A new regularization method for mathematical programs with complementarity constraints with strong convergence properties.

*(English)*Zbl 1282.65069Optimization problems in many areas can be formulated as mathematical programs with equilibrium constraints (MPECs). In this paper, the authors present a new regularization scheme for the solution of MPECs. The limit points of the proposed method are at least M-stationary points, which is a much stronger property than the majority of other existing regularization methods. They also show that the feasible set of the proposed regularized problem has a favourable geometric shape. Some preliminary numerical results are included to demonstrate the performance of the proposed regularization method.

Reviewer: Guoqiang Wang (Shanghai)

##### MSC:

65K05 | Numerical mathematical programming methods |

90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |