Sum of Squares : Theory and Applications

Parrilo, Pablo A. (EDT); Thomas, Rekha R. (EDT)

ISBN 10: 1470450259 / ISBN 13: 9781470450250

Editore: American Mathematical Society, 2020

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Dati bibliografici

• Titolo: Sum of Squares : Theory and Applications
• Editore: American Mathematical Society
• Data di pubblicazione: 2020
• Lingua: Inglese
• ISBN 10: 1470450259
• ISBN 13: 9781470450250
• Rilegatura: Brossura
• Condizione: New

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Riassunto

This volume is based on lectures delivered at the 2019 AMS Short Course ""Sum of Squares: Theory and Applications'', held January 14-15, 2019, in Baltimore, Maryland. This book provides a concise state-of-the-art overview of the theory and applications of polynomials that are sums of squares. This is an exciting and timely topic, with rich connections to many areas of mathematics, including polynomial and semidefinite optimization, real and convex algebraic geometry, and theoretical computer science.

The six chapters introduce and survey recent developments in this area; specific topics include the algebraic and geometric aspects of sums of squares and spectrahedra, lifted representations of convex sets, and the algorithmic and computational implications of viewing sums of squares as a meta algorithm. The book also showcases practical applications of the techniques across a variety of areas, including control theory, statistics, finance and machine learning.