ИСТИНА

We consider a reformulation of mathematical programs with complementarity constraints, where by introducing an artificial variable the constraints are converted into equalities which are once but not twice differentiable. This approach can be regarded as a development of the lifted reformulation of complementarity constraints proposed earlier by O.Stein. We show that the Lagrange optimality system of such a reformulation is semismooth and BD-regular at the solution under reasonable assumptions. Thus, fast local convergence can be obtained by applying the semismooth Newton method. Moreover, it turns out that the squared residual of the Lagrange system is continuously differentiable (even though the system itself is not), which opens the way for a natural globalization of the local algorithm. However, from the practical viewpoint, it seems more promising to use a non-smooth exact penalty function instead of the squared residual of the Lagrange system which leads to the semismooth sequential quadratic programming method. Preliminary numerical results for problems from MacMPEC test collection demonstrate that the approach is very promising.