求解拟单调变分不等式问题的自适应算法

doi:10.15960/j.cnki.issn.1007-6093.2026.02.014

运筹学学报（中英文） ›› 2026, Vol. 30 ›› Issue (2): 179-193.doi: 10.15960/j.cnki.issn.1007-6093.2026.02.014

求解拟单调变分不等式问题的自适应算法

余思洁, 龙宪军^†

重庆工商大学数学与统计学院, 重庆 400067

收稿日期:2025-10-20 发布日期:2026-06-12
通讯作者: 龙宪军 E-mail:xianjunlong@ctbu.edu.cn
基金资助:
重庆市自然科学基金 (Nos. 2024NSCQ-MSX1282, cstc2021jcyj-msxmX0721), 重庆市教委科学技术研究项目 (No. KJZD-K202500805), 重庆市研究生导师团队建设项目 (No. yds223010)

An adaptive algorithm for solving quasimonotone variational inequality problems

YU Sijie, LONG Xianjun^†

School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

Received:2025-10-20 Published:2026-06-12

摘要/Abstract

摘要： 本文在实Hilbert空间中提出了一种求解拟单调变分不等式问题的新的自适应向前向后算法,并在合理的假设下证明了由算法产生的迭代序列强收敛到变分不等式解集的一个元素。最后数值实验阐明了算法的有效性与优越性。

关键词: 变分不等式, 拟单调, 自适应步长, 强收敛

Abstract: In this paper, we propose a new adaptive forward-backward algorithm to solve the quasimonotone variational inequality problem in real Hilbert spaces. Under reasonable assumptions, we prove that the iterative sequence generated by the algorithm converges strongly to an element of the solution set of the variational inequality problem. Finally, numerical experiments show the effectiveness and superiority of the new algorithm.

Key words: variational inequality, quasimonotone, adaptive step-size, strong convergence

中图分类号:

O224

余思洁, 龙宪军. 求解拟单调变分不等式问题的自适应算法[J]. 运筹学学报（中英文）, 2026, 30(2): 179-193.

YU Sijie, LONG Xianjun. An adaptive algorithm for solving quasimonotone variational inequality problems[J]. Operations Research Transactions, 2026, 30(2): 179-193.

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求解拟单调变分不等式问题的自适应算法

An adaptive algorithm for solving quasimonotone variational inequality problems

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