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

作　　者：贺晓瑞 汤京永 HE Xiao-rui;TANG Jing-yong(College of Mathematics and Statistics,Xinyang Normal University,Henan 464000,China)

机构地区：[1]信阳师范学院数学与统计学院,河南信阳464000

出　　处：《数学杂志》2023年第3期253-266,共14页Journal of Mathematics

基　　金：河南省自然科学基金项目(222300420520);河南省高等学校重点科研项目(22A110020)。

摘　　要：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.

关 键 词：加权线性互补问题 光滑牛顿法 全局收敛 二次收敛 

分 类 号：O221.1[理学—运筹学与控制论]