强Wolfe线搜索下一个新的优化算法  

A NEW OPTIMIZATION ALGORITHM UNDER STRONG WOLFE LINE SEARCH

作　　者：朱铁锋 ZHU Tie-feng(School of Statistics and Mathematics,Inner Mongolia University of Finance and Economics,Hohhot 010070,China)

机构地区：[1]内蒙古财经大学统计与数学学院,内蒙古呼和浩特010070

出　　处：《数学杂志》2023年第3期267-276,共10页Journal of Mathematics

基　　金：内蒙古自治区自然科学基金资助(2020MS01001,2022MS07006);国家自然科学基金资助(72163022)。

摘　　要：本文主要研究了一个新的优化算法.首先,利用给出的新的公式和强Wolfe线搜索,证明了该算法在不要求搜索方向满足共轭性条件下具有充分下降性和全局收敛性;其次,利用目标函数为一致凸函数的假设,证明了该算法具有线性收敛速率;最后,利用数值试验,验证了新算法是有效的、可行的.In this paper,a new optimization algorithm is studied.Firstly,by using the new formula and strong Wolfe line search,it is proved that the algorithm has sufficient descent and global convergence without requiring the search direction to satisfy the conjugation.Secondly,using the assumption that the objective function is uniformly convex,it is proved that the algorithm has linear convergence rate.Finally,numerical experiments show that the new algorithm is effective and feasible.

关 键 词：无约束优化 共轭梯度法 强Wolfe线搜索 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]