A BENAMOU-BRENIER APPROACH TO BRANCHED TRANSPORT

The problem of branched transportation aims to describe the movement of masses when, due to concavity effects, they have the impulse to travel together as much as possible, because the cost for a path of length ... covered by a mass m is proportional to ... with 0 < α < 1. The optimization of...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 2011-01, Vol.43 (1-2), p.1023-1040
Main Authors: BRASCO, L, BUTTAZZO, G, SANTAMBROGIO, F
Format: Article
Language:English
Subjects:
Branched
Dynamical systems
Exact sciences and technology
Mathematical analysis
Mathematical models
Mathematics
Movement
Optimization
River networks
Route optimization
Sciences and techniques of general use
Studies
Transport
Transportation
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Summary:The problem of branched transportation aims to describe the movement of masses when, due to concavity effects, they have the impulse to travel together as much as possible, because the cost for a path of length ... covered by a mass m is proportional to ... with 0 < α < 1. The optimization of this criterion let branched structures appear and is suitable to applications like road systems, blood vessels, river networks, etc. Several models have been employed in the literature to present this transport problem, and the present paper looks at a dynamical model similar to the celebrated Benamou-Brenier formulation of Kantorovich optimal transport. The movement is represented by a path ρt of probabilities connecting an initial state µ0 to a final state µ1 and satisfying the continuity equation ... together with a velocity field v (with q = ρv being the momentum). The transportation cost to be minimized is nonconvex and finite on atomic measures: ... (ProQuest: ... denotes formulae/symbols omitted.)
ISSN:0036-1410
1095-7154
DOI:10.1137/10079286X