Optimal geometry of transportation networks
نویسندگان
چکیده
منابع مشابه
The geometry of optimal transportation
A classical problem of transporting mass due to Monge and Kantorovich is solved. Given measures μ and ν on Rd, we find the measure-preserving map y(x) between them with minimal cost — where cost is measured against h(x − y) with h strictly convex, or a strictly concave function of |x − y|. This map is unique: it is characterized by the formula y(x) = x − (∇h)−1(∇ψ(x)) and geometrical restrictio...
متن کامل12w5118 Optimal Transportation and Differential Geometry
Optimal mass transportation can be traced back to Gaspard Monge’s famous paper of 1781: ‘Mémoire sur la théorie des déblais et des remblais’. The problem there is to minimize the cost of transporting a given distribution of mass from one location to another. Since then, it has become a classical subject in probability theory, economics and optimization. At the end of the 80’s, the seminal work ...
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Here c is a given lower semicontinuous cost function, and πi are the marginals of π . In the typical case c(x, y) = ‖x − y‖, p > 1, and the pth root of the minimum in (1.1) is then called the p-Wasserstein distance Wp(μ, μ) between μ and μ. Brancolini and Buttazzo [6], Buttazzo and Stepanov [8], and Buttazzo et al. [7], among other works, consider a variant of the problem with two different med...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2019
ISSN: 2470-0045,2470-0053
DOI: 10.1103/physreve.99.052303