Breaking the Curse of Dimension in Multi-Marginal Kantorovich Optimal Transport on Finite State Spaces
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Publication:3176425
DOI10.1137/17M1150025zbMath1395.49009arXiv1801.00341WikidataQ129558076 ScholiaQ129558076MaRDI QIDQ3176425
Daniela Vögler, Gero Friesecke
Publication date: 20 July 2018
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1801.00341
Variational inequalities (49J40) Variational principles of physics (49S05) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)
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Cites Work
- Model-independent bounds for option prices -- a mass transport approach
- Multi-marginal optimal transport and multi-agent matching problems: uniqueness and structure of solutions
- Infinite-body optimal transport with Coulomb cost
- Matching for teams
- Hedonic price equilibria, stable matching, and optimal transport: Equivalence, topology, and uniqueness
- A three-dimensional matching model for perishable production scheduling
- Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking
- Monge problem for \(n\) probabilities
- Semi-classical limit of the Levy-Lieb functional in density functional theory
- Smoothing of transport plans with fixed marginals and rigorous semiclassical limit of the Hohenberg-Kohn functional
- On the vertices of the \(d\)-dimensional Birkhoff polytope
- A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options
- Combinatorial properties of noninteger vertices of a polytope in a three-index axial assignment problem
- Remarks on the semi-classical Hohenberg–Kohn functional
- Optimal Transport with Proximal Splitting
- Solutions to multi-marginal optimal transport problems concentrated on several graphs
- Uniqueness and Monge Solutions in the Multimarginal Optimal Transportation Problem
- Barycenters in the Wasserstein Space
- Optimal transportation for the determinant
- Optimal maps for the multidimensional Monge-Kantorovich problem
- 9. Optimal transportation theory with repulsive costs
- Density Functional Theory and Optimal Transportation with Coulomb Cost
- Multimarginal Optimal Transport Maps for One–dimensional Repulsive Costs
- Regularized Discrete Optimal Transport
- A Simple Counterexample to the Monge Ansatz in Multimarginal Optimal Transport, Convex Geometry of the Set of Kantorovich Plans, and the Frenkel--Kontorova Model
- Letter to the Editor—The Multidimensional Assignment Problem
- Optimal Transport
- Notions of convexity
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