Kantorovich problem of optimal transportation of measures: new directions of research

被引：6
|
作者：
Bogachev, V. I. [1 ,2 ]
机构：
[1] Lomonosov Moscow State Univ, Moscow, Russia
[2] Natl Res Univ, Higher Sch Econ, Moscow, Russia
来源：
RUSSIAN MATHEMATICAL SURVEYS | 2022年 / 77卷 / 05期
基金：
俄罗斯科学基金会;
关键词：
Kantorovich problem; nonlinear Kantorovich problem; Monge problem; Kantorovich metric; optimal transportation; conditional measure; SCHRODINGER-PROBLEM; CAUSAL TRANSPORT; MONGE; SPACE; PLANS; PARAMETER; EQUALITY; DISTANCE; DUALITY;
D O I：
10.4213/rm10074
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper gives a survey of investigations in the last decade and new results on various recent modifications of the classical Kantorovich problem of the optimal transportation of measures. We discuss in detail nonlinear Kantorovich problems, problems with constraints on the densities of transport plans, and optimal transportation problems with a parameter. In addition, we consider some questions relating to the geometry and topology of spaces of measures connected with these new formulations.
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页码：769 / 817
页数：49
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