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- W4300677114 abstract "There are well-established connections between combinatorial optimization, optimal transport theory and Hydrodynamics, through the linear assignment problem in combinatorics, the Monge-Kantorovich problem in optimal transport theory and the model of inviscid, potential, pressure-less fluids in Hydrodynamics. Here, we consider the more challenging quadratic assignment problem (which is NP, while the linear assignment problem is just P) and find, in some particular case, a correspondence with the problem of finding stationary solutions of Euler's equations for incompressible fluids. For that purpose, we introduce and analyze a suitable gradient flow equation. Combining some ideas of P.-L. Lions (for the Euler equations) and Ambrosio-Gigli-Savar'e (for the heat equation), we provide for the initial value problem a concept of generalized dissipative solutions which always exist globally in time and are unique whenever theyare smooth." @default.
- W4300677114 created "2022-10-04" @default.
- W4300677114 creator A5001818250 @default.
- W4300677114 date "2014-10-01" @default.
- W4300677114 modified "2023-10-02" @default.
- W4300677114 title "Connections between Optimal Transport, Combinatorial Optimization and Hydrodynamics" @default.
- W4300677114 doi "https://doi.org/10.48550/arxiv.1410.0333" @default.
- W4300677114 hasPublicationYear "2014" @default.
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