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―
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- 高津 飛鳥
- 東京都立大学大学院理学研究科数理科学専攻
書誌事項
- タイトル別名
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- Transport Plan, Transport Map and Transport Path—Difference of the Optimal Transport Problem between ℝ<sup>2</sup> and Finite Set—
抄録
<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>
収録刊行物
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- 応用数理
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応用数理 32 (2), 69-79, 2022-06-24
一般社団法人 日本応用数理学会
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詳細情報 詳細情報について
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- CRID
- 1390856539345601920
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- ISSN
- 24321982
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- 本文言語コード
- ja
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- データソース種別
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- JaLC
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- 抄録ライセンスフラグ
- 使用不可