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

V. I. Bogachev

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 77 (2022) no. 5, pp. 769-817

Résumé

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. Bibliography: 134 items.

Détail

Keywords: Kantorovich problem, nonlinear Kantorovich problem, Monge problem, Kantorovich metric, conditional measure.
Mots-clés : optimal transportation

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