Optimal Transport and Applications to Geometric Optics [[electronic resource] /] / by Cristian E. Gutiérrez

• Record Nr.: UNINA9910770271403321
• Autore: Gutiérrez Cristian E
• Pubbl/distr/stampa: Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2023
• ISBN: 981-9948-67-3
• Edizione: [1st ed. 2023.]
• Descrizione fisica: 1 online resource (140 pages)
• Collana: SpringerBriefs on PDEs and Data Science, , 2731-7609
• Disciplina: 519.6
• Soggetti: Optimització matemàtica; Mathematical optimization; Operations research; Management science; Geometrical optics; Wave theory of light; Differential equations; Optimization; Operations Research, Management Science; Classical Optics, Geometric and Wave optics; Differential Equations; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Chapter 1 Introduction -- Chapter 2 The normal mapping or subdifferential.-Chapter 3 Sinkhorn’s theorem and application to the distribution problem -- Chapter4 Monge-Kantorovich distance -- Chapter 5 Multivalued measure preserving maps -- Chapter 6 Kantorovich Dual Problem -- Chapter 7 Brenier and Aleksandrov solutions -- Chapter 8 Cyclical monotonicity -- Chapter 9 Quadratic cost -- Chapter 10 Brenier ’s Polar Factorization Theorem -- Chapter 11 Benamou and Brenier formula -- Chapter 12 Snell’s law of refraction -- Chapter 13 Solution of the far field refractor problem < 1 -- Chapter 14 Proof of the Disintegration Theorem -- Chapter 15 Acknowledgements -- Chapter 16 References.
• Sommario/riassunto: This book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained presentation including a detailed analysis of the Monge problem, the Monge-Kantorovich problem, the transshipment problem, and the network flow problem. A chapter on Monge-Ampère measures is included containing also exercises. A detailed analysis of the Wasserstein metric is also carried out. For the applications to optics, the book describes the necessary background concerning light refraction, solving both far-field and near-field refraction problems, and indicates lines of current research in this area. Researchers in the fields of mathematical analysis, optimal transport, partial differential equations (PDEs), optimization, and optics will find this book valuable. It is also suitable for graduate students studying mathematics, physics, and engineering. The prerequisites for this book include a solid understanding of measure theory and integration, as well as basic knowledge of functional analysis.