Barycenters in the Hellinger-Kantorovich space

DOI10.1007/s00245-020-09695-yzbMath1480.49014arXiv1909.05513OpenAlexW3037652719MaRDI QIDQ2232777

Minh-Nhat Phung, Nhan-Phu Chung

Publication date: 8 October 2021

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.05513

zbMATH Keywords

dualitybarycenteroptimal transportHellinger-Kantorovich distancemultimarginal problem

Mathematics Subject Classification ID

Variational inequalities (49J40) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30) Optimality conditions for problems involving relations other than differential equations (49K21)

Related Items

Unbalanced optimal total variation transport problems and generalized Wasserstein barycenters, Hellinger–Kantorovich barycenter between Dirac measures, Unbalanced multi-marginal optimal transport, Barycenters for the Hellinger--Kantorovich Distance Over $\mathbb{R}^d$, The Linearized Hellinger--Kantorovich Distance

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Wasserstein barycenters over Riemannian manifolds
• A new optimal transport distance on the space of finite Radon measures
• Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures
• Unbalanced optimal transport: dynamic and Kantorovich formulations
• Optimal transportation with infinitely many marginals
• Distribution's template estimate with Wasserstein metrics
• Existence and consistency of Wasserstein barycenters
• Generalized Wasserstein distance and its application to transport equations with source
• Integrals which are convex functionals. II
• Measurable selections of extrema
• Optimal Transport in Competition with Reaction: The Hellinger--Kantorovich Distance and Geodesic Curves
• Convex analysis and optimization in Hadamard spaces
• Multi-marginal optimal transport on Riemannian manifolds
• Uniqueness and Monge Solutions in the Multimarginal Optimal Transportation Problem
• Barycenters in the Wasserstein Space
• Barycenters for the Hellinger--Kantorovich Distance Over $\mathbb{R}^d$
• Numerical methods for matching for teams and Wasserstein barycenters
• Optimal maps for the multidimensional Monge-Kantorovich problem
• Spherical Hellinger--Kantorovich Gradient Flows
• A General Condition for Monge Solutions in the Multi-Marginal Optimal Transport Problem
• Optimal Transport