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Preconditioning of Optimal Transport

SIAM Journal on Scientific Computing, 2017
Summary: A preconditioning procedure is developed for the \(L_2\) and more general optimal transport problems. The procedure is based on a family of affine map pairs which transforms the original measures into two new measures that are closer to each other while preserving the optimality of solutions.
Kuang, Max, Tabak, Esteban G.
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Data‐Driven Optimal Transport

Communications on Pure and Applied Mathematics, 2015
AbstractThe problem of optimal transport between two distributions ρ(x) and μ(y) is extended to situations where the distributions are only known through a finite number of samples {xi} and {yj}. A weak formulation is proposed, based on the dual of the Kantorovich formulation, with two main modifications: replacing the expected values in the objective ...
Trigila, Giulio, Tabak, Esteban G.
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Optimal Transport

2014
The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory
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Optimal Transport of Maps

Journal of Optimization Theory and Applications
The authors investigate the problem of optimal transport of continuous maps, where the cost depends on the distance on the space of continuous maps. They consider transport for the graph of a continuous map to another, instead of the probability measure. Within the space of continuous maps, the authors define a minimal cost distance and investigate the
Woochul Jung, Carlos Morales, Xiao Wen
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Optimal Transportation

2014
The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory
Ollivier, Yann   +2 more
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Multi-species Optimal Transportation

Journal of Optimization Theory and Applications, 2019
The article focuses on optimal transport problem for vector-valued positive measures in Kantorovich's formulation. First, the problem's scalar formulation is extended to the vector case, yielding a linear primal problem. In this formulation, two probability distributions $\mu$ and $\nu$ of two measurable spaces $X$ resp.
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