基于稀疏对角拟牛顿技术的ZhangH.C非单调F-规则的超记忆梯度算法  

A Non-monotone F-rule Super-Memory Gradient Method Based on Diagonal-sparse Quasi-Newton Technique

作　　者：韩志龙 郑尧 孙清滢 HAN Zhi-long;ZHENG Yao;SUN Qing-ying(College of Science,China University of Petroleum,Qingdao 266580,China)

机构地区：[1]中国石油大学(华东)理学院,山东青岛266580

出　　处：《数学的实践与认识》2021年第15期312-320,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(51974343)。

摘　　要：将稀疏对角拟牛顿技术和超记忆梯度算法结合用来寻找迭代方向,利用修正的Zhang H.C.非单调线搜索规则寻找步长,建立了一种新的求解无约束优化问题的超记忆梯度算法.并且对算法的全局收敛性进行证明,数值实验表明算法对求解大规模无约束优化问题是有效的.In this paper,the sparse diagonal quasi Newton technique and the super-memory gradient algorithm are combined to find the iterative direction,and the step size is found by using the modified Zhang H.C.non-monotone line search rule.A new super-memory gradient algorithm for solving unconstrained optimization problems is established.The global convergence of the algorithm is proved,and numerical experiments show that the algorithm is effective for solving large-scale unconstrained optimization problems.

关 键 词：稀疏对角拟牛顿技术 超记忆梯度算法 非单调线搜索规则 收敛性 数值实验 

分 类 号：O224[理学—运筹学与控制论]