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Strong semismoothness of the Fischer-Burmeister SDC and SOC complementarity functions. (English) Zbl 1099.90062
Summary: 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.

MSC:
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C22 Semidefinite programming
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F18 Numerical solutions to inverse eigenvalue problems
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