Boundary $C^{1,\alpha}$ regularity of an optimal transport problem with cost close to $-x\cdot y$

2015 ◽  
Vol 47 (4) ◽  
pp. 2689-2698 ◽  
Author(s):  
Shibing Chen
Keyword(s):  
Optimal Transport ◽  
Transport Problem

A discrete method for the initialization of semi-discrete optimal transport problem

2021 ◽  
Vol 212 ◽  
pp. 106608
Author(s):  
Judy Yangjun Lin ◽  
Shaoyan Guo ◽  
Longhan Xie ◽  
Ruxu Du ◽  
Gu Xu
Keyword(s):  
Optimal Transport ◽  
Transport Problem ◽  
Discrete Method

Duality for the $L^{\infty }$ optimal transport problem

2016 ◽  
Vol 369 (5) ◽  
pp. 3289-3323 ◽  
Author(s):  
E. N. Barron ◽  
M. Bocea ◽  
R. R. Jensen
Keyword(s):  
Optimal Transport ◽  
Transport Problem

MASS TRANSPORTATION IN GROUPS OF TYPE H

2005 ◽  
Vol 07 (04) ◽  
pp. 509-537 ◽  
Author(s):  
S. RIGOT
Keyword(s):  
Cost Function ◽  
Optimal Transport ◽  
Transport Problem ◽  
Mass Transportation ◽  
Heisenberg Groups ◽  
The One ◽  
Carathéodory Distance ◽  
The Cost ◽  
Special Case

We give a solution of the optimal transport problem in groups of type H when the cost function is the square of either the Carnot–Carathéodory or Korányi distance. This generalizes results previously proved for the Heisenberg groups. We use the same strategy that the one which was developed in that special case together with slightly refined technicalities that essentially reflect the fact that the center of the group can be of dimension larger than one. For each distance we prove existence, uniqueness and give a characterization of the optimal transport. In the case of the Carnot–Carathéodory distance we also prove that the optimal transport arises as the limit of the optimal transports in natural Riemannian approximations.

scholarly journals Optimal Mass Transport in Thin Domains

2014 ◽  
Vol 14 (1) ◽  
Author(s):  
José C. Navarro-Climent ◽  
Julio D. Rossi ◽  
Raúl C. Volpe
Keyword(s):  
Mass Transport ◽  
Euclidean Distance ◽  
Optimal Transport ◽  
Transport Problem ◽  
Thin Domains ◽  
Optimal Mass Transport

AbstractWe find the behavior of the solution of the optimal transport problem for the Euclidean distance (and its approximation by p−Laplacian problems) when the involved measures are supported in a domain that is contracted in one direction.

Tractable Relaxations of Composite Functions

2021 ◽  
Author(s):  
Taotao He ◽  
Mohit Tawarmalani
Keyword(s):  
Optimal Transport ◽  
Integral Formula ◽  
Transport Problem ◽  
Inner Function ◽  
Outer Function ◽  
Inner Functions ◽  
Separation Algorithm ◽  
Large Classes ◽  
Composite Functions ◽  
Factorable Programming

In this paper, we introduce new relaxations for the hypograph of composite functions assuming that the outer function is supermodular and concave extendable. Relying on a recently introduced relaxation framework, we devise a separation algorithm for the graph of the outer function over P, where P is a special polytope to capture the structure of each inner function using its finitely many bounded estimators. The separation algorithm takes [Formula: see text] time, where d is the number of inner functions and n is the number of estimators for each inner function. Consequently, we derive large classes of inequalities that tighten prevalent factorable programming relaxations. We also generalize a decomposition result and devise techniques to simultaneously separate hypographs of various supermodular, concave-extendable functions using facet-defining inequalities. Assuming that the outer function is convex in each argument, we characterize the limiting relaxation obtained with infinitely many estimators as the solution of an optimal transport problem. When the outer function is also supermodular, we obtain an explicit integral formula for this relaxation.

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