The Pontryagin Maximum Principle in the Wasserstein Space

Abstract : We prove a Pontryagin Maximum Principle for optimal control problems in the space of probability measures, where the dynamics is given by a transport equation with non-local velocity. We formulate this first-order optimality condition using the formalism of subdifferential calculus in Wasserstein spaces. We show that the geometric approach based on needle variations and on the evolution of the covector (here replaced by the evolution of a mesure on the dual space) can be translated into this formalism.
Document type :
Journal articles
Complete list of metadatas

Cited literature [36 references]  Display  Hide  Download
Contributor : Benoît Bonnet <>
Submitted on : Thursday, October 25, 2018 - 2:09:39 PM
Last modification on : Tuesday, April 9, 2019 - 2:29:48 PM
Long-term archiving on : Saturday, January 26, 2019 - 2:14:59 PM


Files produced by the author(s)


  • HAL Id : hal-01637050, version 5


Benoît Bonnet, Francesco Rossi. The Pontryagin Maximum Principle in the Wasserstein Space. Calculus of Variations and Partial Differential Equations, 2019, 58, pp.11. ⟨hal-01637050v5⟩



Record views


Files downloads