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

A family of Least-Change Secant-Update methods for solving nonlinear comple mentarity problems based on nonsmooth systems of equations is introduced. L ocal and superlinear convergence results for the algorithms are proved. Two different reformulations of the nonlinear complementarity problem as a non smooth system are compared, both from the theoretical and the practical poi nt of view. A global algorithm for solving the nonlinear complementarity pr oblem which uses the algorithms introduced here is also presented. Some num erical experiments show a good performance of this algorithm. (C) 1999 Else vier Science B.V. and IMACS. All rights reserved.