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

Abstract

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 l 2-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.