A New Self Adaptive Inertial Subgradient Extragradient Iterative Algorithm for Solving Variational Inequalities of Pseudomonotone Mappings in Real Hilbert Spaces  

实希尔伯特空间上求解伪单调映射变分不等式的新的自适应惯性次梯度外梯度迭代方法

作　　者：HU Shaotao WANG Yuanheng TANG Yan JING Ping 胡绍涛;王元恒;唐艳;荆平(浙江师范大学数学科学学院,浙江金华321004;重庆师范大学马克思主义学院,重庆401331;重庆工商大学数学与统计学院,重庆400067)

机构地区：[1]School of Mathematical Sciences,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.China [2]School of Marcism,Chongqing Normal University,Chongqing,401331,P.R.China [3]College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing,400067,P.R.China

出　　处：《数学进展》2024年第6期1285-1304,共20页Advances in Mathematics（China）

基　　金：Supported by NSFC(Nos.12171435,12301159)。

摘　　要：The main purpose of this paper is to introduce and deal with a self adaptive inertial subgradient extragradient iterative algorithm with a new and interesting stepsize rule in real Hilbert spaces.Under some proper control conditions imposed on the coefficients and operators,we prove a new strong convergence result for solving variational inequalities with regard to pseudomonotone and Lipschitzian operators.Moreover,some numerical simulation results are given to show the rationality and validity of our algorithm.本文的主要目的是在实希尔伯特空间中引入和处理一种含新的有趣的步长法则的自适应惯性次梯度外梯度迭代算法.在对系数和算子适当的控制条件下,我们证明了求解关于伪单调和利普希茨算子的变分不等式的一个新的强收敛结果.进一步,给出一些数值实验结果说明了我们算法的合理性和正确性.

关 键 词：strong convergence variational inequality extragradient method pseudomonotone operator Hilbert space 

分 类 号：O177.91[理学—数学]