Adaptive extragradient methods for solving variational inequalities in real Hilbert spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-09-19 DOI:10.1515/ijnsns-2021-0459

Duong Viet Thong, Xiao-Huan Li, Q. Dong, Hoang Van Thang, Luong Van Long

引用次数: 0

Abstract

Abstract The projection technique is a very important method and efficient for solving variational inequality problems. In this study, we developed the subgradient extragradient method for solving pseudomonotone variational inequality in real Hilbert spaces. Our first algorithm requires only computing one projection onto the feasible set per iteration and the strong convergence is proved without the prior knowledge of the Lipschitz constant as well as the sequentially weak continuity of the associated mapping. The second algorithm uses the linesearch procedure such that its convergence does not require the Lipschitz continuous condition of the variational inequality mapping. Finally, some numerical experiments are provided to demonstrate the advantages and efficiency of the proposed methods.

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求解实数Hilbert空间中变分不等式的自适应梯度方法

摘要投影技术是求解变分不等式问题的一种非常重要和有效的方法。在这项研究中，我们发展了求解实Hilbert空间中伪单调变分不等式的次梯度外方法。我们的第一个算法每次迭代只需要在可行集上计算一个投影，并且在没有Lipschitz常数的先验知识以及相关映射的顺序弱连续性的情况下证明了强收敛性。第二种算法使用线性搜索过程，使得其收敛性不需要变分不等式映射的Lipschitz连续条件。最后，通过数值实验验证了所提方法的优越性和有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.