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$λ$-geodesic convexity of the squared sliced-Wasserstein distance — arXiv:2610.20972

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.20972
License (as archived): CC0-1.0
Archived: 2026-10-16T10:28:25.171Z
SHA-256 of the archived text: 4b49365aa303be400b38cd6c49bdeb46db857204d1fb95355af3b4c4e4889ecf
Stable URL of this page: https://metraipolis.com/documento/dc_0bb55eb092eb

How to cite

$λ$-geodesic convexity of the squared sliced-Wasserstein distance — arXiv:2610.20972 — arXiv (en), https://arxiv.org/abs/2610.20972 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_0bb55eb092eb (Metraipolis archive dc_0bb55eb092eb, sha256 4b49365aa303be400b38cd6c49bdeb46db857204d1fb95355af3b4c4e4889ecf)

BibTeX

@misc{dc0bb55eb092eb,
  title = {$λ$-geodesic convexity of the squared sliced-Wasserstein distance — arXiv:2610.20972},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.20972},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_0bb55eb092eb; sha256 4b49365aa303be400b38cd6c49bdeb46db857204d1fb95355af3b4c4e4889ecf},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.20972. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The squared Wasserstein distance with respect to a fixed target measure is not a convex function along Wasserstein geodesics over $\mathbb{R}^d$ when $d\geq 2$. Still, in dimension $d=1$, this function is $2$-geodesically convex. We prove that the square of the sliced-Wasserstein distance (which is a distance constructed averaging one-dimensional Wasserstein distances) is $\lambda$-geodesically convex (possibly with $\lambda \leq 0$) on sets of measures satisfying upper bounds on their density, when the target measure satisfies some given geometric conditions. We also present some consequences of this result in the study of the sliced-Wasserstein flow.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.OC, nuovi lavori del giorno).
Categorie arXiv: Optimization and Control (math.OC) ; Analysis of PDEs (math.AP).
Pagina del lavoro: https://arxiv.org/abs/2610.20972 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T08:49:47.918Z dalla pagina https://arxiv.org/list/math.OC/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).