On a Problem of Monge

By L. Kantorovich. 2006

466 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/02b3cc2a93559beeff7277cb51bba6d0ff56e64d

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Martingale optimal transport and robust hedging in continuous time (2012, background): “In his classical papers [15, 16], Kantorovich relaxed this problem by considering a probability measure on R × R, whose marginals agree with ν and μ, instead of a bijection.”
The Monge problem for strictly convex norms in Rd (2010, background): “Then Kantorovich proposed to study the problem min {∫ × ‖x − y‖ dγ (x, y) : γ ∈ 5(µ, ν) } .”
On the sufficiency of c-cyclical monotonicity for optimality of transport plans (2008, background): “The mass transport problem, first proposed by Monge [12] in 1781, can be stated in its relaxed version (due to Kantorovich [9, 10 ]) as follows: we are given two Polish spaces X and Y and two positive measures f + ∈ M + (X ) and f − ∈ M + (Y ) of the same total mass � f + � X =� f − � Y < +∞ .A tran”
Optimal transportation on non-compact manifolds (2007, background): “He proposed in [29], [30] a notion of weak solution of the transport problem.”
Optimal Mass Transport for Registration and Warping (2004, background): “” The problem was given a modern formulation in the work of Kantorovich [21], and so is now known as the Monge–Kantorovich problem.”
On the design of a reflector antenna II (2004, background): “A breakthrough was made by Kantorovich [11, 12] who introduced the dual functional (5.8).”
Plugin estimation of smooth optimal transport maps (2021, methodology): “This observation motivated Kantorovich (1942, 1948) to develop the following convex relaxation of the Monge problem, argmin π∈Π(P,Q) ∫ Ω ‖x− y‖2 dπ(x, y), (7) known as the Kantorovich problem, where Π(P,Q) denotes the set of joint distributions on Ω2 with marginal distributions P and Q, known as…”
Kantorovich Metric: Initial History and Little-Known Applications (2005, background): “Later, in the small note [ 11 ] published in Uspekhi Mat.”
Optimal transportation, topology and uniqueness (2010, background): “On the other hand, there are doubly stochastic measures such as γ := 1 2 (γ0 + γ1) which vanish outside of S but which are manifestly not extremal.”