求解非线性互补问题的一个不动点迭代法_英文_.pdfVIP

17 2 () Vo.l 17 No. 2 2008 4 Journal of Yunnan Nationalities University(Natural Sciences Edition) pr. 2008 A Fixed Point IterativeM ethod for Solving the Nonlinear Complementarity Problem Tang Jia Ma Changfeng (Department of Computer Science andMathematics, Guilin University ofElectronicTechnology, Guilin 541004, China) Abstract: We establish the equivalence between the nonlinear complementarity problem w ith uniform P-func- tion and a class of nonsmooth equations. This equivalence is used to suggest a fixed point iterativemethod for so-l ving the nonlinear complementarity problem. W e also give a convergence analysis of the proposed m ethod under suitable conditions. nd som e num erical results are also reported in the paper. K ey words: nonlinear complementarity problem; nonsmooth equations; iterativemethod; convergence analysis 唐 嘉 马昌凤 ( , 541004) , . . . ;; ; = O22412 = = 1672) 8513( 2008) 02- 0103- 03 change of variable technique to prove the nonlinear 0 Introduction complementarity problem is equivalent to a system of [ 1, 2] The nonlinear complem entarity problem , de- nonsmooth equations. This alternate formulation isvery noted by NCP(F ), is to find a vectorx I Rn such that useful in developing some efficient and powerful nu- T mericalmethods for solving the nonlinear complemen- x E 0, y = F (x ) E 0, x y = 0. ( 1) where