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Literature
The optimal transport problem was first introduced by Monge in 1781
and relaxed by Kantorovich (Nobel prize) in 1940. It defines a distance in
the space of probability distributions, named optimal transport,
Wasserstein distance, or Earth Mover’s distance.
▶ Mapping/Monge-Amp´
ere equation: Gangbo, Brenier, et.al;
▶ Lyapunov methods and Gradient flows: Otto, Villani, Ambrosio,
Gigli, Savare, Carillo, Mielke, et.al;
▶ Hamiltonian flows: Compressible Euler equations, Potential mean
field games, Schrodinger bridge problems, Schrodinger equations:
Benamou, Brenier, Lions, Georgiou, Nelson, Lafferty, et.al.
▶ Numerical OT and MFG: Benamou, Nurbekyan, Oberman, Osher,
Achdou, Lai, et.al.
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