TY - BOOK ID - 119294712 TI - Geometry of Linear Matrix Inequalities : A Course in Convexity and Real Algebraic Geometry with a View Towards Optimization AU - Netzer, Tim AU - Plaumann, Daniel PY - 2023 SN - 303126455X 3031264541 PB - Cham : Springer International Publishing : Imprint: Birkhäuser, DB - UniCat KW - Convex domains. KW - Matrix inequalities. KW - Inequalities (Mathematics) KW - Matrices KW - Convex regions KW - Convexity KW - Calculus of variations KW - Convex geometry KW - Point set theory KW - Algebraic geometry. KW - Convex geometry. KW - Discrete geometry. KW - Mathematical optimization. KW - Algebraic Geometry. KW - Convex and Discrete Geometry. KW - Optimization. KW - Optimization (Mathematics) KW - Optimization techniques KW - Optimization theory KW - Systems optimization KW - Mathematical analysis KW - Maxima and minima KW - Operations research KW - Simulation methods KW - System analysis KW - Discrete mathematics KW - Geometry KW - Combinatorial geometry KW - Algebraic geometry KW - Desigualtats matricials KW - Dominis convexos UR - https://www.unicat.be/uniCat?func=search&query=sysid:119294712 AB - 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. ER -