Softcover ISBN:  9781470450250 
Product Code:  PSAPM/77 
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eBook ISBN:  9781470460402 
Product Code:  PSAPM/77.E 
List Price:  $118.00 
MAA Member Price:  $106.20 
AMS Member Price:  $94.40 
Softcover ISBN:  9781470450250 
eBook: ISBN:  9781470460402 
Product Code:  PSAPM/77.B 
List Price:  $236.00 $177.00 
MAA Member Price:  $212.40 $159.30 
AMS Member Price:  $188.80 $141.60 
Softcover ISBN:  9781470450250 
Product Code:  PSAPM/77 
List Price:  $118.00 
MAA Member Price:  $106.20 
AMS Member Price:  $94.40 
eBook ISBN:  9781470460402 
Product Code:  PSAPM/77.E 
List Price:  $118.00 
MAA Member Price:  $106.20 
AMS Member Price:  $94.40 
Softcover ISBN:  9781470450250 
eBook ISBN:  9781470460402 
Product Code:  PSAPM/77.B 
List Price:  $236.00 $177.00 
MAA Member Price:  $212.40 $159.30 
AMS Member Price:  $188.80 $141.60 

Book DetailsProceedings of Symposia in Applied MathematicsVolume: 77; 2020; 142 ppMSC: Primary 05; 14; 52; 68; 90
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 stateoftheart 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.
ReadershipGraduate students and researchers interested in various aspects of the theory of nonnegative polynomials and applications.

Table of Contents

Articles

Grigoriy Blekherman — A brief introduction to sums of squares

Cynthia Vinzant — The geometry of spectrahedra

Hamza Fawzi — Lifts of convex sets

Mauricio Velasco — Algebraic geometry and sums of squares

Ankur Moitra — Sums of squares in theoretical computer science

Georgina Hall — Applications of sums of squares


Additional Material

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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 stateoftheart 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.
Graduate students and researchers interested in various aspects of the theory of nonnegative polynomials and applications.

Articles

Grigoriy Blekherman — A brief introduction to sums of squares

Cynthia Vinzant — The geometry of spectrahedra

Hamza Fawzi — Lifts of convex sets

Mauricio Velasco — Algebraic geometry and sums of squares

Ankur Moitra — Sums of squares in theoretical computer science

Georgina Hall — Applications of sums of squares