| 关于求解变分不等式问题的2-次梯度外梯度算法收敛性的一个补注 |
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| 引用本文： | 屈彪,徐伟,王新艳. 关于求解变分不等式问题的2-次梯度外梯度算法收敛性的一个补注[J]. 运筹学学报, 2021, 25(2): 144-148. DOI: 10.15960/j.cnki.issn.1007-6093.2021.02.012 |
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| 作者姓名： | 屈彪 徐伟 王新艳 |
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| 作者单位： | 1. 曲阜师范大学运筹学研究院, 山东日照 276826 |
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| 基金项目： | 山东省自然科学基金(ZR2018MA019);国家自然科学基金(11271226) |
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| 摘 要： | Yair Censor,Aviv Gibali和Simeon Reich为求解变分不等式问题提出了 2-次梯度外梯度算法.关于此算法的收敛性,作者给出了部分证明,有一个问题:由算法产生的迭代点列能否收敛到变分不等式问题的一个解上,没有得到解决.此问题作为一个公开问题在文章"Extensions of Korpelevi...
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| 关 键 词： | 变分不等式问题 2-次梯度外梯度算法 收敛性 |
| 收稿时间： | 2019-11-19 |
A remark on the convergence of the two-subgradient extragradient algorithm for the variational inequality problem |
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| Biao QU,Wei XU,Xinyan WANG. A remark on the convergence of the two-subgradient extragradient algorithm for the variational inequality problem[J]. OR Transactions, 2021, 25(2): 144-148. DOI: 10.15960/j.cnki.issn.1007-6093.2021.02.012 |
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| Authors: | Biao QU Wei XU Xinyan WANG |
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| Affiliation: | 1. Institute of Operations Research, Qufu Normal University, Rizhao 276826, Shandong, China |
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| Abstract: | The two-subgradient extragradient algorithm was proposed by Yair Censor, Aviv Gibali and Simeon Reich for solving the variational inequality problem. A question about the convergence of this algorithm, that is, whether the sequences generated by the algorithm converge to a solution of the variational inequality problem, was raised as an open problem in the paper "Extensions of Korpelevich's extragradient method for the variational inequality problem in Euclidean space" (Optimization, 61(9): 1119-1132, 2012). Our goal in this short remark is to give an answer to this question and give an integrated proof of the full convergence of the algorithm. |
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| Keywords: | variational inequality problem the two-subgradient extragradient algorithm full convergence |
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