基于Zhang-Hager线搜索的改进近似最优梯度法

吉林大学学报(理学版) ›› 2024, Vol. 62 ›› Issue (2): 263-0272.

基于Zhang-Hager线搜索的改进近似最优梯度法

李瑶¹, 刘红卫¹, 吕佳敏¹, 游海龙²

1. 西安电子科技大学数学与统计学院, 西安 710126； 2. 西安电子科技大学微电子学院, 西安 710071

收稿日期:2023-07-06 出版日期:2024-03-26 发布日期:2024-03-26
通讯作者: 李瑶 E-mail:ly818400@163.com

Improved Approximate Optimal Gradient Method Based on Zhang-Hager Line Search

LI Yao¹, LIU Hongwei¹, LV Jiamin¹, YOU Hailong²

1. School of Mathematics and Statistics, Xidian University, Xi’an 710126, China;
2. School of Microelectronics, Xidian University, Xi’an 710071, China

Received:2023-07-06 Online:2024-03-26 Published:2024-03-26

摘要/Abstract

摘要： 提出一种改进的近似最优梯度法, 求解图划分问题中的无约束目标函数. 先用修正的BFGS更新公式及选取BB类步长的线性组合作为标量矩阵得到近似最优步长, 再引入参数对经典的Zhang-Hager线搜索形式进行改进, 构建算法框架并给出R线性收敛性证明. 实验结果表明, 改进算法提高了原算法的性能.

关键词: 修正的BFGS更新公式, 近似最优步长, Zhang-Hager线搜索, R线性收敛性, 图划分问题

Abstract: We proposed an improved approximate optimal gradient method to solve the unconstrained objective function in the graph partition problem. We first used the modified BFGS updating formula and selected the linear combination of BB class step sizes as scalar matrices to obtain the approximate optimal step sizes, then we introduced parameters to improve the classical Zhang-Hager line search form, construced the algorithm framework and gave the proof of R-linear convergence. The experimental results show that the improved algorithm improves the performance of the original algorithm.

Key words: modified BFGS updating formula, , approximate optimal step size, Zhang-Hager line search, R-linear convergence, graph partition problem

中图分类号:

O221.7

李瑶, 刘红卫, 吕佳敏, 游海龙. 基于Zhang-Hager线搜索的改进近似最优梯度法[J]. 吉林大学学报(理学版), 2024, 62(2): 263-0272.

LI Yao, LIU Hongwei, LV Jiamin, YOU Hailong. Improved Approximate Optimal Gradient Method Based on Zhang-Hager Line Search[J]. Journal of Jilin University Science Edition, 2024, 62(2): 263-0272.