12 citations · 48 across the 12 of their papers we have counts for
15 papers
Entropic approximations of the semigeostrophic shallow water equations
Jean-David Benamou, Colin J. Cotter, Jacob J. M. Francis +1
We develop a discretisation of the semigeostrophic rotating shallow water equations, based upon their optimal transport formulation. This takes the form of a Moreau-Yoshida regular…
From entropic transport to martingale transport, and applications to model calibration
Jean-David Benamou, Guillaume Chazareix, Grégoire Loeper
We propose a discrete time formulation of the semi-martingale optimal transport problem based on multi-marginal entropic transport. This approach offers a new way to formulate and…
Entropic Semi-Martingale Optimal Transport
Jean-David Benamou, Guillaume Chazareix, Marc Hoffmann +2
Entropic Optimal Transport (EOT), also referred to as the Schrödinger problem, seeks to find a random processes with prescribed initial/final marginals and with minimal relative en…
From entropic transport to martingale transport, and applications to model calibration
Jean-David Benamou, Guillaume Chazareix, Grégoire Loeper
We propose a discrete time formulation of the semi martingale optimal transport problembased on multi-marginal entropic transport. This approach offers a new way to formulate and s…
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…
Second order models for optimal transport and cubic splines on the Wasserstein space
Jean-David Benamou, Thomas Gallouët, François-Xavier Vialard
On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation. After presenting the natura…
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…
Minimal convex extensions and finite difference discretization of the quadratic Monge-Kantorovich problem
Jean-David Benamou, Vincent Duval
We present an adaptation of the MA-LBR scheme to the Monge-Amp{è}re equation with second boundary value condition, provided the target is a convex set. This yields a fast adaptive…
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…
Monotone and Consistent discretization of the Monge-Ampere operator
Jean-David Benamou, Francis Collino, Jean-Marie Mirebeau
We introduce a novel discretization of the Monge-Ampere operator, simultaneously consistent and degenerate elliptic, hence accurate and robust in applications. These properties are…
Discretization of functionals involving the Monge-Ampère operator
Jean-David Benamou, Guillaume Carlier, Quentin Mérigot +1
Gradient flows in the Wasserstein space have become a powerful tool in the analysis of diffusion equations, following the seminal work of Jordan, Kinderlehrer and Otto (JKO). The n…
A viscosity framework for computing Pogorelov solutions of the Monge-Ampere equation
Jean-David Benamou, Brittany D. Froese
We consider the Monge-Kantorovich optimal transportation problem between two measures, one of which is a weighted sum of Diracs. This problem is traditionally solved using expensiv…
Numerical solution of the Optimal Transportation problem using the Monge-Ampere equation
Jean-David Benamou, Brittany D. Froese, Adam M. Oberman
A numerical method for the solution of the elliptic Monge-Ampere Partial Differential Equation, with boundary conditions corresponding to the Optimal Transportation (OT) problem is…
A viscosity solution approach to the Monge-Ampere formulation of the Optimal Transportation Problem
Jean-David Benamou, Brittany D. Froese, Adam M. Oberman
In this work we present a numerical method for the Optimal Mass Transportation problem. Optimal Mass Transportation (OT) is an active research field in mathematics.It has recently…