19 citations · 61 across the 16 of their papers we have counts for
22 papers
First-order -expansion for entropic optimal transport with non-degenerate costs
Luca Nenna, Brendan Pass, Paul Pegon +1
Entropy-regularized optimal transport (EOT) has become a key tool in optimal transport, providing both theoretical insight and efficient computation via the Sinkhorn algorithm. We…
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…
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…
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…
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…
An ordinary differential equation for entropic optimal transport and its linearly constrained variants
Joshua Zoen-Git Hiew, Luca Nenna, Brendan Pass
We characterize the solution to the entropically regularized optimal transport problem by a well-posed ordinary differential equation (ODE). Our approach works for discrete margina…
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…
A sparse approximation of the Lieb functional with moment constraints
Virginie Ehrlacher, Luca Nenna
The aim of this paper is to present new sparsity results about the so-called Lieb functional, which is a key quantity in Density Functional Theory for electronic structure calculat…
Universal diagonal estimates for minimizers of the Levy-Lieb functional
Simone Di Marino, Augusto Gerolin, Luca Nenna
Given a wave-function minimizing the Levy-Lieb functional, the intent of this short note is to give an estimate of the probability of the particles being in positions $(x_1, \ldots…
An ODE characterisation of multi-marginal optimal transport with pairwise cost functions
Luca Nenna, Brendan Pass
The purpose of this paper is to introduce a new numerical method to solve multi-marginal optimal transport problems with pairwise interaction costs. The complexity of multi-margina…
Robust risk management via multi-marginal optimal transport
Hamza Ennaji, Quentin Mérigot, Luca Nenna +1
We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but wh…
A note on Cournot-Nash equilibria and Optimal Transport between unequal dimensions
Luca Nenna, Brendan Pass
This note is devoted to study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by minimisation of some cost related to Optimal Transpo…
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…
Transport type metrics on the space of probability measures involving singular base measures
Luca Nenna, Brendan Pass
We develop the theory of a metric, which we call the -based Wasserstein metric and denote by , on the set of probability measures on a domain $X \subseteq \…
Variational problems involving unequal dimensional optimal transport
Luca Nenna, Brendan Pass
This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the min…
An entropy minimization approach to second-order variational mean-field games
Jean-David Benamou, Guillaume Carlier, Simone Di Marino +1
We propose a new viewpoint on variational mean-field games with diffusion and quadratic Hamiltonian. We show the equivalence of such mean-field games with a relative entropy minimi…
Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm
Jean-David Benamou, Guillaume Carlier, Luca Nenna
Starting from Brenier's relaxed formulation of the incompressible Euler equation in terms of geodesics in the group of measure-preserving diffeomorphisms, we propose a numerical me…
The strictly-correlated electron functional for spherically symmetric systems revisited
Michael Seidl, Simone Di Marino, Augusto Gerolin +3
The strong-interaction limit of the Hohenberg-Kohn functional defines a multimarginal optimal transport problem with Coulomb cost. From physical arguments, the solution of this lim…
Computation of Cournot-Nash equilibria by entropic regularization
Adrien Blanchet, Guillaume Carlier, Luca Nenna
We consider a class of games with continuum of players where equilibria can be obtained by the minimization of a certain functional related to optimal transport as emphasized in [7…
Optimal Transportation Theory with Repulsive Costs
Simone Di Marino, Augusto Gerolin, Luca Nenna
This paper intents to present the state of art and recent developments of the optimal transportation theory with many marginals for a class of repulsive cost functions. We introduc…
A Numerical Method to solve Optimal Transport Problems with Coulomb Cost
Jean-David Benamou, Guillaume Carlier, Luca Nenna
In this paper, we present a numerical method, based on iterative Bregman projections, to solve the optimal transport problem with Coulomb cost. This is related to the strong intera…
Iterative Bregman Projections for Regularized Transportation Problems
Jean-David Benamou, Guillaume Carlier, Marco Cuturi +2
This article details a general numerical framework to approximate so-lutions to linear programs related to optimal transport. The general idea is to introduce an entropic regulariz…