Geodesic
Every convex free basic semi-algebraic set has an LMI representation
J. William Helton1 ; Scott McCullough2
1 Department of Mathematics, University of California San Diego, 9500 Gilman Drive #0112, La Jolla, CA 92093-0112
2 Department of Mathematics, University of Florida, 490 Little Hall, Gainesville, FL 32611-8105
Annals of mathematics, Tome 176 (2012) no. 2, pp. 979-1013.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2012.176.2.6

J. William Helton 1 ; Scott McCullough 2

1 Department of Mathematics, University of California San Diego, 9500 Gilman Drive #0112, La Jolla, CA 92093-0112
2 Department of Mathematics, University of Florida, 490 Little Hall, Gainesville, FL 32611-8105 
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J. William Helton; Scott McCullough. Every convex free basic semi-algebraic set has an LMI representation. Annals of mathematics, Tome 176 (2012) no. 2, pp. 979-1013. doi : 10.4007/annals.2012.176.2.6. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.2.6/

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