基于一个新的NCP函数的光滑牛顿法求解非线性互补问题  

A SMOOTHING NEWTON METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEM BASED ON A NEW NCP FUNCTION

作　　者：许小芳[1] 马昌凤[1] 

机构地区：[1]福建师范大学数学与计算机科学学院,福建福州350007

出　　处：《数学杂志》2011年第4期749-755,共7页Journal of Mathematics

基　　金：国家自然科学基金项目(10661005);福建省自然科学基金项目(2009J01002)

摘　　要：本文研究了非线性互补的光滑化问题.利用一个新的光滑NCP函数将非线性互补问题转化为等价的光滑方程组,并在此基础上建立了求解P0-函数非线性互补问题的一个完全光滑化牛顿法,获得了算法的全局收敛性和局部二次收敛性的结果.并给出数值实验验证了理论分析的正确性.In the article, we study the smoothness of the nonlinear complementarity problem. By means of a new smoothing NCP-function, the nonlinear complementarity problem can be reformulated as the solution of the equivalent smoothness equations, and we propose a new smoothing Newton method for solving nonlinear complementarity problem with P0-function （denoted by P0-NCP）. Under suitable assumptions, we obtain the global and local quadratic convergence results of the proposed algorithm. Numerical experiments indicate that the proposed method is quite effective.

关 键 词：非线性互补问题 完全光滑化牛顿法 全局收敛性 二局部次收敛性 

分 类 号：O224[理学—运筹学与控制论]