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

被引：62
作者：
Helton, J. William [1 ]
McCullough, Scott [2 ]
机构：
[1] Univ Calif San Diego, San Diego, CA 92103 USA
[2] Univ Florida, Gainesville, FL USA
来源：
ANNALS OF MATHEMATICS | 2012年 / 176卷 / 02期
基金：
美国国家科学基金会;
关键词：
C>-ALGEBRAS; SUBALGEBRAS;
D O I：
10.4007/annals.2012.176.2.6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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收藏
页码：979 / 1013
页数：35
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