# Weak optimal transport with unnormalized kernels

arXiv: https://arxiv.org/abs/2203.16227 · HTML: https://mlsanity.com/paper/2203.16227/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2022.

## Built on by (most cited first, 1 of 1)

- [Algorithms for Weak Optimal Transport with an Application to Economics](https://mlsanity.com/paper/2205.09825/) (2022)

## Abstract (arXiv)

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.