求解双层集值混合变分不等式的惯性外梯度算法

doi:10.12288/szjs.s2021-0754

数值计算与计算机应用 ›› 2022, Vol. 43 ›› Issue (2): 221-236.DOI: 10.12288/szjs.s2021-0754

• 论文 • 上一篇

求解双层集值混合变分不等式的惯性外梯度算法

蒋艺, 龙鑫, 王中宝

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

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蒋艺, 龙鑫, 王中宝. 求解双层集值混合变分不等式的惯性外梯度算法[J]. 数值计算与计算机应用, 2022, 43(2): 221-236.

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

School of Mathematics, Southwest Jiaotong University, Chengdu 611731, China

Received:2021-05-03 Published:2022-06-10

本文在Tseng外梯度算法的基础上,引入了一种求解双层集值混合变分不等式的惯性外梯度算法.该算法的步长是非单调自适应的,结合惯性加速技巧,在集值映射是单调且Lipschitz连续的假设下,证明了该算法所产生的序列强收敛到双层集值混合变分不等式的解,进行的数值实验表明惯性外梯度算法优于一些已有的算法.

关键词： 双层变分不等式, 集值映射, Tseng外梯度算法, 非单调自适应步长, 惯性技巧

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.

Key words: Bilevel variational inequality, Multi-valued mapping, Tseng's extragradient algorithm, Adaptive and non-monotonic step sizes, Inertial techniques.

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求解双层集值混合变分不等式的惯性外梯度算法

INERTIAL EXTRAGRADIENT ALGORITHMS FOR SOLVING BILEVEL MULTIVALUED MIXED VARIATIONAL INEQUALITIES

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