SIAM
Cambridge
Amazon
Full book PDF


About the book:
This book provides a selfcontained, 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.
