Displaying similar documents to “A general duality theorem for the Monge-Kantorovich transport problem”

A simple proof in Monge-Kantorovich duality theory

D. A. Edwards (2010)

Studia Mathematica

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A simple proof is given of a Monge-Kantorovich duality theorem for a lower bounded lower semicontinuous cost function on the product of two completely regular spaces. The proof uses only the Hahn-Banach theorem and some properties of Radon measures, and allows the case of a bounded continuous cost function on a product of completely regular spaces to be treated directly, without the need to consider intermediate cases. Duality for a semicontinuous cost function is then deduced via the...

Transport problems and disintegration maps

Luca Granieri, Francesco Maddalena (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds...

A decomposition of complex Monge-Ampère measures

Yang Xing (2007)

Annales Polonici Mathematici

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We prove a decomposition theorem for complex Monge-Ampère measures of plurisubharmonic functions in connection with their pluripolar sets.

Characterization of optimal shapes and masses through Monge-Kantorovich equation

Guy Bouchitté, Giuseppe Buttazzo (2001)

Journal of the European Mathematical Society

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We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both cases some examples are presented.

Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals

S. T. Rachev, R. M.

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CONTENTS§0. Introduction...................................................................................................................................5§1. Notation and terminology..............................................................................................................6§2. A generalization of the Kantorovich-Rubinstein theorem..............................................................8§3. Application: explicit representations for a class of probability metrics.........................................14§4....

On the hessian of the optimal transport potential

Stefán Ingi Valdimarsson (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study the optimal solution of the Monge-Kantorovich mass transport problem between measures whose density functions are convolution with a gaussian measure and a log-concave perturbation of a different gaussian measure. Under certain conditions we prove bounds for the Hessian of the optimal transport potential. This extends and generalises a result of Caffarelli. We also show how this result fits into the scheme of Barthe to prove Brascamp-Lieb inequalities and thus prove a new generalised...

Monge-Ampère boundary measures

Urban Cegrell, Berit Kemppe (2009)

Annales Polonici Mathematici

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We study swept-out Monge-Ampère measures of plurisubharmonic functions and boundary values related to those measures.

A saddle-point approach to the Monge-Kantorovich optimal transport problem

Christian Léonard (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to -conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes infinite values. It leads us to new explicit sufficient and necessary optimality conditions. As by-products, we obtain a new proof of the well-known Kantorovich dual equality and an improvement of the convergence of the minimizing sequences.

Mass transport problem and derivation

Nacereddine Belili, Henri Heinich (1999)

Applicationes Mathematicae

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A characterization of the transport property is given. New properties for strongly nonatomic probabilities are established. We study the relationship between the nondifferentiability of a real function f and the fact that the probability measure λ f * : = λ ◦ ( f * ) - 1 , where f*(x):=(x,f(x)) and λ is the Lebesgue measure, has the transport property.