The time transportation problem
W. Szwarc (1965)
Applicationes Mathematicae
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W. Szwarc (1965)
Applicationes Mathematicae
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Alessio Brancolini, Giuseppe Buttazzo (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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In the framework of transport theory, we are interested in the following optimization problem: given the distributions µ of working people and µ of their working places in an urban area, build a transportation network (such as a railway or an underground system) which minimizes a functional depending on the geometry of the network through a particular cost function. The functional is defined as the Wasserstein distance of µ from µ with respect to a metric which depends on the transportation...
W. Grabowski (1976)
Applicationes Mathematicae
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Ilija Nikolić (2007)
The Yugoslav Journal of Operations Research
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Stefán Ingi Valdimarsson (2007)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We study the optimal solution of the Monge-Kantorovich mass transport problem between measures whose density functions are convolution with a gaussian measure and a log-concave perturbation of a different gaussian measure. Under certain conditions we prove bounds for the Hessian of the optimal transport potential. This extends and generalises a result of Caffarelli. We also show how this result fits into the scheme of Barthe to prove Brascamp-Lieb inequalities and thus prove a new generalised...
Yann Brenier, Marjolaine Puel (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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A multiphase generalization of the Monge–Kantorovich optimal transportation problem is addressed. Existence of optimal solutions is established. The optimality equations are related to classical Electrodynamics.
Aldo Pratelli (2007)
Annales de l'I.H.P. Probabilités et statistiques
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Byron Papathanassiou, Fotini - Niovi Pavlidou (1994)
The Yugoslav Journal of Operations Research
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Marc Bernot, Alessio Figalli (2008)
ESAIM: Control, Optimisation and Calculus of Variations
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The irrigation problem is the problem of finding an efficient way to transport a measure μ onto a measure μ. By efficient, we mean that a structure that achieves the transport (which, following [Bernot, Caselles and Morel, (2005) 417–451], we call traffic plan) is better if it carries the mass in a grouped way rather than in a separate way. This is formalized by considering costs functionals that favorize this property. The aim of this paper is to introduce a dynamical...