Optimal Transport and Applications to Geometric Optics

Cristian E. Gutiérrez (Autor)

Buch | Softcover

135 Seiten

2023 | 1st ed. 2023
Springer Verlag, Singapore
978-981-99-4866-6 (ISBN)

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lt;p>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.

Dr. Cristian E. Gutierrez is a Professor at Temple University. His research areas include partial differential equations, geometric optics, optimal transport, and electromagnetism. He is a Fellow of the American Mathematical Society, a Member of the Academy of Sciences of Argentina, and a Member of the Academy of Sciences of the University of Bologna, Italy.

lt;p>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.

Erscheinungsdatum	03.01.2024
Reihe/Serie	SpringerBriefs on PDEs and Data Science
Zusatzinfo	1 Illustrations, black and white
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
	Naturwissenschaften ► Physik / Astronomie ► Optik
	Wirtschaft ► Betriebswirtschaft / Management
Schlagworte	Benamou and Brenier formula • Brenier polar factorization • cyclical monotonicity • disintegration of measures • Far field refraction • Kantorovich-Rubinstein duality • Legendre Transform • Monge-Ampère equation • Monge-Kantorovich problem • Near field refraction • network flow problem • Optimal maps • Refractor problem • Sinkhorn algorithm • Snell's law of refraction • Snell’s law of refraction • Transhipment problem • Wasserstein distance
ISBN-10	981-99-4866-5 / 9819948665
ISBN-13	978-981-99-4866-6 / 9789819948666
Zustand	Neuware