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Mathematics > Optimization and Control

arXiv:2108.02609 (math)
[Submitted on 5 Aug 2021 (v1), last revised 25 Nov 2021 (this version, v2)]

Title:Semiconcavity and Sensitivity Analysis in Mean-Field Optimal Control and Applications

Authors:Benoît Bonnet, Hélène Frankowska
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Abstract:In this article, we investigate some of the fine properties of the value function associated to an optimal control problem in the Wasserstein space of probability measures. Building on new interpolation and linearisation formulas for non-local flows, we prove semiconcavity estimates for the value function, and establish several variants of the so-called sensitivity relations which provide connections between its superdifferential and the adjoint curves stemming from the maximum principle. We subsequently make use of these results to study the propagation of regularity for the value function along optimal trajectories, as well as to investigate sufficient optimality conditions and optimal feedbacks for mean-field optimal control problems.
Comments: 55 pages
Subjects: Optimization and Control (math.OC)
MSC classes: 30L99, 49K27, 49K40, 49Q12, 49Q22, 58E25
Cite as: arXiv:2108.02609 [math.OC]
  (or arXiv:2108.02609v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2108.02609
Journal reference: Journal de Mathématiques Pures et Appliquéees, Published online (2021)
Related DOI: https://doi.org/10.1016/j.matpur.2021.11.001

Submission history

From: Benoît Bonnet [view email]
[v1] Thu, 5 Aug 2021 13:34:48 UTC (57 KB)
[v2] Thu, 25 Nov 2021 08:20:36 UTC (58 KB)
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