# Optimal Transportation Theory with Repulsive Costs

arXiv: https://arxiv.org/abs/1506.04565 · HTML: https://mlsanity.com/paper/1506.04565/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2015.

## Built on by (most cited first, 5 of 5)

- [Generalized Schr"odinger Bridge Matching](https://mlsanity.com/paper/2310.02233/) (2023)
- [Order Constraints in Optimal Transport](https://mlsanity.com/paper/2110.07275/) (2021)
- [Unsupervised Anomaly Detection through Mass Repulsing Optimal Transport](https://mlsanity.com/paper/2502.12793/) (2025)
- [An algorithmic solution to the Blotto game using multi-marginal couplings](https://mlsanity.com/paper/2202.07318/) (2022)
- [Deep Generalized Schr"odinger Bridges: From Image Generation to Solving Mean-Field Games](https://mlsanity.com/paper/2412.20279/) (2024)

## Abstract (arXiv)

This paper intents to present the state of art and recent developments of the optimal transportation theory with many marginals for a class of repulsive cost functions. We introduce some aspects of the Density Functional Theory (DFT) from a mathematical point of view, and revisit the theory of optimal transport from its perspective. Moreover, in the last three sections, we describe some recent and new theoretical and numerical results obtained for the Coulomb cost, the repulsive harmonic cost and the determinant cost.