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

• 成果类型: Article
• 署名作者: Helton, J. William; McCullough, Scott
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.176.2.6
• 发表日期: 2012
• 页码: 979-1013
• 关键词: c>-algebras; SUBALGEBRAS

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.