American Mathematical Society. Short Course, Sum of Squares : Theory and Applications (2019 : Baltimore, Maryland) author.
Title:
Sum of squares : theory and applications : AMS short course, Sum of Squares : Theory and Applications, January 14-15, 2019, Baltimore, Maryland / Pablo A. Parrilo, Rekha R. Thomas, editors.
Publisher:
American Mathematical Society,
Copyright Date:
2020
Description:
vii, 142 pages : illustrations (some color) ; 26 cm.
"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"-- back cover. Includes bibliographical references and index.
Contents:
A brief introduction to sums of squares / Grigoriy Blekherman -- The geometry of spectrahedra / Cynthia Vinzant -- Lifts of convex sets / Hamza Fawzi -- Algebraic geometry and sums of squares / Mauricio Velasco -- Sums of squares in theoretical computer science / Ankur Moitra -- Applications of sums of squares / Georgina Hall.
Summary:
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.
Series:
Proceedings of symposia in applied mathematics, 0160-7634 ; volume 77
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.