4 papers · 1 filter
A land of monotone plenty, bis repetita: from classical to weak optimal transport
Virginie Ehrlacher, Rodrigue Lelotte, Luca Nenna
The celebrated c-cyclical monotonicity property is shown to boil down to the zeroth-order optimality condition for the optimal transport problem. More precisely, we show that optim…
A PDE approach to Benamou--Brenier formula for the Schrödinger problem
Mattia Garatti, Luca Nenna, Simona Rota Nodari +1
We studied the Benamou--Brenier formulation of the Schrödinger problem, focusing on a gap between theoretical results and applications, that often involve measures with unbounded…
Ordinary differential equations for regularized variational problems involving semi-discrete optimal transport
Adrien Cances, Luca Nenna, Daniyar Omarov +1
We consider entropically regularized, semi-discrete versions of variational problems on the set of probability measures involving optimal transport as well as other terms. We prove…
Particle method for a nonlinear multimarginal optimal transport problem
Adrien Cances, Quentin Mérigot, Luca Nenna
We study a nonlinear multimarginal optimal transport problem arising in risk management, where the objective is to maximize a spectral risk measure of the pushforward of a coupling…