L𝛼-Regularization of the Beckmann Problem

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dc.contributor.authorLorenz, Dirk
dc.contributor.authorMahler, Hinrich
dc.contributor.authorMeyer, Christian
dc.date.accessioned2022-03-23T08:23:55Z
dc.date.available2022-03-23T08:23:55Z
dc.date.issued2022-01
dc.description.abstractWe 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.en
dc.identifier.issn2190-1767
dc.identifier.urihttp://hdl.handle.net/2003/40815
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-22672
dc.language.isoen
dc.relation.ispartofseriesErgebnisberichte des Instituts für Angewandte Mathematik;649
dc.subject.ddc610
dc.titleL𝛼-Regularization of the Beckmann Problemen
dc.typeText
dc.type.publicationtypepreprint
dcterms.accessRightsopen access
eldorado.secondarypublicationfalse

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