Optimal Transport for Applied Mathematicians: Calculus of Variations, Pdes, and Modeling

Santambrogio, Filippo

  • 出版商: Birkhauser
  • 出版日期: 2016-08-23
  • 售價: $2,900
  • 貴賓價: 9.5$2,755
  • 語言: 英文
  • 頁數: 353
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3319365819
  • ISBN-13: 9783319365817
  • 相關分類: 微積分 Calculus
  • 立即出貨 (庫存=1)

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商品描述

This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.

商品描述(中文翻譯)

這本專著提供了一個嚴謹的數學介紹,將最佳運輸視為一個變分問題,並探討其在建模各種現象中的應用及其與偏微分方程的關聯。其主要目標是為讀者提供理解當前最佳運輸研究所需的技術,以及對其應用最有用的工具。書中使用完整的證明來說明數學概念,每一章節都包含一個討論最佳運輸在各個領域應用的部分,例如經濟學、金融、潛在遊戲、影像處理和流體動力學。書中涵蓋了幾個在此主題的書籍中從未出現過的主題,例如Knothe運輸、測度上的泛函性質、Dacorogna-Moser流、通過最小流的給定散度公式的表述、超上成本的情況,以及最經典的數值方法。對於對最佳運輸的問題和應用感興趣的純數學和應用數學的研究生和研究人員來說,這將是一個無價的資源。