Strong Semismoothness of the Fischer-Burmeister SDC and SOC Complementarity Functions
Strong Semismoothness of the Fischer-Burmeister SDC and SOC Complementarity Functions
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DOI：
10.1007/s10107-005-0577-4
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发表时间：
2005-07
影响因子：
2.7
通讯作者：
Defeng Sun;Jie Sun
中科院分区：
文献类型：
--
作者：
Defeng Sun;Jie Sun
证明了分别与半定锥(SDC)和二阶锥(SOC)相关的Fischer-Burmeister互补函数处处强半光滑。有趣的是，证明依赖于非对称矩阵的奇异值分解和对称矩阵的谱分解之间的关系。
We show that the Fischer-Burmeister complementarity functions, associated to the semidefinite cone (SDC) and the second order cone (SOC), respectively, are strongly semismooth everywhere. Interestingly enough, the proof relys on a relationship between the singular value decomposition of a nonsymmetric matrix and the spectral decomposition of a symmetric matrix.