On the Kantorovich-Rubinstein theorem. Expositiones Mathematicae, 29(4):387 - 398, 2011. ISSN 0723-0869. doi: https://doi.org/10.1016/j.exmath.2011.06.005.Edwards, D. A. (2011). "On the Kantorovich-Rubinstein theorem". In: Expositiones Mathematicae 29.4, pages 387-398 (page 9)....
This is called the Weak Duality theorem. As you might have guessed, there also exists a Strong Duality theorem, which states that, should we find an optimal solution for z~, then z=z~. Proving it is a bit more complicated and requires Farkas theorem as an intermediate result.Farkas...
The classical Kantorovich-Rubinstein theorem for mass transshipment is generalized. For Borel measures on with zero mixed moments of order less than k, we obtain a dual representation of the norm where stands for the set of transshipment plans satisfying the balancing condition and is the k-th ...
(2006) Parametrized Kantorovich- Rubinstein theorem and application to the coupling of random variables. Lecture Notes in Statist., 187, Springer, New York.Dedecker, J., Prieur, C. and de Fitte, P. (2004) Parametrized Kantorovich-Rubin'stein theorem and application to the coupling of random ...
Parametrized Kantorovich-Rubinstein theorem and application to the coupling of random variables Theoreme de Kantorovich-Rubinstein avec parametre et application au couplage des variables aleatoiresJerome DedeckerClementine PrieurPaul Raynaud De Fitte
Among the consequences are a new proof of a recent result of Gordon and Petrov ( arXiv:1608.06848 [math.CO]) about $f$-vectors of generic Kantorovich-Rubinstein polytopes and an extension of a theorem of Gelfand, Graev, and Postnikov, about triangulations of the type A, positive root ...
theoremNonlinearfunctionalWassersteinnormThe classical Kantorovich–Rubinstein theory gives necessary conditions for maxima of linear functionals acting on the space of Lipschitzian functions. We show analogous results for some nonlinear functionals of Hammerstein type. Our proofs are based on theorems ...
Among the consequences are a new proof of a recent result of Gordon and Petrov (Arnold Math. J. 3(2):205-218, 2017) about f -vectors of generic Kantorovich-Rubinstein polytopes and an extension of a theorem of Gelfand, Graev, and Postnikov, about triangulations of the type A, positive ...
Kantorovich-rubinstein theoremWasserstein normMcshane extension theoremNonlinear functionalThe classical Kantorovich-Rubinstein theory gives necessary conditions for maxima of linear functionals acting on the space of Lipschitzian functions. We show analogous results for some nonlinear functionals of Hammerstein ...