Precise solutions of the one-dimensional Monge-Kantorovich problem


Autoria(s): Plakhov, A. Y.
Contribuinte(s)

Institute of Mathematics & Physics (ADT)

Mathematics and Physics

Data(s)

05/12/2008

05/12/2008

2004

Resumo

Plakhov, A.Y., (2004) 'Precise solutions of the one-dimensional Monge-Kantorovich problem', Sbornik: Mathematics 195(9) pp.1291-1307 RAE2008

The Monge-Kantorovich problem on finding a measure realizing the transportation of mass from to at minimum cost is considered. The initial and resulting distributions of mass are assumed to be the same and the cost of the transportation of the unit mass from a point to is expressed by an odd function that is strictly concave on . It is shown that under certain assumptions about the distribution of the mass the optimal measure belongs to a certain family of measures depending on countably many parameters. This family is explicitly described: it depends only on the distribution of the mass, but not on . Under an additional constraint on the distribution of the mass the number of the parameters is finite and the problem reduces to the minimization of a function of several variables. Examples of various distributions of the mass are considered.

Peer reviewed

Formato

17

Identificador

Plakhov , A Y 2004 , ' Precise solutions of the one-dimensional Monge-Kantorovich problem ' Sbornik: Mathematics , vol 195 , no. 9 , pp. 1291-1307 . DOI: 10.1070/SM2004v195n09ABEH000845

1064-5616

PURE: 88695

PURE UUID: 474e9cfb-f7b7-4aa5-ad1c-646ff02e84de

dspace: 2160/1407

http://hdl.handle.net/2160/1407

http://dx.doi.org/10.1070/SM2004v195n09ABEH000845

Idioma(s)

eng

Relação

Sbornik: Mathematics

Tipo

/dk/atira/pure/researchoutput/researchoutputtypes/contributiontojournal/article

Article (Journal)

Direitos