Semidefinite Optimization and Convex Algebraic Geometry (MPS-SIAM Series on Optimization, Series Number 13) - Softcover

Softcover

ISBN 10: 1611972280 ISBN 13: 9781611972283

Publisher: Society for Industrial and Applied Mathematics, 2013

Synopsis

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.

About this title

Book Description

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 Author

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.

Edition details

• Publisher: Society for Industrial and Applied Mathematics
• Publication date: 2013
• ISBN 10: 1611972280
• ISBN 13: 9781611972283
• Binding: Paperback
• Language: English
• Number of pages: 495
• Editor: Blekherman Grigoriy, Parrilo Pablo A., Thomas Rekha