解伪单调变分不等式的修正惯性次梯度外梯度法  

Modified Inertial Subgradient Extragradient Method for Pseudomonotone Variational Inequalities

作　　者：张津溶 李紫琪 ZHANG Jinrong;LI Ziqi(School of Mathematics and Information,China West Normal University,Nanchong 637009,Sichuan,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：《韶关学院学报》2024年第6期21-27,共7页Journal of Shaoguan University

基　　金：国家自然学科基金项目(11871059)。

摘　　要：针对实Hilbert空间中的伪单调变分不等式问题,将惯性法和黏性法相结合,构造了一种基于Armijo线性搜索的次梯度外梯度法.在没有Lipschitz连续性的假定下,给出了该算法生成的迭代序列的强收敛性.最后,通过数值实验说明了该算法是有效的.Based on the inertial principle and viscosity method,a subgradient exterior gradient method with Armijo line search is proposed for solving pseudomonotone variational inequalities in real Hilbert spaces.The strong convergence of the iterative sequence generated by the algorithm is proved without the assumption of Lipschitz continuity.Finally,a numerical experiment shows that the algorithm is feasible.

关 键 词：变分不等式 次梯度外梯度算法 Armijo线性搜索 强收敛 伪单调 

分 类 号：O221[理学—运筹学与控制论]