The oriented mailing problem and its convex relaxation

Carioni, Marcello; Marchese, Andrea; Massaccesi, Annalisa; Pluda, Alessandra; Tione, Riccardo

doi:10.1016/j.na.2020.112035

Cited by 1 publication

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“…These three problems, although seemingly describing the optimal transport from different perspectives, turn out to have a lot in common, namely, under some assumptions, branched transport and urban planning problems can be shown to be equivalent [88,89], and the multimaterial transport problem can be shown to be their convex relaxation [92,87]. Multimaterial transport has also been gaining some popularity on its own in recent years, including for example the mailing problem [37] or the power line communication technology modelling [91].…”

Section: Introductionmentioning

confidence: 99%

Adaptive numerical methods for optimal and branched transport problems

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Optimal 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. Special thanks of course to my colleagues, especially, although not exclusively, those who shared with me a lot of espressos during the early 11 o'clock meetings. I would like to thank my main collaborators in the past few years, Dr. Mauro Bonafini, Dr. Julius Lohmann, (again) Prof. Bernhard Schmitzer and Prof. Benedikt Wirth for their expertise and input. I am also thankful to DFG SPP 1962 for the opportunity to perform, present and discuss my research within the framework of the Priority Program. My deepest gratitude without any unnecessary explanations goes to my family. "I move uphill without a stop, I waste no time.

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Section: Introductionmentioning

confidence: 99%

Adaptive numerical methods for optimal and branched transport problems

Minevich

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The oriented mailing problem and its convex relaxation

Cited by 1 publication

References 20 publications

Adaptive numerical methods for optimal and branched transport problems

Adaptive numerical methods for optimal and branched transport problems

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