求解一般非线性互补问题的光滑化方法  

Smoothing Methods for Solving General Nonlinear Complementarity Problems

作　　者：陈为民[1] 杨余飞[2] 

机构地区：[1]湖南大学工商管理学院,湖南长沙 410082 [2]湖南大学数学与计量经济学院,湖南长沙 410082

出　　处：《运筹学学报》2008年第1期93-103,共11页Operations Research Transactions

基　　金：国家自然科学基金(60572114)资助

摘　　要：在利用Fischer-Burmeister函数将非线性互补问题转化为非线性方程组的基础上,本文通过将信赖域方法与线性搜索方法结合起来,提出了求解一般非线性互补问题的光滑化方法.算法中我们给出了一个特定条件,条件满足时,采用信赖步,条件不满足时,采用梯度步.我们证明了算法具有全局收敛性,在解是R-正则的条件下,收敛速度是Q-超线性/Q-二阶收敛的.Based on reformulating the nonlinear complementarity problem as a system of nonsmooth equations by using Fisher-Burmeister function, in this paper, by combining trust region and line search techniques, we present a smoothing method for solving general nonlinear complementarity problems. In the algorithm we give a special condition, when this condition is satisfied, the trust region method is used; otherwise, the gradient is used. We proved that our algorithm possesses global convergence property, and under the condition that the solution is R-regular, the local convergence rate is proved to be Q-superlinear/Q-quadratic.

关 键 词：运筹学 非线性互补问题.信赖域方法 线性搜索 全局收敛性 局部超线性 收敛性 

分 类 号：O221.2[理学—运筹学与控制论] O241.8[理学—数学]