非线性互补问题的光滑牛顿算法

A smoothing Newton method for nonlinear complementarity problem

在将非线性互补问题转化为求解非光滑方程组的基础上,为将非线性互补问题转化为求解光滑方程组,通过构造一个新的光滑非线性互补函数,给出求解NCP问题的光滑牛顿算法。此算法具有良好的适定性,在适当条件下,局部收敛性和全局收敛性也得到了证明。

The nonlinear complementarity problem（denoted by NCP） can be reformulated as the solution of a nonsmooth system of equations.By introducing a new smoothing NCP function,the problem is approximated by a family of paramenterized smooth equations.A smoothing Newton method is proposed for solving the nonlinear complementarity problem.The proposed algorithm has been proved to be well-defined.The rate of convergence and the gobal convergence of the proposed algorithm is verified under mild conditions.