Autor(en): | Lorenz, Dirk Mahler, Hinrich Meyer, Christian |
Titel: | L𝛼-Regularization of the Beckmann Problem |
Sprache (ISO): | en |
Zusammenfassung: | We investigate the problem of optimal transport in the so-called Beckmann form, i.e. given two Radon measures on a compact set, we seek an optimal flow field which is a vector valued Radon measure on the same set that describes a flow between these two measures and minimizes a certain linear cost function. We consider L𝛼 regularization of the problem, which guarantees uniqueness and forces the solution to be an integrable function rather than a Radon measure. This regularization naturally gives rise to a semi-smooth Newton scheme that can be used to solve the problem numerically. Besides motivating and developing the numerical scheme, we also include approximation results for vanishing regularization in the continuous setting. |
URI: | http://hdl.handle.net/2003/40815 http://dx.doi.org/10.17877/DE290R-22672 |
Erscheinungsdatum: | 2022-01 |
Enthalten in den Sammlungen: | Ergebnisberichte des Instituts für Angewandte Mathematik |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
---|---|---|---|---|
Ergebnisbericht Nr. 649.pdf | DNB | 1.75 MB | Adobe PDF | Öffnen/Anzeigen |
Diese Ressource ist urheberrechtlich geschützt. |
Diese Ressource ist urheberrechtlich geschützt. rightsstatements.org