求解P_0-函数非线性互补问题的参数微分法Parametric Differentiation Method for the P_0-function Nonlinear Complementarity Problems
林钊;马昌凤;
摘要(Abstract):
将P0-函数非线性互补问题(NCP(F))转化为求解一个等价的非线性方程组.由于转化后的非线性方程组相应的非线性映射一般是非光滑的,因此利用光滑化的Fischer-Burmeister函数构造与NCP(F)等价的光滑方程组.在此基础上建立求解NCP(F)的参数微分法.数值实验表明,这一方法是有效的.
关键词(KeyWords): 非线性互补问题;光滑Fischer-Burmeister函数;参数微分法
基金项目(Foundation): 国家自然科学基金资助项目(10661005)
作者(Authors): 林钊;马昌凤;
参考文献(References):
- [1]Harker P T,Pang J S.Finite-dimensional variational inequality and nonlinear complementarity problems:a surveyof theory,algorithms and applications[J].Mathematical Programming,1990,48:161-220.
- [2]Ferris M C,Pang J S.Engineering and economic applications of complementarity problems[J].SIAM Review,1997,39:669-713.
- [3]Kanzow C,Pieper H.Jacobian smoothing methods for nonlinear complementarity problems[J].SIAM Journal onOptimization,1999,9(9):342-373.
- [4]Chen B,Harker P T.Smoothing approximations to nonlinear complementarity problems[J].SIAM Journal onOptimization,1997,7(1):403-420.
- [5]Qi H.A regularized smoothing Newton method for box constrained variational inequality problems with P0-func-tions[J].SIAM Journalon Optimization,2000,10(1):315-330.
- [6]Qi L,Sun D,Zhou G.A new look at smoothing Newton methods for nonlinear complementarity problems andbox constrained variational inequality problems[J].Mathematical Programming,2000,87(1):1-35.
- [7]吴勃英.数值分析原理[M].北京:科学出版社,2003.
- [8]李庆扬,莫孜中,祁力群.非线性方程组的数值解法[M].北京:科学出版社,1987.
- [9]Ma Changfeng,Liang Guoping.A new successive approximation damped Newton method for nonlinearcomplementarity problems[J].Journal of Mathematical Research&Exposition,2003,23:1-6.
- [10]Kanzow C.Some noniterior continuation methods for linear complementarity problem[J].SIAM J Matrix AnalAppl,1996,17:851-868.