A globally and superlinearly convergent smoothing Broyden-like method for solving nonlinear complementarity problem

The nonlinear complementarity problem (denoted by NCP(F)) has attracted much attention due to its various applications in economics, engineering and management science. In this paper, we propose a smoothing Broyden-like method for solving nonlinear complementarity problem. The algorithm considered here is based on the smooth approximation Fischer–Burmeister function and makes use of the derivative-free line search rule of Li in [D.H. Li, M. Fukushima, A derivative-free line search and global convergence of Broyden-like method for nonlinear equations, Optim. Meth. Software 13(3) (2000) 181–201]. We show that, under suitable conditions, the iterates generated by the proposed method converge to a solution of the nonlinear complementarity problem globally and superlinearly.