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Adaptive numerical methods for optimal and branched transport problems

dc.contributor.advisorSchmitzer, Bernhard Prof. Dr.
dc.contributor.authorMinevich, Olga
dc.date.accessioned2023-11-20T15:50:23Z
dc.date.available2023-11-27T00:50:10Z
dc.date.issued2023-11-20
dc.identifier.urihttp://resolver.sub.uni-goettingen.de/purl?ediss-11858/14988
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-10213
dc.format.extent112de
dc.language.isoengde
dc.subject.ddc510de
dc.titleAdaptive numerical methods for optimal and branched transport problemsde
dc.typedoctoralThesisde
dc.contributor.refereeSchmitzer, Bernhard Prof. Dr.
dc.date.examination2023-11-15de
dc.description.abstractengOptimal transport is an area of mathematical research that has been gaining popularity in recent years in various application fields such as economics, statistics or machine learning. Two important factors behind its increasing popularity are its modelling flexibility and the ever-expanding range of available dedicated computational tools. Unbalanced optimal transport is a generalization that allows for the comparison of measures with different mass, which is more appropriate in some applications. In this thesis, we consider the barycenter problem (i.e. finding a weighted average) between several input measures with respect to the unbalanced Hellinger–Kantorovich metric. In particular, we focus on the case with an uncountable number of Dirac input measures. We study existence, uniqueness and stability of the solutions, and demonstrate the intricate behavior of the barycenters with respect to the length scale parameter using analytical and numerical tools. Another important variant is branched transport, where the transport cost encourages the formation of branched transportation networks. We focus in this thesis on its convex relaxation in terms of multimaterial transport. In particular, we study the multimaterial problem in a setting when only a single topology of the solution is admissible and describe the simple structure of the dual solution in this case. We then formulate a problem with 3 sources and 1 sink where two candidate solutions of different topologies give the same transportation cost, study its properties and characterize the solution set.de
dc.contributor.coRefereeWirth, Benedikt Prof. Dr.
dc.subject.engOptimal Transportde
dc.subject.engMultimaterial Transportde
dc.subject.engUnbalanced Optimal Transportde
dc.subject.engNumerical Optimizationde
dc.subject.engHellinger--Kantorovich Barycentersde
dc.identifier.urnurn:nbn:de:gbv:7-ediss-14988-0
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullInformatik (PPN619939052)de
dc.description.embargoed2023-11-27de
dc.identifier.ppn1871667356
dc.identifier.orcid0000-0003-3981-2914de
dc.notes.confirmationsentConfirmation sent 2023-11-20T19:45:01de


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