A nonmonotone damped Gauss-Newton method for nonlinear complementarity problems

The damped Gauss-Newton methods have been successfully applied to solve the nonlinear complementarity problem (NCP). This class of methods is usually designed based on a monotone Armijo line search. In this paper, we propose a damped Gauss-Newton method with a nonmonotone line search to solve the NCP. Without requiring any problem assumptions, we prove that the proposed method is well defined and it is globally convergent. Moreover, under the nonsingularity assumption, we show that the proposed method is locally sup erlinearly/quadratically convergent. Some numerical results are reported.