This book provides a self-contained, accessible introduction to the mathematical advances and challenges resulting from the use of semidefinite programming in polynomial optimization. This quickly evolving research area with contributions from the diverse fields of convex geometry, algebraic geometry, and optimization is known as convex algebraic geometry.

Each chapter addresses a fundamental aspect of convex algebraic geometry. The book begins with an introduction to nonnegative polynomials and sums of squares and their connections to semidefinite programming and quickly advances to several areas at the forefront of current research. These include semidefinite representability of convex sets, duality theory from the point of view of algebraic geometry, and nontraditional topics such as sums of squares of complex forms and noncommutative sums of squares polynomials.

Suitable for a class or seminar, with exercises aimed at teaching the topics to beginners, *Semidefinite Optimization and Convex Algebraic Geometry* serves as a point of entry into the subject for readers from multiple communities such as engineering, mathematics, and computer science. A guide to the necessary background material is available in the appendix.

**Audience** This book can serve as a textbook for graduate-level courses presenting the basic mathematics behind convex algebraic geometry and semidefinite optimization. Readers conducting research in these areas will discover open problems and potential research directions.

**Contents:** List of Notation; Chapter 1: What is Convex Algebraic Geometry?; Chapter 2: Semidefinite Optimization; Chapter 3: Polynomial Optimization, Sums of Squares, and Applications; Chapter 4: Nonnegative Polynomials and Sums of Squares; Chapter 5: Dualities; Chapter 6: Semidefinite Representability; Chapter 7: Convex Hulls of Algebraic Sets; Chapter 8: Free Convexity; Chapter 9: Sums of Hermitian Squares: Old and New; Appendix A: Background Material.

*"synopsis" may belong to another edition of this title.*

Convex algebraic geometry is an important and applicable research area featuring contributions from convex and algebraic geometry, semidefinite programming, and optimization. This self-contained introduction to the topic is suitable for readers at the graduate level and can be used for a class or seminar. Researchers will find open problems.

**About the Editors**

**Grigoriy Blekherman** is an assistant professor at Georgia Institute of Technology and a 2012 recipient of the Sloan Research Fellowship. His research interests lie at the intersection of convex and algebraic geometry.

**Pablo A. Parrilo** is a professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology. He has received the SIAG/CST Prize and the IEEE Antonio Ruberti Young Researcher Prize. His research interests include mathematical optimization, systems and control theory, and computational methods for engineering applications.

**Rekha R. Thomas** is a professor of Mathematics at the University of Washington. Her research interests are in optimization and computational algebra.

*"About this title" may belong to another edition of this title.*

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**Book Description **Society for Industrial Applied Mathematics,U.S., United States, 2013. Paperback. Book Condition: New. Language: English . Brand New Book. This book provides a self-contained, accessible introduction to the mathematical advances and challenges resulting from the use of semidefinite programming in polynomial optimization. This important and highly applicable research area, with contributions from convex geometry, algebraic geometry and optimization, is known as convex algebraic geometry. Each chapter addresses a fundamental aspect of the topic, beginning with an introduction to nonnegative polynomials and sums of squares, and their connections to semidefinite programming. The material quickly advances to areas at the forefront of current research, including semidefinite representability of convex sets, duality theory in algebraic geometry, and nontraditional topics such as sums of squares of complex forms. The book is a suitable entry point to the subject for readers at the graduate level or above in mathematics, engineering or computer science. Instructors will find the book appropriate for a class or seminar, and researchers will encounter open problems and new research directions. Bookseller Inventory # AAN9781611972283

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Published by
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ISBN 10: 1611972280
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**Book Description **Society for Industrial and Applied Mathematics, 2013. PAP. Book Condition: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Bookseller Inventory # CE-9781611972283

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Published by
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ISBN 10: 1611972280
ISBN 13: 9781611972283

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**Book Description **Society for Industrial Applied Mathematics,U.S., United States, 2013. Paperback. Book Condition: New. Language: English . Brand New Book. This book provides a self-contained, accessible introduction to the mathematical advances and challenges resulting from the use of semidefinite programming in polynomial optimization. This important and highly applicable research area, with contributions from convex geometry, algebraic geometry and optimization, is known as convex algebraic geometry. Each chapter addresses a fundamental aspect of the topic, beginning with an introduction to nonnegative polynomials and sums of squares, and their connections to semidefinite programming. The material quickly advances to areas at the forefront of current research, including semidefinite representability of convex sets, duality theory in algebraic geometry, and nontraditional topics such as sums of squares of complex forms. The book is a suitable entry point to the subject for readers at the graduate level or above in mathematics, engineering or computer science. Instructors will find the book appropriate for a class or seminar, and researchers will encounter open problems and new research directions. Bookseller Inventory # AAN9781611972283

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**Book Description **SIAM-Society for Industrial and Applied Mathematics, 2013. Paperback. Book Condition: Brand New. 496 pages. 9.90x1.00x6.90 inches. In Stock. Bookseller Inventory # __1611972280

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