• 论文 •

### 求解双层集值混合变分不等式的惯性外梯度算法

1. 西南交通大学数学学院, 四川 611731
• 收稿日期:2021-05-03 发布日期:2022-06-10
• 通讯作者: 王中宝,Email:zhongbaowang@hotmail.com.
• 基金资助:
国家自然科学基金(11701479,11526170)资助

Jiang Yi, Long Xin, Wang Zhongbao. INERTIAL EXTRAGRADIENT ALGORITHMS FOR SOLVING BILEVEL MULTIVALUED MIXED VARIATIONAL INEQUALITIES[J]. Journal on Numerica Methods and Computer Applications, 2022, 43(2): 221-236.

### INERTIAL EXTRAGRADIENT ALGORITHMS FOR SOLVING BILEVEL MULTIVALUED MIXED VARIATIONAL INEQUALITIES

Jiang Yi, Long Xin, Wang Zhongbao

1. School of Mathematics, Southwest Jiaotong University, Chengdu 611731, China
• Received:2021-05-03 Published:2022-06-10

In this paper, based on Tseng's extragradient algorithm, inertial extragradient algorithm for solving bilevel multivalued mixed variational inequalities is presented. The step sizes of the proposed algorithm are adaptive and non-monotonic. Combined with the inertial acceleration techniques, it is proved that the sequence generated by the algorithm converges strongly to solution of the bilevel multivalued mixed variational inequalities, under the assumption that the multi-valued mapping is monotone and Lipschitz continuous. Some numerical experiments have showed that the inertial extragradient algorithm has a competitive advantage over some existing algorithms.

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