Geometry of Linear Matrix Inequalities: A Course in Convexity and Real Algebraic Geometry with a View Towards Optimization

by Tim Netzer, Daniel Plaumann

Overview

This textbook provides a thorough introduction to spectrahedra, which are the solution sets to linear matrix inequalities, emerging in convex and polynomial optimization, analysis, combinatorics, and algebraic geometry. Including a wealth of examples and exercises, this textbook guides the reader in helping to determine the convex sets that can be represented and approximated as spectrahedra and their shadows (projections). Several general results obtained in the last 15 years by a variety of different methods are presented in the book, along with the necessary background from algebra and geometry.

Product Details

ISBN-13:	9783031264559
Publisher:	Birkh�user
Publication date:	06/07/2023
Series:	Compact Textbooks in Mathematics
Sold by:	Barnes & Noble
Format:	eBook
File size:	16 MB
Note:	This product may take a few minutes to download.

About the Author

Tim Netzer is a professor of applied algebra at the University of Innsbruck. He received his PhD in 2008 from the University of Konstanz. His research is in real algebra and geometry, with connections to optimization, functional analysis, and quantum information theory. He has worked at the Universities of Saskatchewan, Leipzig, and Dresden.
Daniel Plaumann is a professor of algebra and its applications at Dortmund University. He received his PhD in 2008 from the University of Konstanz. His research is in real and classical algebraic geometry. He has been a visiting scholar at the University of California, Berkeley, and at Nanyang Technological University, Singapore.

Table of Contents

- 1. Introduction and Preliminaries. - 2. Linear Matrix Inequalities and Spectrahedra. - 3. Spectrahedral Shadows.

Editorial Reviews

"This book is part of Birkhäuser 'Compact Textbooks in Mathematics' series, which aims for concise books that are tailored in size and scope to a single semester course at a late undergraduate or early graduate student level. This book fits that bill precisely. ... There are two appendices, one on real algebraic geometry and one on convexity, which provide background. With these, the book is in principle self-contained … ." (Tamon Stephen, Mathematical Reviews, March, 2025)

From the Publisher