Convergence analysis of subgradient extragradient method with inertial technique for solving variational inequalities and fixed point problems

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-17 DOI:10.1016/j.cnsns.2025.108851

Danni Guo , Gang Cai , Bing Tan

引用次数: 0

Abstract

The paper presents a new iterative algorithm based on Mann-type subgradient extragradient method to solve pseudomonotone variational inequalities and fixed point problems of quasi-nonexpansive mappings in real Hilbert spaces. Our algorithm, employing inertial technique in each iteration, significantly enhances its convergence. We prove a strong convergence theorem under suitable conditions imposed on the operators and parameters, without prior knowledge of the Lipschitz constant. The efficacy and validity of the proposed method are confirmed through several numerical experiments.

查看原文本刊更多论文

用惯性技术求解变分不等式和不动点问题的次梯度法的收敛性分析

本文提出了一种新的基于mann型次梯度外延法的迭代算法，用于求解实数Hilbert空间中拟非扩张映射的伪单调变分不等式和不动点问题。该算法在每次迭代中采用惯性技术，显著提高了算法的收敛性。我们在不知道Lipschitz常数的前提下，在适当的条件下证明了算子和参数的强收敛定理。通过数值实验验证了该方法的有效性和有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.