Displaying similar documents to “Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals”

Pre-supports of linear probability measures and linear Lusin measurable functionals

W. Słowikowski

Similarity:

CONTENTS1. Introduction, review of the results, examples...................................................................................52. Linear probability measures and their representations................................................................103. Linear Lusin measurable functionals...............................................................................................164. Pre-supports and a modification of the definition of the linear probability measure................235....

A general duality theorem for the Monge-Kantorovich transport problem

Mathias Beiglböck, Christian Léonard, Walter Schachermayer (2012)

Studia Mathematica

Similarity:

The duality theory for the Monge-Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be Polish and equipped with Borel probability measures μ and ν. The transport cost function c: X × Y → [0,∞] is assumed to be Borel. Our main result states that in this setting there is no duality gap provided the optimal transport problem is formulated in a suitably relaxed way. The relaxed transport problem is defined as the limiting cost of the partial...

Minimization of functional with integrand expressed as minimum of quasiconvex functions - general and special cases

Piotr Puchała (2014)

Banach Center Publications

Similarity:

We present Z. Naniewicz method of optimization a coercive integral functional 𝒥 with integrand being a minimum of quasiconvex functions. This method is applied to the minimization of functional with integrand expressed as a minimum of two quadratic functions. This is done by approximating the original nonconvex problem by appropriate convex ones.

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

Emmanuel Boissard, Thibaut Le Gouic (2014)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation is the approximation of a probability measure by finitely supported measures (the quantization problem). It is found that rates for empirical or occupation measures match or are close to previously known optimal quantization rates in several cases....

A simple proof in Monge-Kantorovich duality theory

D. A. Edwards (2010)

Studia Mathematica

Similarity:

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...

The product-decomposability of probability measures on Abelian metrizable groups

Krakowiak Wiesław

Similarity:

Introduction.............................................................5I. Preliminaries.........................................................6   1.1. Semigroups........................................7   1.2. Algebraic groups..................................7   1.3. Additive operators in Abelian groups and linear operators in linear spaces................................8   1.4. Abelian metrizable groups........................10   1.5. Locally compact Abelian groups...................13   1.6....