Skip to Main content Skip to Navigation

Unbalanced Optimal Transport : Models, Numerical Methods, Applications

Abstract : This thesis generalizes optimal transport beyond the classical "balanced" setting of probability distributions. We define unbalanced optimal transport models between nonnegative measures, based either on the notion of interpolation or the notion of coupling of measures. We show relationships between these approaches. One of the outcomes of this framework is a generalization of the p-Wasserstein metrics. Secondly, we build numerical methods to solve interpolation and coupling-based models. We study, in particular, a new family of scaling algorithms that generalize Sinkhorn's algorithm. The third part deals with applications. It contains a theoretical and numerical study of a Hele-Shaw type gradient flow in the space of nonnegative measures. It also adresses the case of measures taking values in the cone of positive semi-definite matrices, for which we introduce a model that achieves a balance between geometrical accuracy and algorithmic efficiency.
Document type :
Complete list of metadatas

Cited literature [171 references]  Display  Hide  Download
Contributor : Abes Star :  Contact
Submitted on : Tuesday, September 25, 2018 - 2:59:15 PM
Last modification on : Wednesday, October 14, 2020 - 4:01:02 AM
Long-term archiving on: : Wednesday, December 26, 2018 - 2:40:15 PM


Version validated by the jury (STAR)


  • HAL Id : tel-01881166, version 1



Lénaïc Chizat. Unbalanced Optimal Transport : Models, Numerical Methods, Applications. Numerical Analysis [math.NA]. Université Paris sciences et lettres, 2017. English. ⟨NNT : 2017PSLED063⟩. ⟨tel-01881166⟩



Record views


Files downloads