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- W4295121631 abstract "We investigate the optimal mass transport problem associated to the following ballistic cost functional on phase space $Mtimes M^*$, $$ b_T(v, x):=inf{langle v, gamma (0)rangle +int_0^TL(gamma (t), {dot gamma}(t)), dt, gamma in C^1([0, T), M), gamma(T)=x}, $$ where $M=mathbb{R}^d$, $T>0$, and $L:Mtimes M to mathbb{R}$ is a Lagrangian that is jointly convex in both variables. Under suitable conditions on the initial and final probability measures, we use convex duality `a la Bolza and Monge-Kantorovich theory to lift classical Hopf-Lax formulae from state space to Wasserstein space. This allows us to relate optimal transport maps for the ballistic cost to those associated with the fixed-end cost defined on $Mtimes M$ by $$ c_T(x,y):=inf{int_0^TL(gamma(t), {dot gamma}(t)), dt, gammain C^1([0, T), M), gamma(0)=x, gamma(T)=y}. $$ We also point to links with the theory of mean field games." @default.
- W4295121631 created "2022-09-10" @default.
- W4295121631 creator A5004440950 @default.
- W4295121631 date "2017-05-16" @default.
- W4295121631 modified "2023-09-30" @default.
- W4295121631 title "Optimal Ballistic Transport and Hopf-Lax Formulae on Wasserstein Space" @default.
- W4295121631 doi "https://doi.org/10.48550/arxiv.1705.05951" @default.
- W4295121631 hasPublicationYear "2017" @default.
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