Complementarity and nondegeneracy in semidefinite programming

@article{Alizadeh1997ComplementarityAN,
  title={Complementarity and nondegeneracy in semidefinite programming},
  author={Farid Alizadeh and Jean Pierre Haeberly and Michael L. Overton},
  journal={Mathematical Programming},
  year={1997},
  volume={77},
  pages={111-128}
}
Primal and dual nondegeneracy conditions are defined for semidefinite programming. Given the existence of primal and dual solutions, it is shown that primal nondegeneracy implies a unique dual solution and that dual nondegeneracy implies a unique primal solution. The converses hold if strict complementarity is assumed. Primal and dual nondegeneracy assumptions do not imply strict complementarity, as they do in LP. The primal and dual nondegeneracy assumptions imply a range of possible ranks for… 
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