# Trivial Cases for the Kantorovitch Problem

Serge Dubuc; Issa Kagabo; Patrice Marcotte

RAIRO - Operations Research (2010)

- Volume: 34, Issue: 1, page 49-59
- ISSN: 0399-0559

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topDubuc, Serge, Kagabo, Issa, and Marcotte, Patrice. "Trivial Cases for the Kantorovitch Problem." RAIRO - Operations Research 34.1 (2010): 49-59. <http://eudml.org/doc/197819>.

@article{Dubuc2010,

abstract = {
Let X and Y be two compact spaces endowed with
respective measures μ and ν satisfying the condition µ(X) = v(Y). Let c be a continuous function on the product space X x Y. The mass transfer problem consists in determining a measure ξ on
X x Y whose marginals coincide with μ and ν, and such that
the total cost ∫ ∫ c(x,y)dξ(x,y) be minimized. We first
show that if the cost function c is decomposable, i.e., can be
represented as the sum of two continuous functions defined on X and
Y, respectively, then every feasible measure is optimal. Conversely,
when X is the support of μ and Y the support of ν and when
every feasible measure is optimal, we prove that the cost function is
decomposable.
},

author = {Dubuc, Serge, Kagabo, Issa, Marcotte, Patrice},

journal = {RAIRO - Operations Research},

keywords = {Continuous programming; transportation.; Kantorovich problem; continuous programming; transportation},

language = {eng},

month = {3},

number = {1},

pages = {49-59},

publisher = {EDP Sciences},

title = {Trivial Cases for the Kantorovitch Problem},

url = {http://eudml.org/doc/197819},

volume = {34},

year = {2010},

}

TY - JOUR

AU - Dubuc, Serge

AU - Kagabo, Issa

AU - Marcotte, Patrice

TI - Trivial Cases for the Kantorovitch Problem

JO - RAIRO - Operations Research

DA - 2010/3//

PB - EDP Sciences

VL - 34

IS - 1

SP - 49

EP - 59

AB -
Let X and Y be two compact spaces endowed with
respective measures μ and ν satisfying the condition µ(X) = v(Y). Let c be a continuous function on the product space X x Y. The mass transfer problem consists in determining a measure ξ on
X x Y whose marginals coincide with μ and ν, and such that
the total cost ∫ ∫ c(x,y)dξ(x,y) be minimized. We first
show that if the cost function c is decomposable, i.e., can be
represented as the sum of two continuous functions defined on X and
Y, respectively, then every feasible measure is optimal. Conversely,
when X is the support of μ and Y the support of ν and when
every feasible measure is optimal, we prove that the cost function is
decomposable.

LA - eng

KW - Continuous programming; transportation.; Kantorovich problem; continuous programming; transportation

UR - http://eudml.org/doc/197819

ER -

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