Differentiation and regularity of semi-discrete optimal transport with respect to the parameters of the discrete measure

DOI10.1007/s00211-018-1000-4zbMath1475.49055arXiv1803.00827OpenAlexW4288607991WikidataQ128954010 ScholiaQ128954010MaRDI QIDQ1719564

Léo Lebrat, Frédéric de Gournay, Jonas Kahn

Publication date: 8 February 2019

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.00827

zbMATH Keywords

differentiationblue noise problemsemi-discrete optimal transportstippling problem

Mathematics Subject Classification ID

Newton-type methods (49M15) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Optimal transportation (49Q22)

Related Items (11)

Partial optimal transport for a constant-volume Lagrangian mesh with free boundaries ⋮ Lagrangian Discretization of Variational Mean Field Games ⋮ Minimum-error classes for matching parts ⋮ A new implementation of the geometric method for solving the Eady slice equations ⋮ Sensitivity analysis and tailored design of minimization diagrams ⋮ Optimal Transport Approximation of 2-Dimensional Measures ⋮ Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance case ⋮ 3/4-Discrete Optimal Transport ⋮ Optimal transport: discretization and algorithms ⋮ Curve based approximation of measures on manifolds by discrepancy minimization ⋮ Semi-discrete optimal transport methods for the semi-geostrophic equations

Uses Software

• CGAL
• EMD

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Minkowski-type theorems and least-squares clustering
• Wasserstein discriminant analysis
• Grid generation and optimization based on centroidal Voronoi tessellations
• The earth mover's distance as a metric for image retrieval
• Optimum quantization and its applications
• A linear optimal transportation framework for quantifying and visualizing variations in sets of images
• Foundations of quantization for probability distributions
• Convergence of a Newton algorithm for semi-discrete optimal transport
• Variation and optimization of formes. A geometric analysis
• Optimal Delaunay and Voronoi Quantization Schemes for Pricing American Style Options
• A Numerical Algorithm forL₂Semi-Discrete Optimal Transport in 3D
• The Variational Formulation of the Fokker--Planck Equation
• An Algorithm for Optimal Transport between a Simplex Soup and a Point Cloud
• Centroidal Voronoi Tessellations: Applications and Algorithms
• Power Diagrams: Properties, Algorithms and Applications
• Least squares quantization in PCM
• A Comparison of Two Dual Methods for Discrete Optimal Transport
• Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations

This page was built for publication: Differentiation and regularity of semi-discrete optimal transport with respect to the parameters of the discrete measure