Abstract: 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.

Key words: complementarity problems, non-Lipschtizian continuous, smoothing function, non-monotone line search

摘要： 考虑一类含非Lipschtizian连续函数的非线性互补问题。引入plus函数的一类广义光滑函数，讨论其性质。应用所引入函数将互补问题重构为一系列光滑方程组，提出一个具有非单调线搜索的Newton算法求解重构的方程组以得到原问题的解。在很弱的条件下，该算法具有全局收敛性和局部二次收敛性。利用该算法求解一自由边界问题，其数值结果显示该算法是有效的。

关键词: 互补问题, 非Lipschtizian连续, 光滑函数, 非单调线搜索