| 一种求解非线性互补问题的多步自适应Levenberg-Marquardt算法 |
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| 引用本文： | 胡雅伶,彭拯,章旭,曾玉华.一种求解非线性互补问题的多步自适应Levenberg-Marquardt算法[J].计算数学,2021,43(3):322-336. |
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| 作者姓名： | 胡雅伶 彭拯 章旭 曾玉华 |
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| 作者单位： | 福州大学数学与计算机科学学院,福州350108;湘潭大学数学与计算科学学院,湘潭411105;福州大学数学与计算机科学学院,福州350108;湘潭大学自动化与电子信息学院,湘潭411105;湖南第一师范学院数学与计算科学学院,长沙410205 |
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| 基金项目： | 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. |
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| 摘 要： | 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,...
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| 关 键 词： | 非线性互补问题 Modulus-based变量替换 Levenberg-Marquardt方法 |
| 收稿时间： | 2019-08-14 |
AN ADAPTIVE MULTI-STEP LEVENBERG-MARQUARDT METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEM |
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| 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. |
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| Authors: | Hu Yaling Peng Zheng Zhang Xu Zeng Yuhua |
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| Institution: | 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 |
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| Abstract: | 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. |
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| Keywords: | Nonlinear complementarity problem Modulus-based manipulation LevenbergMarquardt method |
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