A class of strongly convergent subgradient extragradient methods for solving quasimonotone variational inequalities

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
H. Rehman, P. Kumam, Murat Ozdemir, I. Yildirim, W. Kumam
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引用次数: 1

Abstract

Abstract The primary goal of this research is to investigate the approximate numerical solution of variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In this study, the sequence obtained by the proposed iterative technique for solving quasimonotone variational inequalities converges strongly toward a solution due to the viscosity-type iterative scheme. Furthermore, a new technique is proposed that uses an inertial mechanism to obtain strong convergence iteratively without the requirement for a hybrid version. The fundamental benefit of the suggested iterative strategy is that it substitutes a monotone and non-monotone step size rule based on mapping (operator) information for its Lipschitz constant or another line search method. This article also provides a numerical example to demonstrate how each method works.
一类求解拟单调变分不等式的强收敛次梯度外延方法
摘要本文的主要目的是利用拟单调算子研究无穷维实数Hilbert空间中变分不等式的近似数值解。在本研究中,由于采用粘性型迭代格式,拟单调变分不等式的迭代求解序列强收敛于一个解。在此基础上,提出了一种利用惯性机制迭代获得强收敛性的新方法,而不需要混合版本。所建议的迭代策略的根本好处是,它替代单调和非单调的步长规则基于映射(算子)信息的Lipschitz常数或另一种线搜索方法。本文还提供了一个数值示例来演示每种方法的工作原理。
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
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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