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.
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.
出处
《工程数学学报》
CSCD
北大核心
2017年第3期297-306,共10页
Chinese Journal of Engineering Mathematics
基金
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)
关键词
非线性互补问题
非光滑方程组
非光滑分析
nonlinear complementarity problem
nonsmooth equations
nonsmooth analysis