水平线性互补问题的一种非精确光滑牛顿算法  

An Inexact Smooth Newton Algorithm for Monotone Horizontal Linear Complementarity Problem

作　　者：安梦瑶 芮绍平[1] AN Mengyao;RUI Shaoping(College of Mathematics,Huaibei Normal University,Huaibei 235000,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《长春师范大学学报》2024年第8期35-39,共5页Journal of Changchun Normal University

基　　金：安徽省教育厅自然科学研究项目“大规模无约束优化问题的非精确非单调算法及其应用研究”(2023AH050348)。

摘　　要：为了提高求解水平线性互补问题的效率,本文利用一种光滑函数,将水平线性互补问题转化为与之等价的光滑方程组,采用非精确牛顿法求解该方程组,得到了水平线性互补问题的一种非精确光滑牛顿算法.在适当的条件下证明了该算法的适定性和局部二阶收敛性,数值实验表明该算法稳定有效.In order to improve the efficiency of solving horizontal linear complementarity problems,this paper uses smooth functions to transform the problem into an equivalent smooth equation system.An inexact Newton method is employed to solve the equation system,and an inexact smooth Newton algorithm for solving horizontal linear complementarity problems is obtained.Under certain appropriate conditions,it is proved that the algorithm has adaptability and locally quadratic convergence.Numerical results show that the algorithm is effective.

关 键 词：水平线性互补问题 非精确牛顿法 全局收敛 局部二阶收敛 

分 类 号：O221.1[理学—运筹学与控制论]