• 论文 •

### 一种求解非线性互补问题的多步自适应Levenberg-Marquardt算法

1. 1. 福州大学数学与计算机科学学院, 福州 350108;
2. 湘潭大学数学与计算科学学院, 湘潭 411105;
3. 湘潭大学自动化与电子信息学院, 湘潭 411105;
4. 湖南第一师范学院数学与计算科学学院, 长沙 410205
• 收稿日期:2019-08-14 出版日期:2021-08-15 发布日期:2021-08-20
• 通讯作者: 彭拯,E-mail:pzheng@xtu.edu.cn.
• 基金资助:
国家自然科学基金面上项目（12071398），湖南省自然科学基金面上项目（2020JJ4567）和湖南省教育厅重点项目（20A097）资助.

Hu Yaling, Peng Zheng, Zhang Xu, Zeng Yuhua. AN ADAPTIVE MULTI-STEP LEVENBERG-MARQUARDT METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEM[J]. Mathematica Numerica Sinica, 2021, 43(3): 322-336.

### AN ADAPTIVE MULTI-STEP LEVENBERG-MARQUARDT METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEM

Hu Yaling1, Peng Zheng2,1, Zhang Xu3, Zeng Yuhua4

1. 1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China;
2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China;
3. School of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, China;
4. College of Mathematics and Computational Science, Hunan First Normal University, Changsha 410205, China
• Received:2019-08-14 Online:2021-08-15 Published:2021-08-20

A modulus-based manipulation is adopted to transform the nonlinear complementarity problem to a non-smooth system. Then, an adaptive multi-step Levenberg-Marquardt method is generalized to solve the resulting non-smooth system, then obtains a solution of the original problem. Under some suitable conditions, the global convergence of the proposed method is established. Some preliminary numerical experiments show that, compared to the PSA-LMM, the proposed method is more effective.

MR(2010)主题分类:

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