Geometry of Linear Matrix Inequalities

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

Tim Netzer, Daniel Plaumann (Autoren)

Buch | Softcover

VIII, 161 Seiten

2023 | 2023
Springer International Publishing (Verlag)
978-3-031-26454-2 (ISBN)

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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.

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.

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

Erscheinungsdatum	09.06.2023
Reihe/Serie	Compact Textbooks in Mathematics
Zusatzinfo	VIII, 161 p. 34 illus., 29 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	272 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	convex geometry • Convex Optimization • eigenvalues • Extended Formulations • Hyperbolic Polynomials • matrices • Non-Commutative Geometry • polynomial optimization • Real Algebraic Curves • real algebraic geometry • Semidefinitie Programming • Sums of squares
ISBN-10	3-031-26454-1 / 3031264541
ISBN-13	978-3-031-26454-2 / 9783031264542
Zustand	Neuware