Multi-marginal optimal transport and multi-agent matching problems: uniqueness and structure of solutions
By Brendan Pass. 2012
47 citations recorded by the source corpus.
We prove uniqueness and Monge solution results for multi-marginal optimal transportation problems with a certain class of surplus functions; this class arises naturally in multi-agent matching problems in economics. This result generalizes a seminal result of Gangbo and \'Swi\c{e}ch on multi-marginal problems. Of particular interest, we show that this also yields a partial generalization of the Gangbo-\'Swi\c{e}ch result to manifolds; alternatively, we we can think of this as a partial extension of McCann's theorem for quadratic costs on manifolds to the multi-marginal setting. We also show that the class of surplus functions considered here neither contains, nor is contained in, another class of surpluses studied by the present author, which also generalized Gangbo and \'Swi\c{e}ch's result.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/1d168415a3c50e2019030af739e33fce2f0748ca
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In Applied Mathematics
- Young-Heon Kim
- Brendan Pass
- Alessio Figalli
- Cédric Villani
- Thierry Klein
- Jérémie Bigot
- Guido De Philippis
- Robert J. McCann
Citations in the corpus
- An Explicit Martingale Version of the One-Dimensional Brenier's Theorem with Full Marginals Constraint (2016, unknown): “We also refer to the full-marginals case addressed by Pass [46].”
- Wasserstein Barycenters over Riemannian manifolds (2014, background): “Absolute continuity has also been established for more general interpolations over Euclidean space, as well as barycenters on Hadamard manifolds (simply connected Riemannian manifolds with nonpositive curvature) [33].”
- Multi-marginal optimal transport: theory and applications (2014, background): “Let us note that Monge solution results for costs of this form were proved (under successively weaker conditions on the ci) in [47, 62, 66]; the following is a special case of an example in [47], where costs with a more general infimal convolution form were considered.”