A Mixed Algorithm for Nonlinear Complementarity Problems

Combining nonmonotone trust region algorithms and PSO methods, we propose a mixed method for nonlinear complementarity problems. The iterative formula of μ k is very simple. When the determinant of  B k +λ k I is very large or small, the PSO method will obtain a new point which gets us better astringency. Numerical test results show the effectiveness of this algorithm.