求解广义互补问题的 Levenberg-Marquardt 算法

数学物理学报 ›› 2025, Vol. 45 ›› Issue (4): 1311-1326.

求解广义互补问题的 Levenberg-Marquardt 算法

于冬梅^*(),刘大熠

辽宁工程技术大学理学院辽宁阜新 123000

收稿日期:2024-09-05 修回日期:2025-04-13 出版日期:2025-08-26 发布日期:2025-08-01
通讯作者: *E-mail: yudongmei1113@163.com
基金资助:
辽宁省自然科学基金(2024-MS-206);辽宁省教育厅基金(JYTZD2023072);辽宁省教育厅基金(LJ112410147046);辽宁省教育厅基金(LJ242410147027)

The Levenberg-Marquardt Algorithm for Solving the Generalized Complementarity Problems

Yu Dongmei^*(),Liu Dayi

College of Science, Liaoning Technical University, Liaoning Fuxin 123000

Received:2024-09-05 Revised:2025-04-13 Online:2025-08-26 Published:2025-08-01
Supported by:
Supported by the Natural Science Foundation of Liaoning Province(2024-MS-206);Liaoning Provincial Department of Education(JYTZD2023072);Liaoning Provincial Department of Education(LJ112410147046);Liaoning Provincial Department of Education(LJ242410147027)

摘要/Abstract

摘要：

该文提出求解广义互补问题的 Levenberg-Marquardt 型方法. 首先, 结合一类互补函数, 将广义互补问题等价重构为非线性方程组, 进而提出一类带有线搜索的自适应修正 Levenberg-Marquardt 算法对其进行求解. 其次, 在适当的条件下分析了算法的收敛性. 最后, 通过数值实验验证了所提出算法的可行性和有效性.

关键词: 广义互补问题, Levenberg-Marquardt 算法, 线搜索, 收敛性分析

Abstract:

In this paper, the Levenberg-Marquardt type method is proposed for solving the generalized complementarity problems. Firstly, by integrating a class of complementary functions, the generalized complementarity problem is equivalently reformulated as a system of nonlinear equations. An adaptive modified Levenberg-Marquardt algorithm with line search is then introduced to address this reformulated problem. Furthermore, the convergence of the proposed algorithm is analyzed under appropriate conditions. Finally, numerical experiments are conducted to verify the feasibility and effectiveness of the proposed algorithm.

Key words: generalized complementarity problem, Levenberg-Marquardt algorithm, line search, convergence analysis

中图分类号:

O224

于冬梅, 刘大熠. 求解广义互补问题的 Levenberg-Marquardt 算法[J]. 数学物理学报, 2025, 45(4): 1311-1326.

Yu Dongmei, Liu Dayi. The Levenberg-Marquardt Algorithm for Solving the Generalized Complementarity Problems[J]. Acta mathematica scientia,Series A, 2025, 45(4): 1311-1326.

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