单调包含的摄动反射正反向分裂算法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-12-25 DOI:10.1016/j.cnsns.2024.108565

Bing Tan , Yekini Shehu , Tiexiang Li , Xiaolong Qin

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引用次数: 0

摘要

本文研究了一种新的具有自适应步长的反射前向后分裂算法来解决单调包含问题。我们的算法的实现不需要Lipschitz连续单调算子的Lipschitz常数的知识，不像现有的反射前向后分裂算法，在实现过程中需要这些信息。在标准条件下，给出了该算法的弱收敛定理。通过在信号处理和图像去模糊中的应用，将本文算法与文献中其他相关算法进行了数值比较。

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Perturbed reflected forward backward splitting algorithm for monotone inclusion

In this paper, we investigate a new reflected forward–backward splitting algorithm with self-adaptive step sizes to solve monotone inclusion problems. The implementation of our algorithm does not require the knowledge of the Lipschitz constant for the Lipschitz continuous monotone operator, unlike existing reflected forward–backward splitting algorithms, which necessitate this information during implementation. The weak convergence theorem of the proposed algorithm is given under standard conditions. We compare numerically our algorithm with other related ones in the literature through its applications in signal processing and image deblurring.

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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.