A filter method for solving nonlinear complementarity problems based on derivative-free line search

In this work, we first translate the nonlinear complementarity problem (denoted by NCP(F)) into Newton equation with disturbance. When Jacobian of the NCP function is not invertible, we use the Broyden-like formulae to update it. Taking advantage of the virtue of filter technique, we propose a filter method for the nonlinear complementarity problem with derivative-free line search. The proposed algorithm is proved to be globally convergent under mild assumptions. Furthermore, we get superlinear convergence of the method under the proper conditions.