Adaptive double-inertial projection rules for variational inequalities and CFPPs of finite Bregman relative demicontractions and asymptotical nonexpansivity operators

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-03-20 DOI:10.1016/j.cnsns.2025.108763

Lu-Chuan Ceng , Yue Zhang, Liu-Fang Zheng, Xie Wang, Cong-Shan Wang, Hui-Ying Hu

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引用次数: 0

Abstract

Presume the uniform smooth Banach space

E

to possess

p

-uniform convexity for

p \geq 2

. In

E

, the VIP stands for a variational inequality problem and the CFPP a common fixed point problem of Bregman’s relative asymptotic nonexpansivity operator and finite Bregman’s relative demicontractions. We design and deliberate two adaptive double-inertial Bregman’s projection schemes with linesearch procedure for tackling the CFPP and a pair of VIPs. Through appropriate postulations, it is substantiated that the generated sequences in the proposed schemes, are weakly and strongly convergent to a common solution of the CFPP and two VIPs, respectively. At length, an illustration is offered to substantiate the utility and performability of the schemes put forward.

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自适应双惯性投影规则的变分不等式和 CFPP 的有限布雷格曼相对非扩张性和渐近非扩张性算子

假设均匀光滑巴拿赫空间 E 在 p≥2 时具有 p-均匀凸性。在 E 中，VIP 代表变分不等式问题，CFPP 代表布雷格曼相对渐近非扩张性算子和有限布雷格曼相对去收缩的公共定点问题。我们设计并讨论了两个自适应双惯性布雷格曼投影方案，其中的线性搜索程序可用于解决 CFPP 和一对 VIP 问题。通过适当的假设，证明了所提方案中生成的序列分别弱收敛和强收敛于 CFPP 和两个 VIP 的共同解。最后，还提供了一个示例来证明所提方案的实用性和可执行性。

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

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.