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Lectures on Optimal Transport

2021-07-22 Mathematics
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Release : 2021-07-22
Genre : Mathematics
Kind : eBook
Book Rating : 620/5 ( reviews)

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Book Synopsis Lectures on Optimal Transport by : Luigi Ambrosio

Download or read book Lectures on Optimal Transport written by Luigi Ambrosio. This book was released on 2021-07-22. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations.

Optimal Transportation Networks

2009 Business & Economics
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Release : 2009
Genre : Business & Economics
Kind : eBook
Book Rating : 149/5 ( reviews)

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Book Synopsis Optimal Transportation Networks by : Marc Bernot

Download or read book Optimal Transportation Networks written by Marc Bernot. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt: The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.

Optimal Transportation and Applications

2003-01-01 Mathematics
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Release : 2003-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 578/5 ( reviews)

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Book Synopsis Optimal Transportation and Applications by : Luigi Ambrosio

Download or read book Optimal Transportation and Applications written by Luigi Ambrosio. This book was released on 2003-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampère and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view. The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory.

Optimal Transport

2008-10-26 Mathematics
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Release : 2008-10-26
Genre : Mathematics
Kind : eBook
Book Rating : 507/5 ( reviews)

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Book Synopsis Optimal Transport by : Cédric Villani

Download or read book Optimal Transport written by Cédric Villani. This book was released on 2008-10-26. Available in PDF, EPUB and Kindle. Book excerpt: At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.

Topics in Optimal Transportation

2021-08-25 Education
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Release : 2021-08-25
Genre : Education
Kind : eBook
Book Rating : 267/5 ( reviews)

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Book Synopsis Topics in Optimal Transportation by : Cédric Villani

Download or read book Topics in Optimal Transportation written by Cédric Villani. This book was released on 2021-08-25. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive introduction to the theory of mass transportation with its many—and sometimes unexpected—applications. In a novel approach to the subject, the book both surveys the topic and includes a chapter of problems, making it a particularly useful graduate textbook. In 1781, Gaspard Monge defined the problem of “optimal transportation” (or the transferring of mass with the least possible amount of work), with applications to engineering in mind. In 1942, Leonid Kantorovich applied the newborn machinery of linear programming to Monge's problem, with applications to economics in mind. In 1987, Yann Brenier used optimal transportation to prove a new projection theorem on the set of measure preserving maps, with applications to fluid mechanics in mind. Each of these contributions marked the beginning of a whole mathematical theory, with many unexpected ramifications. Nowadays, the Monge-Kantorovich problem is used and studied by researchers from extremely diverse horizons, including probability theory, functional analysis, isoperimetry, partial differential equations, and even meteorology. Originating from a graduate course, the present volume is intended for graduate students and researchers, covering both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis.

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