四川师范大学学报（自然科学版）2025，Vol.48Issue(3)：406-416,11.DOI:10.3969/j.issn.1001-8395.2025.03.012
拟单调变分不等式的新双惯性次梯度外梯度算法
A New Double Inertial Subgradient Extragradient Algorithm for Quasi-monotone Variational Inequalities
摘要
Abstract
In this paper,we introduce a double inertial subgradient extragradient algorithm for solving quasi-monotone variational inequality problems in real Hilbert space.The advantage of this algorithm is that each iteration only calculates the mapping value once and the projection to the feasible set once,and combines the double inertial and relaxation techniques to improve the convergence speed of the subgradient extragradient method for solving variational inequality problems.Under the condition that the mapping is quasi-mono-tone and Lipschitz continuous,where the solution set of dual variational inequalities is non-empty,the weak convergence results of the algorithm are established.At the same time,the strong convergence results in Hilbert space are obtained under the assumption of strong quasi-monotone mapping.Finally,numerical experiments show the effectiveness of the algorithm.关键词
变分不等式/拟单调/次梯度外梯度算法/双惯性加速Key words
variational inequality/quasi-monotone/subgradient extragradient algorithm/double inertial acceleration分类
数理科学引用本文复制引用
李卓,夏福全..拟单调变分不等式的新双惯性次梯度外梯度算法[J].四川师范大学学报（自然科学版）,2025,48(3):406-416,11.基金项目
国家自然科学基金(11901414) （11901414）
