中文摘要：

在利用Fischer—Burmeister函数将非线性互补问题转化为非线性方程组的基础上，本文通过将信赖域方法与线性搜索方法结合起来，提出了求解一般非线性互补问题的光滑化方法．算法中我们给出了一个特定条件，条件满足时，采用信赖步，条件不满足时，采用梯度步．我们证明了算法具有全局收敛性。在解是R-正则的条件下，收敛速度是Q-超线性／Q-二阶收敛的．

英文摘要：

Based on reformulating the nonlinear complementarity problem as a system of nonsmooth equations by using Fisher-Burmeister function, in this paper, by combining trust region and line search techniques, we present a smoothing method for solving general nonlinear complementarity problems. In the algorithm we give a special condition, when this condition is satisfied, the trust region method is used; otherwise, the gradient is used. We proved that our algorithm possesses global convergence property, and under the condition that the solution is R-regular, the local convergence rate is proved to be Q-superlinear/Q-quadratic.