Weak optimal transport with unnormalized kernels
Functional Analysis
2024-04-22 v2 Optimization and Control
Probability
Abstract
We introduce a new variant of the weak optimal transport problem where mass is distributed from one space to the other through unnormalized kernels. We give sufficient conditions for primal attainment and prove a dual formula for this transport problem. We also obtain dual attainment conditions for some specific cost functions. As a byproduct we obtain a transport characterization of the stochastic order defined by convex positively 1-homogenous functions, in the spirit of Strassen theorem for convex domination.
Cite
@article{arxiv.2203.16227,
title = {Weak optimal transport with unnormalized kernels},
author = {Philippe Choné and Nathael Gozlan and Francis Kramarz},
journal= {arXiv preprint arXiv:2203.16227},
year = {2024}
}