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ArticleOriginal scientific text

Title

Optimal solutions of multivariate coupling problems

Authors 1

Affiliations

  1. Institut für Mathematische Stochastik, Hebelstr. 27, 79104 Freiburg, Germany

Abstract

Some necessary and some sufficient conditions are established for the explicit construction and characterization of optimal solutions of multivariate transportation (coupling) problems. The proofs are based on ideas from duality theory and nonconvex optimization theory. Applications are given to multivariate optimal coupling problems w.r.t. minimal lp-type metrics, where fairly explicit and complete characterizations of optimal transportation plans (couplings) are obtained. The results are of interest even in the one-dimensional case. For the first time an explicit criterion is given for the construction of optimal multivariate couplings for the Kantorovich metric l1.

Keywords

ENG
lp-metric, c-convex functions, optimal couplings, transportation problem

Bibliography

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Applicationes Mathematicae
1995-1996/23/3
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Pages:
325-338
Main language of publication
English
Received
1994-12-02
Published
1995
Exact and natural sciences