Duality theory for multi-marginal optimal transport with repulsive costs in metric spaces

TL;DR

This paper extends duality theory for multi-marginal optimal transport problems with certain distance-dependent costs, relevant to density functional theory, broadening theoretical understanding in this area.

Contribution

It generalizes duality results to unbounded, decreasing cost functions in metric spaces, applicable to problems in density functional theory.

Findings

Extended duality theory to unbounded cost functions

Applicable to problems in density functional theory

Provides a theoretical foundation for new cost functions

Abstract

In this paper we extend the duality theory of the multi-marginal optimal transport problem for cost functions depending on a decreasing function of the distance (not necessarily bounded). This class of cost functions appears in the context of SCE Density Functional Theory introduced in "Strong-interaction limit of density-functional theory" by M. Seidl.