Strong Semismoothness of the Fischer-Burmeister SDC and SOC Complementarity Functions

Authors:
Defeng Sun;Jie Sun
Affiliations:
Department of Mathematics, National University of Singapore, Republic of Singapore;School of Business and Singapore-MIT Alliance, National University of Singapore, Republic of Singapore
Venue:
Mathematical Programming: Series A and B
Year:
2005

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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.