**Proceedings of Symposia in Applied Mathematics**

Volume: 77;
2020;
142 pp;
Softcover

MSC: Primary 05; 14; 52; 68; 90;

**Print ISBN: 978-1-4704-5025-0
Product Code: PSAPM/77**

List Price: $118.00

AMS Member Price: $94.40

MAA Member Price: $106.20

**Electronic ISBN: 978-1-4704-6040-2
Product Code: PSAPM/77.E**

List Price: $118.00

AMS Member Price: $94.40

MAA Member Price: $106.20

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# Sum of Squares: Theory and Applications

Share this page *Edited by *
*Pablo A. Parrilo; Rekha R. Thomas*

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.

#### Readership

Graduate students and researchers interested in various aspects of the theory of non-negative polynomials and applications.

# Table of Contents

## Sum of Squares: Theory and Applications

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- A brief introduction to sums of squares 110
- The geometry of spectrahedra 1120
- Lifts of convex sets 3746
- Algebraic geometry and sums of squares 5968
- Sums of squares in theoretical computer science 8392
- Applications of sums of squares 103112
- Part 1. Dynamical systems and control 104113
- Part 2. Probability and measure theory 114123
- Part 3. Statistics and machine learning 121130
- Part 4. Other applications 127136
- Part 5. Conclusion: a word on implementation challenges 133142
- Back Cover Back Cover1154