| 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. |
| 关键词: 加权线性互补问题 光滑牛顿法 全局收敛 二次收敛 |
| DOI： |
| 分类号:O221.1 |
| 基金项目:河南省自然科学基金项目(222300420520)和河南省高等学校重点科研项目(22A110020). |
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| A NEW NON-MONOTONE SMOOTHING NEWTON METHOD FOR SOLVING WEIGHTED LINEAR COMPLEMENTARITY PROBLEMS |
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HE Xiao-rui, TANG Jing-yong
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College of Mathematics and Statistics, Xinyang Normal University, Henan 464000, China
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| Abstract: |
| 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. |
| Key words: weighted linear complementary problem smoothing newton method global convergence quadratic convergence |
