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

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

引用次数: 1

Abstract

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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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

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。

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

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