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 forQuasi-monotone Variational Inequalities

作　　者：李卓 夏福全 LI Zhuo;XIA Fuquan(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《四川师范大学学报(自然科学版)》2025年第3期406-416,共11页Journal of Sichuan Normal University(Natural Science)

基　　金：国家自然科学基金(11901414)。

摘　　要：在实Hilbert空间中提出一种求解拟单调变分不等式问题的双惯性次梯度外梯度算法.该算法每次迭代只计算一次映射值和一次向可行集上的投影,并且将双惯性和松弛技术相结合,提高了次梯度外梯度方法求解变分不等式问题的收敛速度.在映射拟单调、Lipschitz连续和对偶变分不等式解集非空的假设条件下,获得了该算法的弱收敛结果.同时,在强拟单调的假设下得到了算法在Hilbert空间中强收敛结果.最后,数值实验表明该算法的有效性.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-monotone 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 

分 类 号：O178[理学—数学] O221[理学—基础数学]