摘要
变分不等式问题在经济金融、交通运输、数学规划、力学等领域都有着广泛的应用。近年来,变分不等式问题受到许多学者的研究,且这些研究主要集中在求解单调或者伪单调变分不等式问题。文章在实希尔伯特空间中,针对非单调变分不等式问题,提出了求解该问题的算法。借助惯性原理和Mann型方法,构造了一个带Armijo线性搜索的修正惯性次梯度外梯度算法;在没有Lipschitz连续性的假设下,证明了由算法产生的迭代序列强收敛于变分不等式问题的解,值得注意的是,定理的证明并没有要求映射的任何单调性假设;最后,给出了两个数值实验,阐明了文章算法的有效性和优越性,所得结果推广和改进了许多最新的结果。
Variational inequality problems have a wide range of applications in economics and finance,transportation,mathematical planning,mechanics,and other fields.In recent years,the problem of variational inequalities has been studied by many scholars,and these studies have mainly focused on solving monotone or pseudo-monotone variational inequalities.This article presented an algorithm for solving non-monotone variational inequality problems in real Hilbert spaces.A modified inertial subgradient extragradient algorithm with Armijo linear search was constructed using the inertia principle and Mann-type method.Under the assumption of non-Lipschitz continuity,it was proved that the sequence of iterations generated by the algorithm converged strongly to the solution of the variational inequality problems.It is worth noting that the proof of the theorem does not require any monotonicity assumption for the mapping.Finally,two numerical experiments were given to illustrate the effectiveness and superiority of the algorithm in the paper.The results obtained extend and improve many recent results.
作者
方珍洁
龙宪军
FANG Zhenjie;LONG Xianjun(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China)
出处
《重庆工商大学学报（自然科学版）》
2023年第5期89-95,共7页
Journal of Chongqing Technology and Business University:Natural Science Edition
基金
重庆市自然科学基金(CSTC2021JCYJ-MSXMX0721)
重庆市教育委员会科学技术研究重点项目(KJZD-K201900801)
重庆工商大学科研团队项目(ZDPTTD201908).
关键词
变分不等式
次梯度外梯度算法
Armijo线性搜索
强收敛
非单调
variational inequalities
subgradient extragradient algorithm
Armijo linear search
strong convergence
non-monotone
