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

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2023-01-01 DOI:10.1515/dema-2022-0202

H. Rehman, P. Kumam, Murat Ozdemir, I. Yildirim, W. Kumam

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.

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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

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.