Pontryagin maximum principle for non-smooth state-constrained control problems over Wasserstein spaces
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Urrea, Fernanda, Treumún, Ernesto
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213396415