一类基于新光滑化函数求解NCP的牛顿法  

A class of newton methods for NCP based on a new smoothing function

作　　者：王学斌[1] 李梅艳[1] 马昌凤[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2010年第1期78-80,共3页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(10661005);广西研究生教育创新计划资助项目(2009105950701M31)

摘　　要：非线性互补问题(NCP)可转化为等价的非光滑方程组。基于光滑化的思想,引入一个新光滑化函数,将此非光滑方程近似为一簇参数化的光滑方程。利用一个光滑化牛顿算法求解这簇光滑方程,而间接得到NCP的解。在一定的条件下,证明该算法产生的序列全局收敛且局部二次收敛到NCP的解。The nonlinear complementarity problem （denoted by NCP） can be reformulated as a nonsmooth system of equations. Based on smoothing ideas, the nonsmooth equation is approximated by a family of parameterized smooth equations by introducing a new smoothing function. A smoothing Newton method is proposed for the solution of the parameterized smooth equations. Under appropriate assumptions, it is proved that the algorithmic sequence globally and quadratically converges to a solution of NCP.

关 键 词：非线性互补问题 光滑化牛顿法 全局收敛 局部二次收敛 

分 类 号：O224.2[理学—运筹学与控制论]