Every convex free basic semi-algebraic set has an LMI representation

• Autores: J. William Helton, Scott McCullough
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 176, Nº 2, 2012, págs. 979-1013
• Idioma: inglés
• DOI: 10.4007/annals.2012.176.2.6
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• Resumen

  • The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex free basic open semi-algebraic set. The main theorem of this paper is a converse, each such set arises from some LMI. The result has implications for semi-definite programming and systems engineering as well as for free semi-algebraic geometry.