基于新光滑函数的P_(0)映射非线性互补问题的光滑牛顿法  

The Smoothing Newton Method for NCP with P_0-Mapping Based on a New Smoothing Function

作　　者：马昌凤 王婷[2] MA Changfeng;WANG Ting(Key Laboratory of Digital Technology and Intelligent Computing,School of Big Data,Fuzhou University of International Studies and Trade,Fuzhou 350202,China;School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China)

机构地区：[1]福州外语外贸学院大数据学院数字技术与智能计算重点实验室,福建福州350202 [2]福建师范大学数学与统计学院,福建福州350117

出　　处：《应用数学》2023年第3期589-601,共13页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China (11901098);Fujian Natural Science Foundation (2020J05034)。

摘　　要：非线性互补问题(NCP)可以重新表述为一个非光滑方程组的解.通过引入一个新的光滑函数,将问题近似为参数化光滑方程组.基于这个光滑函数,我们提出了一个求解P_(0)映射和R_(0)映射非线性互补问题的光滑牛顿法.该算法每次迭代只求解一个线性方程和一次线搜索.在适当的条件下,证明了该方法是全局和局部二次收敛的.数值结果表明,该算法是有效的.The nonlinear complementarity problem(NCP) can be reformulated as the solution of a nonsmooth system of equations.By introducing a new smoothing function,the problem is approximated by a family of parameterized smooth equations.Based on this smoothing function,we propose a smoothing Newton method for NCP with P_0-mapping and R_0-mapping.The proposed algorithm solves only one linear equations and performs only one line search per iteration.Under suitable conditions,the method is proved to be globally and local quadratically convergent.Numerical results show that the proposed algorithm is effective.

关 键 词：非线性互补问题 光滑牛顿法 光滑函数 全局收敛性 局部二阶收敛性 

分 类 号：O241[理学—计算数学]