基于新光滑函数的P_(0)映射非线性互补问题的光滑牛顿法

The Smoothing Newton Method for NCP with P_0-Mapping Based on a New Smoothing Function

非线性互补问题(NCP)可以重新表述为一个非光滑方程组的解.通过引入一个新的光滑函数,将问题近似为参数化光滑方程组.基于这个光滑函数,我们提出了一个求解P_(0)映射和R_(0)映射非线性互补问题的光滑牛顿法.该算法每次迭代只求解一个线性方程和一次线搜索.在适当的条件下,证明了该方法是全局和局部二次收敛的.数值结果表明,该算法是有效的.

The nonlinear complementarity problem(NCP) can be reformulated as the solution of a nonsmooth system of equations.By introducing a new smoothing function,the problem is approximated by a family of parameterized smooth equations.Based on this smoothing function,we propose a smoothing Newton method for NCP with P_0-mapping and R_0-mapping.The proposed algorithm solves only one linear equations and performs only one line search per iteration.Under suitable conditions,the method is proved to be globally and local quadratically convergent.Numerical results show that the proposed algorithm is effective.