Overview

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.

Full Product Details

Author:   Grigoriy Blekherman (Georgia Institute of Technology) ,  Pablo A. Parrilo (Massachusetts Institute of Technology) ,  Rekha Thomas (University of Washington)
Publisher:   Society for Industrial & Applied Mathematics,U.S.
Imprint:   Society for Industrial & Applied Mathematics,U.S.
Volume:   13
Dimensions:   Width: 17.70cm , Height: 2.40cm , Length: 25.40cm
Weight:   0.890kg
ISBN:  

9781611972283

ISBN 10:   1611972280
Pages:   495
Publication Date:   21 March 2013
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In stock  
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Author Information

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.

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