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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2017, Vol. 34 ›› Issue (3): 297-306.doi: 10.3969/j.issn.1005-3085.2017.03.006

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求解垂直互补问题的一种修正非光滑Levenberg-Marquardt算法（英）

宋林森1,2,   高  岩1   

  1. 1- 上海理工大学管理学院，上海  200093
    2- 河南科技学院数学科学学院，新乡  453003
  • 收稿日期:2016-05-12 接受日期:2017-01-13 出版日期:2017-06-15 发布日期:2017-08-15
  • 基金资助:
    国家自然科学基金(11171221)；高等教育博士点研究基金(20123120110004)；上海市自然科学基金(14ZR1429200)；上海市教委创新项目(15ZZ073)．

A Modified Nonsmooth Levenberg-Marquardt Method for Vertical Complementarity Problem

SONG Lin-sen1,2,   GAO Yan1   

  1. 1- School of Management, University of Shanghai for Science and Technology, Shanghai 200093
    2- School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003
  • Received:2016-05-12 Accepted:2017-01-13 Online:2017-06-15 Published:2017-08-15
  • Supported by:
    The National Natural Science Foundation of China (11171221); the Research Fund for the Doctoral Program of Higher Education of China (20123120110004); the Natural Science Foundation of Shanghai (14ZR1429200); the Innovation Program of Shanghai Municipal Education Commission (15ZZ073).

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摘要： 本文提出了一种求解垂直互补问题的修正非光滑Levenberg-Marquardt算法．与以往算法相比，该算法不但采用了新的微分形式取代了B-微分，还运用了一种LM参数的自适应调整策略以确保每次迭代时LM步不至于过小，从而保证了算法的快速收敛．最后，数值实验表明了算法的有效性．

关键词: 非线性互补问题, 非光滑方程组, 非光滑分析

Abstract: A modified nonsmooth Levenberg-Marquardt (LM) method is presented for vertical complementarity problem (VCP) in this paper. Compared with the existing ones, the method employs not only a new subdifferential, which is easier to obtain than B-differential, but also an adjusting strategy for the LM parameter to ensure that the LM step is not too small, so that the iterations move fast to the solution set. Moreover, the global convergence of the algorithm is obtained under some mild conditions and two numerical examples are given to illustrate its feasibility.

Key words: nonlinear complementarity problem, nonsmooth equations, nonsmooth analysis

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