The quadratic convergence of a smoothing Levenberg-Marquardt method for nonlinear complementarity problem

The nonlinear complementarity problem (denoted by NCP(F)) can be reformulated as the solution of a possibly inconsistent nonsmooth system of equations. Based on the ideas developed in smoothing Newton methods, we approximated the problem of the least l2-norm solution of the equivalent nonsmooth equations of NCP(F) with a family of parameterized optimization problem with twice continuously differentiable objective functions by making use of a new smoothing function. Then we presented a smoothing Levenberg-Marquardt method to solve the parameterized smooth optimization problem. By using the smooth and semismooth technique, the local quadratic convergence of the proposed method is proved under some suitable assumptions.