Zobrazeno 1 - 10
of 252
pro vyhledávání: '"FRANKOWSKA, HÉLÈNE"'
Publikováno v:
SIAM Journal on Mathematical Analysis 56 (3), 2863-2914 (2024)
In this article, we derive conditions for the existence of solutions to state-constrained continuity inclusions in Wasserstein spaces whose right-hand sides may be discontinuous in time. These latter are based on a fine investigation of the infinites
Externí odkaz:
http://arxiv.org/abs/2304.11945
Publikováno v:
Nonlinear Analysis, Theory, Methods and Applications, 247:113595 (2024)
In this article, we extend the foundations of the theory of differential inclusions in the space of compactly supported probability measures, introduced recently by the authors, to the setting of general Wasserstein spaces. In this context, we prove
Externí odkaz:
http://arxiv.org/abs/2302.00963
Autor:
Bonnet, Benoît, Frankowska, Hélène
In this article, we prove a general viability theorem for continuity inclusions in Wasserstein spaces, and provide an application thereof to the existence of exponentially stable trajectories obtained via the second method of Lyapunov.
Externí odkaz:
http://arxiv.org/abs/2209.03640
Autor:
Bonnet, Benoît, Frankowska, Hélène
Publikováno v:
Journal de Math\'ematiques Pures et Appliqu\'eees, Published online (2021)
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,
Externí odkaz:
http://arxiv.org/abs/2108.02609
Autor:
Bonnet, Benoît, Frankowska, Hélène
In this paper, we obtain several structural results for the value function associated to a mean-field optimal control problem of Bolza type in the space of measures. After establishing the sensitivity relations bridging between the costates of the ma
Externí odkaz:
http://arxiv.org/abs/2107.13912
Autor:
Bonnet, Benoît, Frankowska, Hélène
In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To this end, we introduce a new notion of localised metric subdifferential f
Externí odkaz:
http://arxiv.org/abs/2101.10668
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 January 2024 529(2)
Autor:
Bonnet, Benoît, Frankowska, Hélène
In this article, we propose a new unifying framework for the investigation of multi-agent control problems in the mean-field setting. Our approach is based on a new definition of differential inclusions for continuity equations formulated in the Wass
Externí odkaz:
http://arxiv.org/abs/2009.06467
Autor:
Bonnet, Benoît, Frankowska, Hélène
In this article, we propose a general framework for the study of differential inclusions in the Wasserstein space of probability measures. Based on earlier geometric insights on the structure of continuity equations, we define solutions of differenti
Externí odkaz:
http://arxiv.org/abs/2007.08906
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