Banach空间上变分不等式问题的新投影算法

谢忠兵, 蔡钢

数学学报 ›› 2022, Vol. 65 ›› Issue (5) : 907-918.

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数学学报 ›› 2022, Vol. 65 ›› Issue (5) : 907-918. DOI: 10.12386/A20210056
论文

Banach空间上变分不等式问题的新投影算法

    谢忠兵, 蔡钢
作者信息 +

A New Projection Algorithm for Solving Variational Inequality Problems in Banach Spaces

    Zhong Bing XIE, Gang CAI
Author information +
文章历史 +

摘要

本文在Banach空间上提出一种关于伪单调变分不等式问题的新算法.在对参数强加适当的条件下,我们证明由算法生成的序列强收敛到变分不等式的一个元素.所得结果推广和提高了很多最新结果.

Abstract

We introduce a new algorithm for solving pseudomonotone variational inequality problems in Banach spaces. We prove that the sequence generated by this algorithm converges strongly an element of solutions for variational inequality problems under some suitable conditions imposed on the parameters. The results obtained in this paper extend and improve many recent ones in the literature.

关键词

强收敛 / Tseng超梯度算法 / 变分不等式 / Banach空间 / 伪单调算子

Key words

strong convergence / Tseng's extragradient method / variational inequality / banach spaces / pseudomonotone operator

引用本文

导出引用
谢忠兵, 蔡钢. Banach空间上变分不等式问题的新投影算法. 数学学报, 2022, 65(5): 907-918 https://doi.org/10.12386/A20210056
Zhong Bing XIE, Gang CAI. A New Projection Algorithm for Solving Variational Inequality Problems in Banach Spaces. Acta Mathematica Sinica, Chinese Series, 2022, 65(5): 907-918 https://doi.org/10.12386/A20210056

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基金

国家自然科学基金资助项目(11771063);重庆市自然科学基金(cstc2020jcyj-msxmX0455)及重庆市教委资助项目(KJZD-K201900504)
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