一类保证充分下降性的YT型共轭梯度算法  

A Class Of Yt-type Conjugate Gradient Algorithms With Sufficient Descent

作　　者：程万友 叶剑豪 张嘉昊 CHENG Wanyou;YE Jianhao;Zhang Jiahao(School of Computer Science and Technology,Dongguan University of Technology,Dongguan,523820,Guangdong,China)

机构地区：[1]东莞理工学院计算机科学与技术学院,广东东莞523808

出　　处：《惠州学院学报》2023年第6期28-38,106,共12页Journal of Huizhou University

基　　金：国家自然科学面上基金项目(11961011,11971106)。

摘　　要：基于施密特正交化与YT型共轭条件,给出一类修正的YT型共轭梯度算法。新算法的一个重要特性是产生的方向总是满足充分下降条件,且不依赖于任何线搜索。当使用精确线搜索时和合适的参数下,新算法退化为标准的HS方法。在一定条件下,作者证明算法在标准Wolfe线搜索条件下对于一致凸函数与一般函数具有全局收敛性。数值结果表明新算法具有优良的数值性能。Based on Schmidt orthogonalization and YT-type conjugate condition,we present a class of modified YT-type conjugate gradient algorithm.An important property of the new algorithm is that the generated directions always satisfy the sufficient descent condition without relying on any line search.By using exact line search under suitable parameters,the new algorithm reduces to the standard HS method.Under certain conditions,we prove that the algorithm is globally convergent for uniform convex functions and general functions under standard Wolfe line search conditions.Numerical results show that the new algorithm has excellent numerical performance.

关 键 词：共轭梯度算法 非精确线搜索 全局收敛性 无约束优化 

分 类 号：O224[理学—运筹学与控制论]