Kantorovich-Rubinstein dualityOptimal transportAn easy consequence of Kantorovich-Rubinstein duality is the following: if f:[0,1]d→R is Lipschitz and {x1,…,xN}[0,1]d, then|∫[0,1]df(x)dx1N∑k=1Nf(xk)|≤‖f‖L
Instead, we will focus mainly on one detail that is only mentioned quickly, but I think lies in some sense at the heart of it: the Kantorovich-Rubinstein duality, or rather a special case of it. This is of course not a new result, but the application is very clever and attractive....
Kellerer, using his own work on Monge–Kantorovich duality, obtained a rapid proof for Radon measures on an arbitrary metric space. The object of the present expository article is to give an account of Kellerer's generalization of the Kantorovich–Rubinstein theorem, together with related matters...
Kantorovich-Rubinstein problemInfinite linear programThis paper studies the Kantorovich-Rubinstein mass transshipment (KR) problem on metric spaces and with an unbounded cost function. Some assumptions are given under which the strong duality condition holds; that is, the KR problem and its dual are ...
Kantorovich–Rubinstein dualityA precise characterization of the extremal points of sublevel sets of nonsmooth penalties provides both detailed information about minimizers, and optimality conditions in general classes of minimization problems involving them. Moreover, it enables the application of fully ...
Strong Duality of the Kantorovich-Rubinstein Mass Transshipment Problem in Metric Spaces: 4th International Conference, LOD 2018, Volterra, Italy, September 13-16, 2018, Revised Selected Papersdoi:10.1007/978-3-030-13709-0_24Jose Rigoberto Gabriel Argueelles...
Lecture 3: The Kantorovich–Rubinstein DualityThis lecture is devoted to the proof of the most basic result of the theory of Optimal Transport, namely the Kantorovich–Rubinstein duality.doi:10.1007/978-3-030-72162-6_3L. AmbrosioElia Brué...
We prove a version for random measures of the celebrated Kantorovich-Rubinstein duality theorem and we give an application to the coupling of random variables which extends and unifies known results.doi:10.1007/0-387-36062-X_5Dedecker, Jerome...