Mathematical Programs with Semidefinite Cone Complementarity Constraints: Constraint Qualifications and Optimality Conditions

@article{Wu2014MathematicalPW,
  title={Mathematical Programs with Semidefinite Cone Complementarity Constraints: Constraint Qualifications and Optimality Conditions},
  author={Jia Wu and Liwei Zhang and Yi Zhang},
  journal={Set-Valued and Variational Analysis},
  year={2014},
  volume={22},
  pages={155-187}
}
The tangent cone of gph$N_{S^n_+}$ plays an important role in developing necessary conditions for mathematical programs with semidefinite cone complementarity constraints. We demonstrate an elegant formula for the tangent cone of gph$N_{S^n_+}$, based on which the Bouligand stationary point is characterized explicitly. The relationships among different stationary points under certain constraint qualifications are discussed. Then we propose a second order sufficient condition which can be… CONTINUE READING