Multi-marginal optimal transport: theory and applications

By Brendan Pass. 2014

215 citations recorded by the source corpus.

Over the past five years, multi-marginal optimal transport, a generalization of the well known optimal transport problem of Monge and Kantorovich, has begun to attract considerable attention, due in part to a wide variety of emerging applications. Here, we survey this problem, addressing fundamental theoretical questions including the uniqueness and structure of solutions. The (partial) answers to these questions uncover a surprising divergence from the classical two marginal setting, and reflect a delicate dependence on the cost function. We go one to describe two applications of the multi-marginal problem.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/af01a6eed816967566ce20a336725105b56b9b3a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Qing Nie
2. Filippo Santambrogio
3. Zixuan Cang
4. Pratik Chaudhari
5. Stefano Soatto

In Geometry and Topology

1. Qing Nie
2. Filippo Santambrogio
3. Zixuan Cang
4. Pratik Chaudhari
5. Stefano Soatto

Citations in the corpus

• Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, background): “For a comprehensive survey about multi-marginal transport problems and their applications in physics and economics, see [249].”
• Screening cell–cell communication in spatial transcriptomics via collective optimal transport (2023, background): “While traditional optimal transport is powerful at integrating a pair of data-sets and multimarginal optimal transport 69 integrates multiple data-sets, the collective optimal transport is able to effectively control the coupling and deal with competing species, which is useful for a broad range of…”