Strongly convergent two-step inertial subgradient extragradient methods for solving quasi-monotone variational inequalities with applications

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-06-09 DOI:10.1016/j.cnsns.2025.108959

Pongsakorn Sunthrayuth , Abubakar Adamu , Kanikar Muangchoo , Sakulbuth Ekvittayaniphon

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引用次数: 0

Abstract

In this paper, we introduce two modified subgradient extragradient methods with two-inertial steps based on Halpern-type and Mann-type iterations for approximating solutions of variational inequalities involving quasi-monotone operators in real Hilbert spaces. The step-size of our proposed algorithms are designed to select self-adaptively without requiring the knowledge of the Lipschitz constant of the cost operator. The strong convergence results of the proposed algorithms are proved without assuming on-line rule. We also utilize the proposed algorithms to solve the quasi-convex programming problems. Moreover, we provide some numerical examples to demonstrate the better performance over those algorithms of the recent literature. Finally, the proposed algorithms are also applied to solve regularized decentralized logistic regression problems that appear in classification problems in machine learning.

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求解拟单调变分不等式的强收敛两步惯性次梯度法及其应用

本文介绍了两种改进的基于halpern型和mann型迭代的双惯性步次梯度外聚方法，用于逼近实数Hilbert空间中涉及拟单调算子的变分不等式的解。我们提出的算法的步长设计为自适应选择，而不需要知道代价算子的Lipschitz常数。在不假设在线规则的情况下，证明了算法的强收敛性。我们还利用所提出的算法求解拟凸规划问题。此外，我们还提供了一些数值例子来证明该算法优于最近文献中的那些算法。最后，本文提出的算法还应用于解决机器学习分类问题中出现的正则化分散逻辑回归问题。

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.