B. Pass, Multi-marginal optimal transport: theory and applications, ESAIM: Mathematical Modelling and Numerical Analysis 49 (2015), 1771-1790.Brendan Pass. Multi-marginal optimal transport: theory and applicati
Optimal transport theory provides a distance between two probability distributions. It ?nds the cheapest transport map that moves one measure to the other measure for some ground cost. With its deep theoretical properties, the optimal transport distance has been used in diverse areas such as partial...
GAN idea 至此可以很自然引入接下来的Optimal Transport Theorem!核心思路就是找到一个可以处理non-overlapping情况的probability measures! OT theory involved Optimal Transport OT可以刻画分布之间很自然的变化过程,进而能给出衡量各种分布类型之间距离的度量(定义研究对象的distance,OT自动给出研究对象分布的distance)。比如...
In this paper, we give an overview of (nonlinear) pricing-hedging duality and of its connection with the theory of entropy martingale optimal transport (EM
Course Description: formulation of the optimal transport problem, Kantorovich duality theory, existence and uniqueness theory, c-monotonicity and structure of solutions, discrete optimal transport. Economic applications including: transferable utility models in matching theory, hedonic and discrete choice models...
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Computational optimal transport. Preprint at http://arxiv.org/abs/1803.00567 (2018). Klatt, M., Tameling, C. & Munk, A. Empirical regularized optimal transport: statistical theory and applications. SIAM J. Math. Data Sci. 2, 419–443 (2020). MathSciNet Google Scholar Monge, G. ...
Engineering multilayer networks that efficiently connect sets of points in space is a crucial task in all practical applications that concern the transport of people or the delivery of goods. Unfortunately, our current theoretical understanding of the shape of such optimal transport networks is quite ...
Optimal transport theory arises from a question posed in economics, and specifically, in the allocation of resources. It deals with optimizing transport modes when geographically displacing resources. Its mathematical formulation was established in the 18th century and has been well-studied since, resulti...
By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored. Furthermore, applications in science and engineering, including economics, social sciences, ...