An Adaptive Spectral Conjugate Gradient Method with Restart Strategy  

一个带重启策略的自适应谱共轭梯度法

作　　者：Zhou Jincheng Jiang Meixuan Zhong Zining Wu Yanqiang Shao Hu 周金诚;蒋枚萱;钟梓宁;吴彦强;邵虎(中国矿业大学数学学院,徐州221116)

机构地区：[1]School of Mathematics,China University of Mining and Technology,Xuzhou 221116,China

出　　处：《数学理论与应用》2024年第3期106-118,共13页Mathematical Theory and Applications

基　　金：supported by the National Natural Science Foundation of China(No.72071202);the Key Laboratory of Mathematics and Engineering Applications,Ministry of Education。

摘　　要：As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.谱共轭梯度法作为二项共轭梯度法的一种推广,是求解无约束优化的有效方法之一.本文借助凸组合技术对Jiang等提出的JJSL共轭参数(Computational and Applied Mathematics,2021,40:174)进行改进,再结合构造的谱梯度型重启策略,给出一个自适应搜索方向?使用非精确线搜索产生步长,进而得到一个新的谱共轭梯度法.利用弱Wolfe线搜索,我们获得新搜索方向的充分下降性.此外,在一般的假设下,通过使用强Wolfe线搜索计算步长,我们证明新算法的全局收敛性.最后,给出的无约束优化测试结果表明,新算法是有效的.

关 键 词：Unconstrained optimization Spectral conjugate gradient method Restart strategy Inexact line search Global convergence 

分 类 号：O224[理学—运筹学与控制论]