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 1.1 Q2 MATHEMATICS, APPLIED

Numerical Algebra Control and Optimization 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

Numerical Algebra Control and Optimization MATHEMATICS, APPLIED-

CiteScore

3.10

自引率

0.00%

发文量

期刊介绍： Numerical Algebra, Control and Optimization (NACO) aims at publishing original papers on any non-trivial interplay between control and optimization, and numerical techniques for their underlying linear and nonlinear algebraic systems. Topics of interest to NACO include the following: original research in theory, algorithms and applications of optimization; numerical methods for linear and nonlinear algebraic systems arising in modelling, control and optimisation; and original theoretical and applied research and development in the control of systems including all facets of control theory and its applications. In the application areas, special interests are on artificial intelligence and data sciences. The journal also welcomes expository submissions on subjects of current relevance to readers of the journal. The publication of papers in NACO is free of charge.