两类问题公共解集上的变分不等式解的算法  

An Algorithm to Solve the Variational Inequality Problem Based on the Common Solutions of Two Classes of Problems

作　　者：王元恒 许甜甜 姚任之 姜炳男 Yuan Heng WANG;Tian Tian XU;Jen-Chih YAO;Bing Nan JIANG(College of Humanities,Zhejiang Guangsha Vicationl and Technical University of Constraction,Jinhua 322100,P.R.China;School of Mathematical Sciences,Zhejiang Normal Uinversity,Jinhua 321004,P.R.China)

机构地区：[1]浙江广厦建设职业技术大学人文学院,金华322100 [2]浙江师范大学数学科学学院,金华321004

出　　处：《数学学报（中文版）》2024年第4期704-718,共15页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(12171435)。

摘　　要：本文研究了Hilbert空间中求解分裂可行性问题和拟非扩张算子不动点问题的公共解的一种新算法,并在这两类问题公共解的基础上求解了变分不等式问题.与前人相比,增加了自适应的步长和惯性迭代算法,加快了算法生成的迭代序列的收敛速度.同时,将先前涉及的非扩张映射推广到拟非扩张映射,且在算法中加入了一个强正有界算子,将原来的黏性迭代算法推广到更一般的黏性迭代算法.在数值算例中验证了算法的有效性.We study a new algorithm to solve a common solution of the split feasibility problem and the fixed point problem involving quasi-nonexpansive mappings in Hilbert spaces.Based on the common solutions of these two classes of problems,we solve the variational inequality problem.Compared with the predecessors,the self-adaptive technique and the inertial iteration method are added,which can speed up the convergence rate of the iterative sequence generated by our algorithms.At the same time,we extend the involving previous nonexpansive mappings to extensive quasi-nonexpansive mappings.In addition,a strong positive bounded operator is added to the algorithm,which extends the original viscous iterative algorithm to a more general viscous iterative algorithm.The effectiveness of the algorithm is verified by numerical examples.

关 键 词：惯性黏性迭代算法 拟非扩张算子 强正有界算子 变分不等式问题 分裂可行性问题 

分 类 号：O177.91[理学—数学]