Positive Polynomials and Projections of Spectrahedra
Positive Polynomials and Projections of Spectrahedra
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DOI：
10.1137/100801913
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发表时间：
2009-11
期刊：
影响因子：
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通讯作者：
J. Gouveia;Tim Netzer
中科院分区：
文献类型：
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作者：
J. Gouveia;Tim Netzer
这篇文章关注的是不同方面的谱面体和他们的投影，集是重要的半定优化。我们证明结果的限制，所谓的拉瑟尔和θ体松弛方法的半代数集和品种。作为一种特殊情况，我们得到了Netzer，Plaumann和Schweighthorn [SIAM J. Optim.，20（2010），pp. 1944年-1955年，在未曝光的脸上。我们还解决了这项工作中的开放问题。进一步统一了曲线凸包和多项式映射象的几个结果。最后证明了谱面体投影的一个正性定理，它超过了只适用于基本闭半代数集的已知结果。
This article is concerned with different aspects of spectrahedra and their projections, sets that are important in semidefinite optimization. We prove results on the limitations of so-called Lasserre and theta body relaxation methods for semialgebraic sets and varieties. As a special case we obtain the main result of Netzer, Plaumann, and Schweighofer [SIAM J. Optim., 20 (2010), pp. 1944–1955] on nonexposed faces. We also solve the open problems from that work. We further give a unified account of several results on convex hulls of curves and images of polynomial maps. We finally prove a Positivstellensatz for projections of spectrahedra, which exceeds the known results that only work for basic closed semialgebraic sets.