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

胡雅伶1, 彭拯2,1, 章旭3, 曾玉华4   

  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.

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.

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
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.
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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