| Author Name | Affiliation | | Xiaoyin 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 | | Jiangli Cheng | School of Mathematics and Statistics, Xidian University, Xi’an 710126, China | | Dongyao Zhang | School of Mathematics and Statistics, Xidian University, Xi’an 710126, China |
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| Abstract: |
| Many approaches inquiring into variational inequality problems have been put forward, among which subgradient extragradient method is of great significance. A novel algorithm is presented in this article for resolving quasi-nonexpansive fixed point problem and pseudomonotone variational inequality problem in a real Hilbert interspace. In order to decrease the execution time and quicken the velocity of convergence, the proposed algorithm adopts an inertial technology. Moreover, the algorithm is by virtue of a non-monotonic step size rule to acquire strong convergence theorem without estimating the value of Lipschitz constant. Finally, numerical results on some problems authenticate that the algorithm has preferable efficiency than other algorithms. |
| Key words: inertial method fixed point variational inequality strong convergence subgradient extragradient method |
| DOI：10.11916/j.issn.1005-9113.2021121 |
| Clc Number:O224 |
| Fund: |
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| Descriptions in Chinese: |
| 变分不等式问题和不动点问题的修正次梯度外梯度方法 李肖银，刘红卫，程江丽，张东耀 （西安电子科技大学，数学与统计学院，西安，710126） 中文说明：本文提出一种求解实 Hilbert 空间中拟非扩张不动点问题和伪单调变分不等式问题的新算法。为减少运行时间和加快收敛速度，提出的算法采用了惯性技术。此外，该算法借助于非单调步长规则，在不估计利普希茨常数的情况下获得了强收敛定理。最后数值结果表明该算法比其它算法有更好的效率。 关键词：惯性方法，不动点，变分不等式，强收敛性，次梯度外梯度方法 |
