5 papers · 1 filter
Convergence rates for regularized unbalanced optimal transport: the discrete case
Luca Nenna, Paul Pegon, Louis Tocquec
Unbalanced optimal transport (UOT) is a natural extension of optimal transport (OT) allowing comparison between measures of different masses. It arises naturally in machine learnin…
A Rockafellar Theorem for cyclically quasi-monotone maps: the regular non-vanishing case
Luigi De Pascale, Paul Pegon
We study the connection between cyclic quasi-monotonicity and quasi-convexity, focusing on whether every cyclically quasi-monotone (possibly multivalued) map is included in the nor…
Full characterization of optimal transport plans for concave costs
Paul Pegon, Davide Piazzoli, Filippo Santambrogio
This paper slightly improves a classical result by Gangbo and McCann (1996) about the structure of optimal transport plans for costs that are concave functions of the Euclidean dis…
Optimal quantization with branched optimal transport distances
Paul Pegon, Mircea Petrache
We consider the problem of optimal approximation of a target measure by an atomic measure with atoms, in branched optimal transport distance. This is a new branched transport v…
Convergence rate of entropy-regularized multi-marginal optimal transport costs
Luca Nenna, Paul Pegon
We investigate the convergence rate of multi-marginal optimal transport costs that are regularized with the Boltzmann-Shannon entropy, as the noise parameter tends to…