一个新的求解加权线性互补问题的非单调光滑牛顿法

A NEW NON-MONOTONE SMOOTHING NEWTON METHOD FOR SOLVING WEIGHTED LINEAR COMPLEMENTARITY PROBLEMS

本文研究了求解加权线性互补问题的光滑牛顿法.利用一类光滑函数将加权线性互补问题等价转化成一个光滑方程组,然后提出一个新的光滑牛顿法去求解它.在适当条件下,证明了算法具有全局和局部二次收敛性质.与现有的光滑牛顿法不同,我们的算法采用一个非单调无导数线搜索技术去产生步长,从而具有更好的收敛性质和实际计算效果.

In this paper,we investigate the smoothing Newton method for solving the weighted linear complementarity problem.By using a class of smoothing functions,we reformulate the weighted linear complementary problem as a system of smooth equations and then propose a new smoothing Newton method to solve it.Under suitable conditions,we prove that the algorithm has global and local quadratic convergence.Different from current smoothing Newton-type methods,our method uses a non-monotone derivative-free line search technique to generate the step size,which makes it have better convergence properties and practical calculation effects.