie du Contrôle & Optimisation
    Format : MP4 (.mp4) - HD
    Durée : 00:43:03
    Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2024-05-28_Charon.mp4

Informations sur la Rencontre

Nom de la Rencontre : Geometric Sciences in Action: from geometric statistics to shape analysis / Les sciences géometriques en action: des statistiques géometriques à l'analyse de forme
Organisateurs de la Rencontre : Bauer, Martin ; Buet, Blanche ; Le Brigant, Alice ; Pennec, Xavier ; Sommer, Stefan
Dates : 27/05/2024 - 31/05/2024
Année de la rencontre : 2024
URL de la Rencontre : https://conferences.cirm-math.fr/2974.html

Données de citation

DOI : 10.24350/CIRM.V.20184503
Citer cette vidéo: Charon, Nicolas (2024). Path constrained unbalanced optimal transport. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20184503
URI : http://dx.doi.org/10.24350/CIRM.V.20184503

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