Pontryagin maximum principle for non-smooth state-constrained control problems over Wasserstein spaces
Abstract
We study a state-constrained Bolza optimal control problem governed by a non-local continuity equation in the Wasserstein space sP2(Rd). 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 sP2(Rd). 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.
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BibTeX
@misc{urrea2026pontryagin,
title = {{Pontryagin maximum principle for non-smooth state-constrained control problems over Wasserstein spaces}},
author = {Fernanda Urrea and Ernesto Treumún},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17197},
eprint = {2609.17197},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05752008v1},
}
RIS
TY - UNPB
TI - Pontryagin maximum principle for non-smooth state-constrained control problems over Wasserstein spaces
AU - Fernanda Urrea
AU - Ernesto Treumún
PY - 2026
DA - 2026/09/15
PB - HAL
DO - 10.48550/arxiv.2609.17197
UR - https://hal.science/hal-05752008v1
AB - 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.
ER -