变分不等式的惯性次梯度外梯度算法  

An Inertial Subgradient Extragradient Algorithm for Solving Variational Inequalities

作　　者：杨志 夏福全 YANG Zhi;XIA Fuquan(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2023年第5期591-600,共10页Journal of Sichuan Normal University（Natural Science）

基　　金：教育部科学技术重点项目(212147)。

摘　　要：在实Hilbert空间中提出求解单调变分不等式的惯性次梯度外梯度算法,其中变分不等式的可行集是一个光滑凸函数的水平集.新算法应用惯性加速技巧,迭代过程中对映射F赋值一次,并只需向两个半空间作投影两次.在适当的假设下,证明该算法的弱收敛性.新算法改进和推广相关文献中的相应结果.In this paper,we propose a new inertial subgradient extragradient algorithm for solving monotone variational inequalities in Hilbert space,where the feasible set of variational inequality is the level set of a smooth convex function.The new algorithm uses the inertial acceleration technique.The value of F is calculated once during per iteration,only needs to project to two half spaces twice.Under the appropriate assumptions,the weak convergence of the algorithm is proved.The new algorithm improves and generalizes the corresponding results in the relevant literature.

关 键 词：次梯度外梯度算法 单调 LIPSCHITZ连续 惯性方法 变分不等式 

分 类 号：O117[理学—数学] O178[理学—基础数学]