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

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

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...

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Hauptverfasser: Netzer, Tim, Plaumann, Daniel
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Sprache:eng
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Algebraic Geometry
Convex and Discrete Geometry
Convex domains
Mathematics
Mathematics and Statistics
Matrix inequalities
Optimization
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description 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.
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subjects Algebraic Geometry
Convex and Discrete Geometry
Convex domains
Mathematics
Mathematics and Statistics
Matrix inequalities
Optimization
title Geometry of Linear Matrix Inequalities: A Course in Convexity and Real Algebraic Geometry with a View Towards Optimization
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