A new smoothing Broyden‐like method for solving nonlinear complementarity problem with a P 0‐function

In this paper, we propose a new smoothing Broyden‐like method for solving nonlinear complementarity problem with P 0 function. The presented algorithm is based on the smoothing symmetrically perturbed minimum function φ(a, b) = min{a, b} and makes use of the derivative‐free line search rule of Li et al. (J Optim Theory Appl 109(1):123–167, 2001). Without requiring any strict complementarity assumption at the P 0‐NCP solution, we show that the iteration sequence generated by the suggested algorithm converges globally and superlinearly under suitable conditions. Furthermore, the algorithm has local quadratic convergence under mild assumptions. Some numerical results are also reported in this paper.