Free semidefinite representation of matrix power functions

DOI10.1016/j.laa.2014.09.038zbMath1307.90130arXiv1305.4289OpenAlexW2029424027MaRDI QIDQ471947

J. William Helton, Jeremy S. Semko, Jia-Wang Nie

Publication date: 17 November 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.4289

zbMATH Keywords

linear matrix inequalitieslinear pencilepigraphmatrix convexityfree semidefinite representationhypographsemidefinite programing

Mathematics Subject Classification ID

Semidefinite programming (90C22) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07)

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Cites Work

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• Every convex free basic semi-algebraic set has an LMI representation
• First order conditions for semidefinite representations of convex sets defined by rational or singular polynomials
• Semidefinite representation of convex sets
• On semidefinite representations of non-closed sets
• Linear matrix inequality tests for frequency domain inequalities with affine multipliers
• Singularities of rational functions and minimal factorizations: the noncommutative and the commutative setting
• Convex sets with semidefinite representation
• Lectures on Modern Convex Optimization
• Polynomial Matrix Inequality and Semidefinite Representation
• Theta Bodies for Polynomial Ideals
• Extended H 2 and H norm characterizations and controller parametrizations for discrete-time systems
• Linear matrix inequality representation of sets
• Sufficient and Necessary Conditions for Semidefinite Representability of Convex Hulls and Sets
• Convexity in SemiAlgebraic Geometry and Polynomial Optimization
• Convex Noncommutative Polynomials Have Degree Two or Less