Topics in optimal transportation
By: Villani, Cedric.
Material type: BookSeries: Graduate studies in mathematics; v.58. Publisher: Providence American Mathematical Society 2003Description: xiv, 370p.ISBN: 9781470425623.Subject(s): Transportation problems (Programming) | Monge-Ampere equationsDDC classification: 519.72 | V712t Summary: 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.Item type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
---|---|---|---|---|---|---|---|
Books | PK Kelkar Library, IIT Kanpur | General Stacks | 519.72 V712t (Browse shelf) | Checked out to DIVYANSH AGARWAL (S20817034900) | 04/10/2024 | GB1540 |
Browsing PK Kelkar Library, IIT Kanpur Shelves , Collection code: General Stacks Close shelf browser
519.72 T346i3 An introduction to linear programming and game theory | 519.72 V283L LINEAR PROGRAMMING | 519.72 V283l3 Linear programming | 519.72 V712t Topics in optimal transportation | 519.72 Y3I INTERIOR POINT ALGORITHMS | 519.76 Ad95 ADVANCES IN GEOMETRIC PROGRAMMING | 519.76 Ao43 INTRODUCTION TO OPTIMIZATION TECHNIQUES |
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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