Optimal mass transport on metric graphs
We study an optimal mass transport problem between two equal masses on a metric graph where the cost is given by the distance in the graph. To solve this problem we find a Kantorovich potential as the limit of p-Laplacian-type problems in the graph where at the vertices we impose zero total flux bou...
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paper:paper_10526234_v25_n3_p1609_Mazon2023-06-08T16:02:58Z Optimal mass transport on metric graphs Rossi, Julio Daniel Convex optimization Metric graphs Optimal transport P-Laplacian Boundary conditions Convex optimization Laplace transforms Approximation procedure Metric graphs Optimal mass transport Optimal transport P-Laplacian Total flux Transport densities Problem solving We study an optimal mass transport problem between two equal masses on a metric graph where the cost is given by the distance in the graph. To solve this problem we find a Kantorovich potential as the limit of p-Laplacian-type problems in the graph where at the vertices we impose zero total flux boundary conditions. In addition, the approximation procedure allows us to find a transport density that encodes how much mass has to be transported through a given point in the graph, and also provides a simple formula of convex optimization for the total cost. © 2015 Society for Industrial and Applied Mathematics. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10526234_v25_n3_p1609_Mazon http://hdl.handle.net/20.500.12110/paper_10526234_v25_n3_p1609_Mazon |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
Convex optimization Metric graphs Optimal transport P-Laplacian Boundary conditions Convex optimization Laplace transforms Approximation procedure Metric graphs Optimal mass transport Optimal transport P-Laplacian Total flux Transport densities Problem solving |
spellingShingle |
Convex optimization Metric graphs Optimal transport P-Laplacian Boundary conditions Convex optimization Laplace transforms Approximation procedure Metric graphs Optimal mass transport Optimal transport P-Laplacian Total flux Transport densities Problem solving Rossi, Julio Daniel Optimal mass transport on metric graphs |
topic_facet |
Convex optimization Metric graphs Optimal transport P-Laplacian Boundary conditions Convex optimization Laplace transforms Approximation procedure Metric graphs Optimal mass transport Optimal transport P-Laplacian Total flux Transport densities Problem solving |
description |
We study an optimal mass transport problem between two equal masses on a metric graph where the cost is given by the distance in the graph. To solve this problem we find a Kantorovich potential as the limit of p-Laplacian-type problems in the graph where at the vertices we impose zero total flux boundary conditions. In addition, the approximation procedure allows us to find a transport density that encodes how much mass has to be transported through a given point in the graph, and also provides a simple formula of convex optimization for the total cost. © 2015 Society for Industrial and Applied Mathematics. |
author |
Rossi, Julio Daniel |
author_facet |
Rossi, Julio Daniel |
author_sort |
Rossi, Julio Daniel |
title |
Optimal mass transport on metric graphs |
title_short |
Optimal mass transport on metric graphs |
title_full |
Optimal mass transport on metric graphs |
title_fullStr |
Optimal mass transport on metric graphs |
title_full_unstemmed |
Optimal mass transport on metric graphs |
title_sort |
optimal mass transport on metric graphs |
publishDate |
2015 |
url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10526234_v25_n3_p1609_Mazon http://hdl.handle.net/20.500.12110/paper_10526234_v25_n3_p1609_Mazon |
work_keys_str_mv |
AT rossijuliodaniel optimalmasstransportonmetricgraphs |
_version_ |
1768544695878680576 |