On the asymmetric eigenvalue complementarity problem
Optimization Methods & Software - GLOBAL OPTIMIZATION
A New Relaxation Scheme for Mathematical Programs with Equilibrium Constraints
SIAM Journal on Optimization
An $\ell_1$ Elastic Interior-Point Method for Mathematical Programs with Complementarity Constraints
SIAM Journal on Optimization
A smoothing-regularization approach to mathematical programs with vanishing constraints
Computational Optimization and Applications
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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.