Moment constrained optimal transport problem

Virginie Ehrlacher
Jeudi, 6 Juin, 2019 - 11:00 - 12:00
(joint work with A. Alfonsi, R. Coyaud and D. Lombardi)
The aim of this talk is to present recent results a relaxation of multi-marginal optimal transport problems with a view to the design of numerical schemes to approximate the exact optimal transport problem. More precisely, the approximate problem considered in this talk consists in relaxing the marginal constraints into a finite number of moments constraints. Using Tchakaloff's theorem, it is possible to prove the existence of minimizers of this relaxed problem and characterize them as discrete measures charging a number of points which scales at most linearly with the number of marginals in the problem. We illustrate this point on the case of a symmetric Kantorovich multi-marginal problem appearing in quantum chemistry. This result opens the way to the design of new numerical schemes exploiting the structure of these minimizers, and preliminary numerical results will be presented.