| Author Name | Affiliation | | Yao Li | School of Mathematics and Statistics, Xidian University, Xi'an, 710126, China | | Hongwei Liu | School of Mathematics and Statistics, Xidian University, Xi'an, 710126, China | | Jiamin Lv | School of Mathematics and Statistics, Xidian University, Xi'an, 710126, China |
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| Abstract: |
| Many solutions of variational inequalities have been proposed, among which the subgradient extragradient method has obvious advantages. Two different algorithms are given for solving variational inequality problem in this paper. The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition. Two new algorithms adopt inertial technology and non-monotonic step size rule, and their convergence can still be proved when the value of L is not given in advance.Finally, some numerical results are designed to demonstrate the computational efficiency of our two new algorithms. |
| Key words: variational inequality inertial method non-monotonic step size rule Lipschitz continuity pseudomonotone mapping |
| DOI：10.11916/j.issn.1005-9113.2023028. |
| Clc Number:O224 |
| Fund: |
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| Descriptions in Chinese: |
| 自适应惯性次梯度外梯度技术求解变分不等式问题的强弱收敛算法 李瑶，刘红卫， 吕佳敏 (西安电子科技大学 数学与统计学院，西安710126，中国) 摘要：次梯度外梯度算法在众多解决变分不等式的算法中具有显著的优势。本文给出两种不同的算法来解决变分不等式问题，并将变分不等式问题定义在实希尔伯特空间中，且具有利普希茨连续和伪单调条件。本文的两种新方法采用惯性技术和非单调的步长准则，当利普希茨常数没有提前给出时，仍然可以证明它们的收敛性。最后通过设计数值结果验证了两个新算法的有效性。 关键词: 变分不等式问题; 惯性算法; 非单调步长规则; 利普希茨连续; 伪单调映射 |
