Abstract.
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.
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The author’s research was partially supported by Grant R146-000-035-101 of National University of Singapore.
The author’s research was partially supported by Grant R314-000-042/057-112 of National University of Singapore and a grant from the Singapore-MIT Alliance.
Mathematics Subject Classification (2000): 90C33, 90C22, 65F15, 65F18
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Sun, D., Sun, J. Strong Semismoothness of the Fischer-Burmeister SDC and SOC Complementarity Functions. Math. Program. 103, 575–581 (2005). https://doi.org/10.1007/s10107-005-0577-4
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DOI: https://doi.org/10.1007/s10107-005-0577-4