Convergence of a New Bregman Projection Method with a Self-adaptive Stepsize for Solving Monotone Inclusion Problems and Variational Inequality Problems in Reflexive Banach Spaces  

自反Banach空间上解决单调包含问题和变分不等式问题的带自适应步长的新Bregman投影方法的收敛性

作　　者：CHEN Lulu CAI Gang 陈璐璐;蔡钢(重庆师范大学数学科学学院,重庆401331)

机构地区：[1]School of Mathematical Sciences,Chongqing Normal University,Chongqing,401331,P.R.China

出　　处：《数学进展》2025年第1期141-163,共23页Advances in Mathematics(China)

基　　金：Supported by NSFC(No.12171062);the Natural Science Foundation of Chongqing(No.CSTB2022NSCQ-JQX0004);the Chongqing Talent Support Program(No.cstc2024ycjh-bgzxm0121);Science and Technology Project of Chongqing Education Committee(No.KJZD-M202300503)。

摘　　要：The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces.The strong convergence result for our method is established under some standard assumptions without any requirement of the knowledge of the Lipschitz constant of the mapping.Several numerical experiments are provided to verify the advantages and efficiency of proposed algorithms.本文的主要目的是在自反的Banach空间中引入一种新的具有自适应步长的方法来逼近单调包含和变分不等式问题的公共解,我们所提出方法的强收敛性建立在一些标准假设下,且不需要知道映射的利普希茨常数.一些数值实验说明了我们的算法比其他算法更有优势且更有效.

关 键 词：Bregman distance variational inequality monotone inclusion maximal operator reflexive Banach space 

分 类 号：O177.91[理学—数学]