On the local convergence of quasi-Newton methods for nonlinear complementarity problems Original Research Article

A family of Least-Change Secant-Update methods for solving nonlinear complementarity problems based on nonsmooth systems of equations is introduced. Local and superlinear convergence results for the algorithms are proved. Two different reformulations of the nonlinear complementarity problem as a nonsmooth system are compared, both from the theoretical and the practical point of view. A global algorithm for solving the nonlinear complementarity problem which uses the algorithms introduced here is also presented. Some numerical experiments show a good performance of this algorithm.