关于伪单调变分不等式与伪压缩算子不动点的自适应惯性次梯度外梯度算法  

On Inertial Adaptive Subgradient Extragradient Algorithm for Pseudo-Monotone Variational Inequalities and Fixed Points of Pseudo-Contractive Operators

作　　者：赵亚莉 李新昊 董淇馨 ZHAO Ya-li;LI Xin-hao;DONG Qi-xin(School of Mathematical Science,Bohai University,Jinzhou 121013,China)

机构地区：[1]渤海大学数学科学学院,辽宁锦州121013

出　　处：《数学的实践与认识》2025年第3期187-196,共10页Mathematics in Practice and Theory

基　　金：辽宁省教育厅科学基金(LJKMZ20221491)。

摘　　要：构造一种自适应惯性梯度外梯度方法,用于求解实Hilbert空间中伪单调变分不等式和伪压缩算子不动点的公共元,并给出了该算法的强收敛性分析。在不需要预先估计Lipschitz常数的情形下自适应技术保证了该算法的收敛性,数值实验结果说明该算法的有效性.所得结果改进了相关文献的相应结果.In this paper,an inertial adaptive subgradient extragradient method is constructed to solve a common elements of pseudo-monotone variational inequalities and fixed points of pseudo-contractive operators in a real Hilbert space,and the strong convergence analysis of the algorithm under consideration is given.The adaptive technique guarantees the convergence of the algorithm without estimating the Lipschitz constant in advance.Numerical experiments show the effectiveness of our algorithm.The results presented here improve the corresponding results of related literature.

关 键 词：伪单调变分不等式 伪压缩算子 不动点 算法 强收敛性 

分 类 号：O177.2[理学—数学]