解P0非线性互补问题的非单调光滑牛顿法

摘要

基于CHKS光滑函数,将非线性互补问题转化为非线性光滑方程组,再构造光滑算子,将非线性光滑方程组转化为优化问题,且构造了一个新的牛顿算法,该算法引入了非单调线搜索,并在一定条件下证明了它的全局收敛性,及在非奇异条件而非严格互补条件条件下,证明了它的局部二次收敛性。最后给出数值实验结果。%Based on CHKS smoothing function, we reformulate nonlinear complementarity problem as a nonlinear nonsmooth system of equations. Then we reformulate the system of equations as a optimization problem by constructing a smooth operator. And we present a new smoothing Newton algorithm. which used the nonmonotone line search technique. The proposed algorithm is shown to globally convergent under suitable condition , and locally quadratically convergent without the strict complementarity assumption. At last the preliminary numerical results are reported.