P_0函数非线性互补问题的一步非内点连续方法的收敛性  

THE CONVERGENCE OF AN ONE-STEPNON-INTERIOR CONTINUATION METHODFOR SOLVING THE P_0 FUNCTION NCP

作　　者：黄正海[1] 韩继业[1] 陈中文[2] 

机构地区：[1]中国科学院数学与系统科学研究院应用数学研究所,北京100080 [2]苏州大学数学系,江苏苏州215006

出　　处：《数学年刊（A辑）》2002年第2期175-186,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.19871016;No.19731001)资助的项目

摘　　要：本文对于Ｐ０函数非线性互补问题提出了一个基于Ｋａｎｚｏｗ光滑函数的一步非内点连续方法,在适当的假设条件下,证明了方法的全局线性及局部二次收敛性．特别,在方法的全局线性收敛性的分析中,不需要假定非线性互补问题的函数的Ｊａｃｏｂｉ阵是Ｌｉｐｓｃｈｉｔｚ连续的．文献中为了得到非内点连续方法的全局线性收敛性,这一假定是被广泛使用的．本文提出的方法在每一次迭代只须解一个线性方程式组．In this paper, we propose an one-step non-interior continuation method for solving P0 function nonlinear complementarity problems (NCP) based on Kanzow's smoothing func-tion, which is shown to be globally linearly and locally quadratically convergent under suitable assumptions. In particular, in our analysis for the global linear convergence of the method we do not need the assumption that the Jacobian of the function involved in the NCP is Lipschitz continuous, which is used widely in the non-interior continuation methods in order to achieve global linear convergence result of the methods. The proposed method only needs to solve a linear system of equations at each iteration.

关 键 词：P0函数非线性互补问题 非内点连续方法 全局线性收敛性 局部二次收敛性 

分 类 号：O224[理学—运筹学与控制论] O241.5[理学—数学]