A two-sided relaxation scheme for Mathematical Programs with Equilibrium Constraints

@article{DeMiguel2005ATR,
  title={A two-sided relaxation scheme for Mathematical Programs with Equilibrium Constraints},
  author={Victor DeMiguel and Michael P. Friedlander and Francisco J. Nogales and Stefan Scholtes},
  journal={SIAM J. Optim.},
  year={2005},
  volume={16},
  pages={587-609}
}
We propose a relaxation scheme for mathematical programs with equilibrium constraints (MPECs). In contrast to previous approaches, our relaxation is two-sided: both the complementarity and the nonnegativity constraints are relaxed. The proposed relaxation update rule guarantees (under certain conditions) that the sequence of relaxed subproblems will maintain a strictly feasible interior---even in the limit. We show how the relaxation scheme can be used in combination with a standard interior… 

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