Geometry of Linear Matrix Inequalities

A Course in Convexity and Real Algebraic Geometry with a View Towards Optimization
2023
ISBN: 978-3-031-26454-2
Verlag: Springer International Publishing

Buch, Englisch, 161 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 303 g

Reihe: Compact Textbooks in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Plaumann, Daniel

Netzer, Tim

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung

Inhaltsverzeichnis

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

Über Autor(innen)

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.