Optimal Transportation with Traffic Congestion and Wardrop Equilibria
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In this paper, the authors propose a variant of the Monge-Kantorovich problem, taking into account congestion, and prove the existence and the variational characterization of equilibria in a continuous space setting.Abstract:
In the classical Monge-Kantorovich problem, the transportation cost depends only on the amount of mass sent from sources to destinations and not on the paths followed by this mass. Thus, it does not allow for congestion effects. Using the notion of traffic intensity, we propose a variant, taking into account congestion. This variant is a continuous version of a well-known traffic problem on networks that is studied both in economics and in operational research. The interest of this problem is in its relations with traffic equilibria of Wardrop type. What we prove in the paper is exactly the existence and the variational characterization of equilibria in a continuous space setting.read more
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Topics in Optimal Transportation
TL;DR: In this paper, the metric side of optimal transportation is considered from a differential point of view on optimal transportation, and the Kantorovich duality of the optimal transportation problem is investigated.
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Convex analysis and measurable multifunctions
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TL;DR: In this paper, the authors consider convex functions with topological properties of the profile of a convex multifunction with compact convex values and prove the compactness theorems of measurable selections and integral representation theorem.
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Polar Factorization and Monotone Rearrangement of Vector-Valued Functions
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