求解加权水平线性互补问题的非单调光滑非精确牛顿法  

Nonmonotone Smoothing Inexact Newton Algorithm for Solving Weighted Horizontal Linear Complementarity Problems

作　　者：范甜甜 汤京永 周金川 Tiantian Fan;Jingyong Tang;Jinchuan Zhou(School of Mathematics and Statistics,Xinyang Normal University,Henan Xinyang 464000;College of Mathematics and Statistics,Shandong University of Technology,Shandong Zibo 255000)

机构地区：[1]信阳师范大学数学与统计学院,河南信阳464000 [2]山东理工大学数学与统计学院,山东淄博255000

出　　处：《数学物理学报(A辑)》2025年第1期165-179,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(12371305);山东省自然科学基金(ZR2023MA020);河南省自然科学基金(222300420520);河南省高等学校重点科研项目(22A110020)。

摘　　要：该文研究一个求解加权水平线性互补问题的非单调光滑非精确牛顿法.该算法利用一个光滑函数将加权水平线性互补问题等价转化成一个非线性方程组,然后利用非精确牛顿法求解此方程组.由于非精确方向一般不是下降方向,算法采用一个新的非单调线搜索技术来确保其全局收敛性.特别地,在P对条件下,证明了算法生成的迭代序列有界.进一步,分析了算法在H?lderian局部误差界条件下的收敛速率,而该条件比局部误差界条件更广泛.算法在每次迭代时只需求解方程组的近似解,从而可以节省大量的计算时间,数值实验结果验证了这一优点.In this paper,we study a nonmonotone smoothing inexact Newton algorithm for solving the weighted horizontal linear complementarity problem(wHLCP).The algorithm uses a smoothing function to reformulate the wHLCP as a nonlinear system of equations and then solve it by inexact Newton's method.Since inexact directions are not necessarily descent,the algorithm adopts a new nonmonotone line search technique to ensure its globalization.Especially,we prove that the generated iteration sequence is bounded under the P-pair condition.Moreover,we analyze the local convergence rate of the algorithm under the Hölderian local error bound condition which is more general than the local error bound condition.The algorithm solves the nonlinear equations only approximately so that a lot of computation time can be saved.Numerical experiment results confirm the advantage of the algorithm.

关 键 词：加权水平线性互补问题 光滑算法 非精确牛顿法 非单调技术 H?lderian局部误差界 

分 类 号：O221.1[理学—运筹学与控制论]