胡雅伶¹, 彭拯^2,1, 章旭³, 曾玉华⁴

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.

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

Hu Yaling¹, Peng Zheng^2,1, Zhang Xu³, Zeng Yuhua⁴

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:2019-08-14Online:2021-08-15Published:2021-08-20







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本文采用Modulus-based变换将非线性互补问题转化为非光滑方程组，并将一种多步自适应Levenberg-Marquardt方法推广应用于求解所得的非光滑方程组，从而得到原问题的解.在适当条件下，本文证明了算法的全局收敛性.与一种已有的参数自适应Levenberg-Marquardt方法（PSA-LMM）相比较，数值实验结果表明了本文所提出的算法具有更好的效率.
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