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.

Format:

Book

Author/Creator:

American Mathematical Society. Short Course, Sum of Squares : Theory and Applications (2019 : Baltimore, Maryland), author.

Contributor:

Parrilo, Pablo A., editor.

Thomas, Rekha R., 1967- editor.

Series:

Proceedings of symposia in applied mathematics ; 0160-7634 v. 77.

Proceedings of symposia in applied mathematics, 0160-7634 ; volume 77

Language:

English

Subjects (All):

Polynomials.

Convex geometry.

Convex sets.

Geometry, Algebraic.

Semidefinite programming.

Mathematical optimization.

Physical Description:

vii, 142 pages : illustrations ; 26 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2020]

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.

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.

Notes:

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.

Includes bibliographical references and index.

ISBN:

9781470450250

1470450259

OCLC:

1157604983