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# π Semidefinite optimization and convex algebraic geometry by Grigoriy Blekherman, Pablo A. Parrilo, Rekha Thomas (ed.) β free epub

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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:

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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:

Focuses on the interaction between algebra and algebraic geometry, including high-level research papers and surveys contributed by over 40 top specialists representing more than 15 countries worldwide. Describes abelian groups and lattices, algebras and...

This volume contains the proceedings of the NSF-CBMS Regional Conference on Algebraic Geometry, held in Sundance, Utah, in July 1988. The conference focused on algebraic curves and related varieties. Some of the papers collected here represent lecture...

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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...

Convex Optimization & Euclidean Distance Geometry I thought I'd use this book as a reference since the unusually large Index is a good place to locate the definitions. Dattorro starts from the basic premises and works through the algebra with many examp...

The book is an introduction to the theory of convex polytopes and polyhedral sets, to algebraic geometry, and to the connections between these fields, known as the theory of toric varieties. The first part of the book covers the theory of polytopes and pr...

The book is an introduction to the theory of convex polytopes and polyhedral sets, to algebraic geometry, and to the connections between these fields, known as the theory of toric varieties. The first part of the book covers the theory of polytopes and pr...

The aim of this book is to provide an introduction for students and nonspecialists to a fascinating relation between combinatorial geometry and algebraic geometry, as it has developed during the last two decades. This relation is known as the theory of to...

The theory of toric varieties (also called torus embeddings) describes a fascinating interplay between algebraic geometry and the geometry of convex figures in real affine spaces. This book is a unified up-to-date survey of the various results and interes...