一类改进的拟牛顿算法  

An Improved Quasi-Newtonian Algorithm

作　　者：罗文军 吴泽忠 贺盛瑜 LUO Wenjun;WU Zezhong;HE Shengyu(College of Applied Mathematics,Chengdu University of Information Technology,Chengdu 610225,China;Sichuan Institute of Socialism,Chengdu 610037,China)

机构地区：[1]成都信息工程大学应用数学学院,四川成都610225 [2]四川社会主义学院,四川成都610037

出　　处：《成都信息工程大学学报》2024年第3期374-381,共8页Journal of Chengdu University of Information Technology

基　　金：国家自然科学基金资助项目(71962030);四川省社科重点研究基地资助项目(Xq21B06);国家社会科学基金资助项目(21BTQ099)。

摘　　要：在拟牛顿方程基础上,推导出一种新的DFP校正公式,并在强Wolfe步长规则下给出一类新的DFP算法。随后提出一种改进的强Wolfe线性搜索法,改善由于精度所导致的线性搜索失败的问题,并在一定假设下证明改进的算法具有全局收敛性。最后用算例来改进前后的DFP算法的性能作对比,结果表明改进的算法行之有效,并且具有更好的收敛性。In this paper,based on the new quasi-Newtonian equation,a new DFP correction formula is derived,and a new class of DFP algorithm is proposed under the strong Wolfe condition.Then,we propose an improved strong Wolfe linear search method to solve the problem of linesearch failure due to accuracy,and prove that the improved algorithm has global convergence under certain assumptions.Finally,an example is introduced to compare the performance of the DFP algorithm before and after the improvement.The results show that the improved algorithm is moreeffective and has better convergence.

关 键 词：DFP算法 共轭梯度 拟牛顿法 无约束最优化 线性搜索 

分 类 号：O221.2[理学—运筹学与控制论]