Preprint A637/2009
Semismooth Newton method for the lifted reformulation of mathematical programs with complementarity constraints

M.V. Solodov | Izmailov, A.F. | Pogosyan, A.L.

**Keywords: **

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.
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.
Preliminary numerical results are also reported.