Strong semismoothness of the fischer-burmeister SDC and SOC complementarity functions
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.
strong semismoothness sdc soc fischer-burmeister function svd