Hilbert空间中一类多集分裂变分不等式问题和公共不动点问题的自适应块迭代过程

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.3934/naco.2022007

H. Rehman, P. Kumam, Y. I. Suleiman, Widaya Kumam

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引用次数: 1

摘要

本文将Lohawech et al. (J. Ineq Appl. 358, 2018)的一类分裂变分不等式问题和不动点问题推广到Hilbert空间中的一类多集分裂变分不等式问题和公共不动点问题(CMSSVICFP)。利用变分不等式问题的Halpern次梯度外扩定理，提出了求解CMSSVICFP问题的自适应步长并行Halpern次梯度外扩cq方法。我们证明了由该算法生成的序列强收敛于CMSSVICFP的解。最后给出了一个数值算例，并进行了一些初步的数值试验，以说明该方法的数值有效性。

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An adaptive block iterative process for a class of multiple sets split variational inequality problems and common fixed point problems in Hilbert spaces

In this paper, we present extension of a class of split variational inequality problem and fixed point problem due to Lohawech et al. (J. Ineq Appl. 358, 2018) to a class of multiple sets split variational inequality problem and common fixed point problem (CMSSVICFP) in Hilbert spaces. Using the Halpern subgradient extragradient theorem of variational inequality problems, we propose a parallel Halpern subgradient extragradient CQ-method with adaptive step-size for solving the CMSSVICFP. We show that a sequence generated by the proposed algorithm converges strongly to the solution of the CMSSVICFP. We give a numerical example and perform some preliminary numerical tests to illustrate the numerical efficiency of our method.

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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.