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Lecture 2: The Kantorovich Problem

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Lectures on Optimal Transport

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Abstract

We can now introduce Kantorovich’s formulation of the optimal transport problem. It involves the concept of transport plan (also called coupling in the Probability literature) between probability measures. In the discrete setting of Example 1.10, transport plans correspond to bi-stochastic matrices.

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Authors and Affiliations

  1. Scuola Normale Superiore, Pisa, Italy

    Luigi Ambrosio

  2. Institute for Advanced Study, School of Mathematics, Princeton, NY, USA

    Elia Brué

  3. Mathematical Institute, University of Oxford, Oxford, UK

    Daniele Semola

Authors
  1. Luigi Ambrosio
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  2. Elia Brué
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  3. Daniele Semola
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Ambrosio, L., Brué, E., Semola, D. (2021). Lecture 2: The Kantorovich Problem. In: Lectures on Optimal Transport. UNITEXT(), vol 130. Springer, Cham. https://doi.org/10.1007/978-3-030-72162-6_2

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