5 papers
Characterizing and computing solutions to regularized semi-discrete optimal transport via an ordinary differential equation
Luca Nenna, Daniyar Omarov, Brendan Pass
This paper investigates the semi-discrete optimal transport (OT) problem with entropic regularization. We characterize the solution using a governing, well-posed ordinary different…
A variational formulation of a Multi-Population Mean Field Games with non-local interactions
Luigi De Pascale, Luca Nenna
We propose a MFG model with quadratic Hamiltonian involving populations. This results in a system of Hamilton-Jacobi-Bellman and Fokker-Planck equations with non-local…
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…
Grand-Canonical Optimal Transport
Simone Di Marino, Mathieu Lewin, Luca Nenna
We study a generalization of the multi-marginal optimal transport problem, which has no fixed number of marginals and is inspired of statistical mechanics. It consists in optim…
Ground state energy is not always convex in the number of electrons
Simone Di Marino, Mathieu Lewin, Luca Nenna
We provide the first counterexample showing that the ground state energy of electrons in an external Coulomb potential is not always a convex function of the number of electrons. T…