求解拟单调变分不等式的修正外梯度次梯度法  

Modified subgradient extragradient algorithm for solving quasimonotone variational inequality

作　　者：何丹露 张津溶 HE Danlu;ZHANG Jinrong(School of Mathematics and Information,China West Normal University,Nanchong,Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《内江师范学院学报》2023年第8期29-36,共8页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(11871059);四川省高校创新团队项目(16TD0019)。

摘　　要：在实Hilbert空间中提出一种新的算法来求解拟单调变分不等式.新算法基于次梯度外梯度法、惯性技术和Halpern方法,且不要求映射是Lipschitz连续,并采用Armijio线搜索准则.最后在合适的条件下得到新算法产生的序列强收敛到变分不等式的解.数值实验结果表明了算法的可行性.A new algorithm is proposed to solve quasimonotone variational inequalities in real Hilbert space.The algorithm is based on the subgradient extragradient algorithm,the inertial technique and halpern method,and the mapping is not required to be Lispschitz continuous,and Armijio line search criterion is used.Finally,under the appropriate conditions,the solutions of the sequence converging strongly to the variational inequality are obtained.Numerical experiment results show the feasibility of the algorithm.

关 键 词：拟单调变分不等式 外梯度次梯度法 惯性技术 一致连续 Halpern方法 Armijio线搜索准则 

分 类 号：O178[理学—数学]