Non-monotone line search to solve class of complementarity problem

A class of nonlinear complementarity problems with non-Lipschtizian continuous function are considered.A family of generalized smoothing functions are introduced,and their properties are discussed.The complementarity problem is reformulated as some smoothing equations with the smoothing functions,and a Newton algorithm involving non-monotone line search is proposed to solve the equations in order to obtain the solution of original problem.With great weak condition,this method is globally convergent and locally quadratically convergent.The method is used for solving some free boundary problem,and the numerical results show that the proposed method is promising.