# A two-sided relaxation scheme for mathematical programs with equilibrium constraints

V. Demiguel, M. P. Friedlander, F. J. Nogales, S. Scholtes
SIAM Journal on Optimization, 16(1):587–609, 2005

## Abstract

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-point method to achieve superlinear convergence. Numerical results on the MacMPEC test problem set demonstrate the fast local convergence properties of the approach.

## BiBTeX

@article{DeMiFrieNogaScho:2005,
Author = {A.-V. DeMiguel and M. P. Friedlander and
F. J. Nogales and S. Scholtes},
Journal = {SIAM J. on Optimization},
Number = 1,
Pages = {587-609},
Title = {A two-sided relaxation scheme for mathematical
programs with equilibrium constraints},
Volume = 16,
Year = 2005,
doi = {10.1109/TIT.2005.860448}
}