Transport Plan, Transport Map and Transport Path—Difference of the Optimal Transport Problem between ℝ<sup>2</sup> and Finite Set—

DOI
  • Takatsu Asuka
    東京都立大学大学院理学研究科数理科学専攻

Bibliographic Information

Other Title
  • 輸送計画，輸送写像，輸送経路―有限集合とℝ<sup>2</sup>の最適輸送理論の違い―

Abstract

<p>This paper is concerned with a variational problem on the space of probability measures over either ℝ2 or a finite set, the so-called optimal transport problem. We discussed three ways to formulate the optimal transport problem on ℝ2 as follows: the use of a probability measure (transport plan) on ℝ2 × ℝ2, a map (transport map) from ℝ2 to ℝ2, and a family of paths (transport path) on ℝ2. The definition of transport path requires the property that each pair of points in ℝ2 should be connected by a length minimizing curve. To define transport paths on a finite set, we explained how to modify the optimal transport problem on a finite set. </p>

Journal

Keywords

Details 詳細情報について

  • CRID
    1390856539345601920
  • DOI
    10.11540/bjsiam.32.2_69
  • ISSN
    24321982
  • Text Lang
    ja
  • Data Source
    • JaLC
  • Abstract License Flag
    Disallowed

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