求解绝对值方程组的单调坐标下降法  

A MONOTONE COORDINATE DESCENT METHOD FOR SOLVING THE SYSTEM OF ABSOLUTE VALUE EQUATIONS

作　　者：李雪花 陈林婕[2] 陈彩荣 Li Xuehua;Chen Linjie;Chen Cairong(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China;School of Mathematics and Statistics&Key Laboratory of Analytical Mathematics and Applications(Ministry of Education)&Fujian Provincial Key Laboratory of Statistics and Artificial Intelligence,Fujian Normal University,Fuzhou 350117,China)

机构地区：[1]福建师范大学数学与统计学院,福州350117 [2]福建师范大学数学与统计学院,统计学与人工智能福建省高校重点实验室,福州350117 [3]福建师范大学数学与统计学院,分析数学及应用教育部重点实验室,统计学与人工智能福建省高校重点实验室,福州350117

出　　处：《计算数学》2025年第1期122-134,共13页Mathematica Numerica Sinica

基　　金：福建省自然科学基金(2021J01661)资助。

摘　　要：本文提出了求解绝对值方程组的单调坐标下降算法,在适当的条件下分析了算法的全局收敛性并用数值实验验证了所提算法的可行性及有效性.本文的另一个目的是指出文献[Optim.Lett.,6:1027-1033,2012]在构造目标函数的下降方向时误用其二阶泰勒展开导致的错误.In this paper,a monotone coordinate descent algorithm for solving absolute value equa-tions is presented,and the global convergence of the algorithm is analyzed under appropriate conditions.The feasibility and effectiveness of the proposed algorithm are verified by numer-ical experiments.Another purpose of this paper is to point out a mistake in the paper by Noor et al.[Optim.Lett.,6:1027-1033,2012],which is caused by misuse of the second-order Taylor expansion in constructing the descending direction of the objective function.

关 键 词：绝对值方程组 坐标下降法 精确线搜索 

分 类 号：O241.6[理学—计算数学]