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Gradient-Enhanced Proximal Algorithms for Mean Field Planning on Surfaces — arXiv:2609.10370

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.10370
License (as archived): CC0-1.0
Archived: 2026-10-16T10:13:24.023Z
SHA-256 of the archived text: 97362db8870d685fda5e29ca3af5ca0d78c9604b61ce547ecf0f451d361bc304
Stable URL of this page: https://metraipolis.com/documento/dc_cd5fa615b37a

How to cite

Gradient-Enhanced Proximal Algorithms for Mean Field Planning on Surfaces — arXiv:2609.10370 — arXiv (en), https://arxiv.org/abs/2609.10370 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cd5fa615b37a (Metraipolis archive dc_cd5fa615b37a, sha256 97362db8870d685fda5e29ca3af5ca0d78c9604b61ce547ecf0f451d361bc304)

BibTeX

@misc{dccd5fa615b37a,
  title = {Gradient-Enhanced Proximal Algorithms for Mean Field Planning on Surfaces — arXiv:2609.10370},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.10370},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cd5fa615b37a; sha256 97362db8870d685fda5e29ca3af5ca0d78c9604b61ce547ecf0f451d361bc304},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.10370. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Mean field planning on a surface prescribes initial and terminal densities and minimizes a transport energy subject to the continuity equation. Proximal algorithms for this problem repeatedly solve a time--space Poisson equation, whose temporal derivative and surface gradient determine the density and momentum corrections. We study a gradient-enhanced approximation of this constraint projection using finite differences in time, surface finite elements in space, temporal polynomial preserving recovery, and spatial parametric polynomial preserving recovery. The same construction is incorporated into ISTA, FISTA, and Douglas--Rachford splitting. We distinguish the recovered update from an exact discrete projection and derive residual identities and conditional finite-iteration perturbation bounds that retain data, boundary, and linear-solver errors. Existing derivative-recovery estimates identify a higher-order contribution under suitable regularity and mesh assumptions; they do not by themselves establish convergence of the outer optimization iteration. Available numerical illustrations on the sphere and a more complicated algebraic surface are discussed together with the limits of the recorded refinement data.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-10 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2609.10370 — 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 2026-10-16T08:46:35.712Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-10?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).