Multiresolution Analysis Applied to the Monge-Kantorovich Problem
We give a scheme of approximation of the MK problem based on the symmetries of the underlying spaces. We take a Haar type MRA constructed according to the geometry of our spaces. Thus, applying the Haar type MRA based on symmetries to the MK problem, we obtain a sequence of transportation problem th...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2018/1764175 |
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| author | Armando Sánchez-Nungaray Carlos González-Flores Raquiel R. López-Martínez |
| author_facet | Armando Sánchez-Nungaray Carlos González-Flores Raquiel R. López-Martínez |
| author_sort | Armando Sánchez-Nungaray |
| collection | DOAJ |
| description | We give a scheme of approximation of the MK problem based on the symmetries of the underlying spaces. We take a Haar type MRA constructed according to the geometry of our spaces. Thus, applying the Haar type MRA based on symmetries to the MK problem, we obtain a sequence of transportation problem that approximates the original MK problem for each of MRA. Moreover, the optimal solutions of each level solution converge in the weak sense to the optimal solution of original problem. |
| format | Article |
| id | doaj-art-6d24b7afbc8e4023a43c0d8ef34caa3a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6d24b7afbc8e4023a43c0d8ef34caa3a2025-02-03T05:43:56ZengWileyAbstract and Applied Analysis1085-33751687-04092018-01-01201810.1155/2018/17641751764175Multiresolution Analysis Applied to the Monge-Kantorovich ProblemArmando Sánchez-Nungaray0Carlos González-Flores1Raquiel R. López-Martínez2Facultad de Matemáticas, Universidad Veracruzana, Xalapa, VER, MexicoEscuela Superior de Ingeniera Mecánica y Eléctrica, Instituto Politécnico Nacional, Mexico City, MexicoFacultad de Matemáticas, Universidad Veracruzana, Xalapa, VER, MexicoWe give a scheme of approximation of the MK problem based on the symmetries of the underlying spaces. We take a Haar type MRA constructed according to the geometry of our spaces. Thus, applying the Haar type MRA based on symmetries to the MK problem, we obtain a sequence of transportation problem that approximates the original MK problem for each of MRA. Moreover, the optimal solutions of each level solution converge in the weak sense to the optimal solution of original problem.http://dx.doi.org/10.1155/2018/1764175 |
| spellingShingle | Armando Sánchez-Nungaray Carlos González-Flores Raquiel R. López-Martínez Multiresolution Analysis Applied to the Monge-Kantorovich Problem Abstract and Applied Analysis |
| title | Multiresolution Analysis Applied to the Monge-Kantorovich Problem |
| title_full | Multiresolution Analysis Applied to the Monge-Kantorovich Problem |
| title_fullStr | Multiresolution Analysis Applied to the Monge-Kantorovich Problem |
| title_full_unstemmed | Multiresolution Analysis Applied to the Monge-Kantorovich Problem |
| title_short | Multiresolution Analysis Applied to the Monge-Kantorovich Problem |
| title_sort | multiresolution analysis applied to the monge kantorovich problem |
| url | http://dx.doi.org/10.1155/2018/1764175 |
| work_keys_str_mv | AT armandosancheznungaray multiresolutionanalysisappliedtothemongekantorovichproblem AT carlosgonzalezflores multiresolutionanalysisappliedtothemongekantorovichproblem AT raquielrlopezmartinez multiresolutionanalysisappliedtothemongekantorovichproblem |