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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.## About book:

## About file:

Security code:

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

- Series:
**MPS-SIAM Series on Optimization** - Author:
**Grigoriy Blekherman, Pablo A. Parrilo, Rekha Thomas (ed.)** - Year:
**2013** - Publisher:
**SIAM** - Language:
**English** - ISBN:
**1611972280,978-1-611972-28-3,341-349-366-3,447-450-453-4**

- File size:
**7 945 661** - Format:
**pdf**

Security code:

Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise pol...

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This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. ...

This volume of the Encyclopaedia contains two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory. The first part is written by T.A. Springer, a well-known expert in the first mentioned field. He presents ...

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