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Birkhäuser

Geometry of Linear Matrix Inequalities

A Course in Convexity and Real Algebraic Geometry with a View Towards Optimization

  • Textbook
  • © 2023

Overview

Authors:
  1. Tim Netzer

    1. Institut für Mathematik, Universität Innsbruck, Innsbruck, Austria

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    You can also search for this author in PubMed   Google Scholar

  2. Daniel Plaumann

    1. Fakultät für Mathematik, Technische Universität Dortmund, Dortmund, Germany

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    You can also search for this author in PubMed   Google Scholar

  • Unifies recent key results, along with elementary proofs
  • Includes many exercises for active learning
  • Appeals to mathematical researchers across diverse fields

Part of the book series: Compact Textbooks in Mathematics (CTM)

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction and Preliminaries

    • Tim Netzer, Daniel Plaumann
    Pages 1-7

  3. Linear Matrix Inequalities and Spectrahedra

    • Tim Netzer, Daniel Plaumann
    Pages 9-64

  4. Spectrahedral Shadows

    • Tim Netzer, Daniel Plaumann
    Pages 65-116

  5. Back Matter

    Pages 117-161
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Keywords

About this book

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.

Authors and Affiliations

  • Institut für Mathematik, Universität Innsbruck, Innsbruck, Austria

    Tim Netzer

  • Fakultät für Mathematik, Technische Universität Dortmund, Dortmund, Germany

    Daniel Plaumann

About the authors

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.


Bibliographic Information

  • Book Title: Geometry of Linear Matrix Inequalities

  • Book Subtitle: A Course in Convexity and Real Algebraic Geometry with a View Towards Optimization

  • Authors: Tim Netzer, Daniel Plaumann

  • Series Title: Compact Textbooks in Mathematics

  • DOI: https://doi.org/10.1007/978-3-031-26455-9

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Softcover ISBN: 978-3-031-26454-2Published: 08 June 2023

  • eBook ISBN: 978-3-031-26455-9Published: 07 June 2023

  • Series ISSN: 2296-4568

  • Series E-ISSN: 2296-455X

  • Edition Number: 1

  • Number of Pages: VIII, 161

  • Number of Illustrations: 5 b/w illustrations, 29 illustrations in colour

  • Topics: Algebraic Geometry, Convex and Discrete Geometry, Optimization

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