The convergence of a smoothing damped Gauss–Newton method for nonlinear complementarity problem

The nonlinear complementarity problem (denoted by NCP(FF)) can be reformulated as the least l2l2-norm solution of a possibly inconsistent nonsmooth system of equations. In this paper, by introducing a novel smoothing function, the least square problem is approximated by a sequence of parameterized optimization problems which are of twice continuously differentiable objective functions. A smoothing damped Gauss–Newton method is utilized to solve the parameterized optimization problems. The global convergence of the proposed algorithm is proved under mild conditions, and local quadratic convergence of the method is obtained with suitable assumptions.