| 一种新修正的求解变分不等式的双次梯度外梯度算法 |
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| 引用本文： | 陈家欣,叶明露.一种新修正的求解变分不等式的双次梯度外梯度算法[J].数学研究及应用,2022,42(4):402-412. |
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| 作者姓名： | 陈家欣 叶明露 |
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| 作者单位： | 四川师范大学数学科学学院, 四川 成都 610066;西华师范大学数学与信息学院, 四川 南充 637002 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11871059; 11801455),四川省科技计划(Grant No.2019YFG0299), 西华师范大学一般培育项目(Grant No.20A024). |
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| 摘 要： | 当可行集为一光滑凸函数的下水平集时, 本文提出一种修正的双次梯度外梯度算法(MTSEGA)用于求解Hilbert空间中单调且Lipschitz连续的变分不等式. MTSEGA在每步迭代过程中仅需计算向半空间的两次投影及一次映射的值. 在与已知算法相同的假设条件下, 证明了新算法产生的序列能弱收敛到相关问题的一个解.
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| 关 键 词： | 双次梯度外梯度算法 单调 Lipschitz连续 变分不等式 Hilbert空间 |
| 收稿时间： | 2021/7/4 0:00:00 |
| 修稿时间： | 2021/12/23 0:00:00 |
A New Modified Two-Subgradient Extragradient Algorithm for Solving Variational Inequality Problems |
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| Jiaxin CHEN,Minglu YE.A New Modified Two-Subgradient Extragradient Algorithm for Solving Variational Inequality Problems[J].Journal of Mathematical Research with Applications,2022,42(4):402-412. |
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| Authors: | Jiaxin CHEN Minglu YE |
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| Institution: | School of Mathematical Sciences, Sichuan Normal University, Sichuan 610066, P. R. China; School of Mathematics and Information, China West Normal University, Sichuan 637002, P. R. China |
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| Abstract: | In this paper, we propose a modified two-subgradient extragradient algorithm (MTSEGA) for solving monotone and Lipschitz continuous variational inequalities with the feasible set being a level set of a smooth convex function in Hilbert space. The advantage of MTSEGA is that all the projections are computed onto a half-space per iteration. Moreover, MTSEGA only needs one computation of the underlying mapping per iteration. Under the same assumptions with the known algorithm, we show that the sequence generated by this algorithm is weakly convergent to a solution of the concerned problem. |
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| Keywords: | two-subgradient extragradient algorithm monotone Lipschitz continuous variational inequality Hilbert space |
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