Mass transportation problems

By Svetlozar T. Rachev, Ludger Rüschendorf. 1998

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Citations in the corpus

Wasserstein Fair Classification (2019, methodology): “This method corresponds to an approximate Wasserstein-1 optimal transport map by the formulation of Rachev and R¨uschendorf (1998): The procedure is detailed in Algorithm 2.”
Hilbert Space Embeddings and Metrics on Probability Measures (2009, background): “The concept of distance between probability measures is a fundamental one and has found many applications in probability theory, information theory and statistics (Rachev, 1991; Rachev and Rüschendorf, 1998; Liese and Vajda, 2006).”
On integral probability metrics, φ-divergences and binary classification (2009, background): “Let P be the set of all Borel probability measures on A .”
Constructive quantization: Approximation by empirical measures (2011, unknown): “Important results about the Wasserstein metric were achieved within the scope of transportation theory, for instance by Kantorovich [Kan42], Kantorovich and Rubinstein [KR58], Wasserstein [Was69], Rachev and Rüschendorf [RR98a, RR98b] and others.”
Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures (2015, background): “In the classical Kantorovich formulation, Optimal Transport problems [37, 46, 2, 47] deal with minimization of a linear cost functional”
Optimal transportation on non-compact manifolds (2007, background): “Suppose that g is a complete smooth Riemannian metric on M , and r > 1.”
A survey of max-type recursive distributional equations (2004, background): “We content ourselves with recording a simple contraction argument (essentially that of [53] equation 9.”
Bisimulation Metrics for Continuous Markov Decision Processes (2011, result): “We present it here in greater generality; all results are taken from the books by Rachev and Rueschendorf [54] and Villani [60], unless otherwise stated.”
Optimal Financial Portfolios (2007, unknown): “For the general dualty theorems of the type of Problems (1) and (2), see Rachev and Rüschendorf (1998).”
A new class of transport distances between measures (2008, background): “VILLANI [9,18,25,17,27], the theory of Optimal Transportation has received a lot of attention and many deep applications to various math ematical fields, such as PDE’s, Calculus of Variations, functional and geometric inequali ties, geometry of metric-measure spaces, have been found (we refer here t”
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem (2000, methodology): “A recent comprehensive review can be found in the new books by Rachev and R üschendorf [31], the lecture notes by Evans [19] and the review paper by Mc Cann and Gangbo [21].”
On the Monge–Kantorovich problem with additional linear constraints (2014, methodology): “Proof of the similar version of the theorem can be found in [13] or [9].”