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PreprintCC BY 4.0arXiv

Centroids for weak optimal transport with barycentric cost

  • Friedemann Krannich
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Abstract

We generalize the theory of Wasserstein barycenters between N given measures from the Wasserstein distance to the weak optimal transport problem with barycentric cost. We find a multi-marginal formulation and its dual problem. The multi-marginal problem is new in itself; contrary to the classical multi-marginal optimal transport problem, the first M marginals of its competitors are not fixed but instead only need dominate the first M given measures in convex order, while the last N-M marginals of its competitors are dominated in convex order by the last N-M given measures.

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Cite

BibTeXRIS
BibTeX
@misc{krannich2026centroids,
  title = {{Centroids for weak optimal transport with barycentric cost}},
  author = {Friedemann Krannich},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17784},
  eprint = {2609.17784},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17784},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Centroids for weak optimal transport with barycentric cost
AU  - Friedemann Krannich
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17784
UR  - https://arxiv.org/abs/2609.17784
AB  - We generalize the theory of Wasserstein barycenters between N given measures from the Wasserstein distance to the weak optimal transport problem with barycentric cost. We find a multi-marginal formulation and its dual problem. The multi-marginal problem is new in itself; contrary to the classical multi-marginal optimal transport problem, the first M marginals of its competitors are not fixed but instead only need dominate the first M given measures in convex order, while the last N-M marginals of its competitors are dominated in convex order by the last N-M given measures.
ER  -