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Pontryagin maximum principle for non-smooth state-constrained control problems over Wasserstein spaces — arXiv:2609.17197

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.17197
License (as archived): CC0-1.0
Archived: 2026-10-15T20:43:44.276Z
SHA-256 of the archived text: b7544e8a55ddeb41aab95b43927d24affb4659fdf54428949316b10b60c2d6b7
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How to cite

Pontryagin maximum principle for non-smooth state-constrained control problems over Wasserstein spaces — arXiv:2609.17197 — arXiv (en), https://arxiv.org/abs/2609.17197 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_87cb2cc2db97 (Metraipolis archive dc_87cb2cc2db97, sha256 b7544e8a55ddeb41aab95b43927d24affb4659fdf54428949316b10b60c2d6b7)

BibTeX

@misc{dc87cb2cc2db97,
  title = {Pontryagin maximum principle for non-smooth state-constrained control problems over Wasserstein spaces — arXiv:2609.17197},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.17197},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_87cb2cc2db97; sha256 b7544e8a55ddeb41aab95b43927d24affb4659fdf54428949316b10b60c2d6b7},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.17197. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study a state-constrained Bolza optimal control problem governed by a non-local continuity equation in the Wasserstein space $\sP_2(\R^d)$. We develop a Pontryagin maximum principle for these problems in which both the cost functionals and the constraints are only locally Lipschitz, and the initial measure does not necessarily have compact support. To derive the main result, we introduce a notion of a Clarke-type deterministic subdifferential over $\sP_2(\R^d)$. The proof of the main result combines a careful adaptation of the Lasry-Lions regularization to the Wasserstein space coupled with stability results of the Clarke subdifferential that allow us to recover the first-order information. We also show that, for functionals convex along plans, this subdifferential admits a global supporting characterization and provides a first-order characterization of global minimizers.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-16 in math.OC).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2609.17197 — 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 2026-10-15T19:36:35.859Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-16?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).