On cone-invariant linear matrix inequalities

Parrilo P.A.; Khatri S.

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On cone-invariant linear matrix inequalities

机译：锥不变线性矩阵不等式

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An exact solution for a special class of cone-preserving linear matrix inequalities (LMIs) is developed. By using a generalized version of the classical Perron-Frobenius theorem, the optimal value is shown to be equal to the spectral radius of an associated linear operator. This allows for a much more efficient computation of the optimal solution using, for instance, power iteration-type algorithms. This particular LMI class appears in the computation of upper bounds for some generalizations of the structured singular value μ (spherical μ) and in a class of rank minimization problems previously studied. Examples and comparisons with existing techniques are provided

机译：针对一类特殊的锥保持线性矩阵不等式（LMI），提出了一种精确的解决方案。通过使用经典Perron-Frobenius定理的广义形式，最优值显示为等于关联的线性算子的谱半径。这允许使用例如幂迭代型算法对最佳解决方案进行更有效的计算。这种特殊的LMI类出现在结构化奇异值μ（球面μ）的某些泛化的上限计算中，并且出现在先前研究的秩最小化问题中。提供示例和与现有技术的比较

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《IEEE Transactions on Automatic Control》 |2000年第8期|p.1558-1563|共6页
作者
Parrilo P.A.; Khatri S.;
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正文语种 eng
中图分类自动化系统;
关键词
iterative methods; matrix algebra; minimisation; classical Perron-Frobenius theorem; cone-invariant linear matrix inequalities; linear operator; optimal solution; optimal value; power iteration-type algorithms; rank minimization problems; spectral radius; structure;

机译：迭代方法;矩阵代数;最小化;经典Perron-Frobenius定理;锥不变线性矩阵不等式;线性算子;最优解;最优值;幂次迭代型算法;秩最小化问题;谱半径;结构;

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1. On cone-invariant linear matrix inequalities [J] . Parrilo P.A., Khatri S. IEEE Transactions on Automatic Control . 2000,第8期

机译：锥不变线性矩阵不等式
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On cone-invariant linear matrix inequalities

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