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Master's Dissertation
DOI
10.11606/D.45.2009.tde-04052009-162654
Document
Author
Full name
Estefano Alves de Souza
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2009
Supervisor
Committee
Galves, Jefferson Antonio (President)
Garcia, Nancy Lopes
Leonardi, Florencia Graciela
Title in Portuguese
O problema de Monge-Kantorovich para duas medidas de probabilidade sobre um conjunto finito
Keywords in Portuguese
acoplamento
Monge-Kantorovich
problema do transporte ótimo
Programação Linear
Abstract in Portuguese
Apresentamos o problema do transporte ótimo de Monge-Kantorovich com duas medidas de probabilidade conhecidas e que possuem suporte em um conjunto de cardinalidade finita. O objetivo é determinar condições que permitam construir um acoplamento destas medidas que minimiza o valor esperado de uma função de custo conhecida e que assume valor nulo apenas nos elementos da diagonal. Apresentamos também um resultado relacionado com a solução do problema de Monge-Kantorovich em espaços produto finitos quando conhecemos soluções para o problema nos espaços marginais.
Title in English
The Monge-Kantorovich problem related to two probability measures on a finite set
Keywords in English
coupling
Linear Programming
Monge-Kantorovich
optimal transportation problem
Abstract in English
We present the Monge-Kantorovich optimal problem with two known probability measures on a finite set. The objective is to obtain conditions that allow us to build a coupling of these measures that minimizes the expected value of a cost function that is known and is zero only on the diagonal elements. We also present a result that is related with the solution of the Monge-Kantorovich problem in finite product spaces in the case that solutions to the problem in the marginal spaces are known.
 
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DISSERTACAO.pdf (479.90 Kbytes)
Publishing Date
2009-07-06
 
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