Five lectures on optimal transportation: Geometry, regularity and applications
By Nestor Guillen, Robert J. McCann. 2010
87 citations recorded by the source corpus.
In this series of lectures we introduce the Monge-Kantorovich problem of optimally transporting one distribution of mass onto another, where optimality is measured against a cost function c(x,y). Connections to geometry, inequalities, and partial differential equations will be discussed, focusing in particular on recent developments in the regularity theory for Monge-Ampere type equations. An application to microeconomics will also be described, which amounts to finding the equilibrium price distribution for a monopolist marketing a multidimensional line of products to a population of anonymous agents whose preferences are known only statistically.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6adb0df12537dcc2f6d39cb856708ca0ac307fb3
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
- G. Em Karniadakis
- Liu Yang
- Filippo Santambrogio
- G. Peyr'e
- Marco Cuturi
- Luigi Ambrosio
- Tudor Manole
- Jonathan Niles-Weed
Citations in the corpus
- Monge's Optimal Transport Distance for Image Classification (2016, unknown): “For a more complete discussion on the topic of optimal transport and recent developments, we refer the reader to Evans [2], Villani [4, 5] and McCann [6].”
- Bayesian Learning with Wasserstein Barycenters (2018, unknown): “, xn) ∼ NIG(μn, λn, αn, βn) where μn = λ0μ0+nx̄n λ0+n , λn = λ0 + n, αn = α0 + n 2 and βn = β0 + 12 ( ns̄n + nλ0(x̄n−μ0)(2) λ0+n ) with x̄n = 1 n ∑n i=1 xi and s̄n = 1 n ∑n i=1(xi − x̄n)(2), see Murphy [2007]. As n→∞, the posterior converges almost surely in the weak topology to a point mass at (x̄,”
- Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, background): “We also mention two very recent survey, [63] and [228]: the former accounts for the main achievements on the theory on the occasion of the centennial of the birth of L.”
- Potential Flow Generator With L2 Optimal Transport Regularity for Generative Models (2019, methodology): “We refer the readers to Gangbo and McCann [1996] and McCann and Guillen [2011] for the details.”