Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1
Chinese Journal of Engineering Mathematics

Chinese Journal of Engineering Mathematics ›› 2017, Vol. 34 ›› Issue (3): 297-306.doi: 10.3969/j.issn.1005-3085.2017.03.006

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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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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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